TECHNICAL FIELD

The present disclosure relates generally to the field of digital communication; and more specifically to a method of transmitting a digital message, a digital transmitter device, and a digital receiver device.

BACKGROUND

In digital communications, the messages to be transmitted from a transmitter to a receiver are usually mapped on discrete alphabets, often referred to as symbol constellations. Generally, the size of the symbol constellations determines how many bits can be mapped on each symbol. For example, a symbol constellation of size 2 ^m symbols can carry m bits per symbol. The bijection between symbols and binary m-tuples is known as bit mapping and can be performed by use of a bit-mapper. Furthermore, a practical approach to channel coding, may be a bitinterleaved coded modulation (BICM), which includes cascading of a binary forward error correction (FEC) encoder and the bit-mapper at a conventional transmitter and a bit-demapper and a binary decoder at a conventional receiver. For a symbol constellation of size 2 ^m and the binary FEC encoder with binary rate R _FEC , channel coded m X R _FEC bits per symbol can be transmitted. For a symbol time T seconds and required frequency band 1/T Hz, bits per symbol can be termed as spectral efficiency (SE) in bits/s/Hz.

Modern optical communication systems require flexibility in supporting varying spectral efficiency. The varying spectral efficiency can be obtained in different ways for realizing the required flexibility. The different ways of obtaining the varying spectral efficiency include either changing the symbol distribution ( ), or changing the FEC rate (R _FEC ) or changing the modulation order (m). In typical optical transceivers, only a few options for the FEC rate (R _F EC) ^are implemented, due to high cost both in development and chip area. For the choice of modulation order and the symbol distribution, two aspects are considerable. First is, increasing the modulation order (m) requires the transceiver application specific integrated circuit (ASIC) to transport more bits per symbol. Consequently, the modulation order (m) should be kept low. Second is, decreasing entropy of the symbol distribution ( ), that means, shaping more increases peak-to-average-power-ratio (PAPR), resulting in an amplified quantization noise. Consequently, shaping overhead should be kept low. Therefore, a suitable combination of the symbol constellation with a bit-mapper and shaping that can be done using a probabilistic amplitude shaping (PAS) architecture, is required in order to obtain low modulation order (m) and PAPR value.

Currently, certain techniques have been proposed to combine the symbol constellation with the PAS architecture, in order to obtain low number of bits (m) for symbols and low PAPR value. For example, conventionally, 2 ^2m quadrature amplitude modulation, QAM (m is a positive integer) constellations like 4 QAM, 16 QAM, 64 QAM are considered for many communications standards. The conventional 2 ^2m QAM constellations may or may not be integrated with the PAS architecture, depending on an application scenario. The 2 ^2m QAM constellations can be interpreted as Cartesian product of two 2 ^m amplitude shift keying (ASK) constellations. The rectangular QAM constellations (e.g., 8 QAM constellations) includes ASK constellations of different size for different quadratures. For example, for modulation onto in- phase (I) component and quadrature-phase (Q) component of two polarizations x and y, a rectangular QAM constellation may be configured like, xl: binary phase shift keying (BPSK), xQ: 4ASK, yl: 4ASK, yQ: 4ASK. In another case, when the conventional QAM constellations are integrated with the PAS architecture, probabilistically shaped, PS, (2M) QAM (M is a positive integer) square QAM constellations like 36 QAM, 100 QAM are considered. The use of square QAM constellations require the PAS architecture for integrating with binary FEC, since the bitmapping is inherited from the next largest 2 ^2m QAM constellations. For example, 36 QAM constellation uses 64 QAM bitmapping that means each symbol is identified by 6 bits and the bit-mapper generates 6 bit tuples that map to 36 QAM symbols. Thus, the existing works includes the use of the rectangular QAM constellations and the square QAM constellations, which uses large number of bits per symbol. The conventional PAS architecture requires even sized, symmetric constellations, for example, 4 ASK (16 QAM), 6 ASK (36 QAM), 8 ASK (64 QAM), so that uniformly distributed parity bits output by the FEC encoder can be optimally assigned to choosing the signal point sign. Thus, there exists a technical problem of inefficient optical communication systems, which have low flexibility in supporting varying spectral efficiency and high PAPR value because of using the conventional rectangular and square QAM constellations with or without the PAS architecture.

Therefore, in light of the foregoing discussion, there exists a need to overcome the aforementioned drawbacks associated with the conventional rectangular and square QAM constellations with or without the PAS architecture.

SUMMARY

The present disclosure provides a method of transmitting a digital message, a digital transmitter device, and a digital receiver device. The present disclosure further provides a solution to the existing problem of inefficient optical communication systems, which have low flexibility in supporting varying spectral efficiency and high PAPR value because of using the conventional rectangular and square QAM constellations with or without the PAS architecture. An aim of the present disclosure is to provide a solution that overcomes at least partially the problems encountered in prior art, and provides an improved method of transmitting a digital message, a digital transmitter device, and a digital receiver device that manifests a desired flexibility in supporting varying spectral efficiency and low PAPR value.

The object of the present disclosure is achieved by the solutions provided in the enclosed independent claims. Advantageous implementations of the present disclosure are further defined in the dependent claims.

In one aspect, the present disclosure provides a method of transmitting a digital message. The method comprises mapping a first component of the digital message to a first symbol sequence, the first symbol sequence consisting of symbols from a constellation of M real symbols. The method further comprises mapping a second component of the digital message to a second symbol sequence, the second symbol sequence consisting of symbols from a constellation of P real symbols, where at least one of M and P is an odd number. The method further comprises transmitting the first symbol sequence and the second symbol sequence.

The disclosed method enables use of lower number of bits per quadrature amplitude modulation (QAM) symbol in comparison to a conventional QAM constellation. The method allows integration of the first symbol sequence comprising the symbols from an odd amplitude shift keying (ASK) constellation and the second symbol sequence comprising the symbols from an even ASK constellation. Thus, the disclosed method enables an integration of an odd-even QAM constellation (e.g., 3x2 QAM constellation) or an even-odd QAM constellation (e.g., 2x3 QAM constellation), which in turn makes possible using low number of bits per QAM symbol. For example, the odd-even QAM constellation (i.e., 3x2 QAM constellation) has 3 bits per QAM symbol and the conventional QAM constellation (e.g., 4x4 QAM constellation) has 4 bits per QAM symbol. Due to low number of bits per QAM symbol, the odd-even QAM constellation (i.e., 3x2 QAM constellation) can provide a reduced peak-to-average-power-ratio (PAPR) value, as detailed in the detailed description of embodiments below.

In an implementation form, mapping the first and second components comprises applying probabilistic amplitude shaping (PAS) to impose a non-uniform distribution on the output symbol sequences.

The disclosed method enables use of the odd-even QAM constellation (i.e., 3x2 QAM constellation) with PAS that may result into varying spectral efficiency and low PAPR value as well.

In a further implementation form, the non-uniform distribution is configured to reduce an average power of the output symbol sequences by reducing an occurrence of symbols having a higher amplitude.

The use of the non-uniform distribution enables high entropy with constraints on the average power of the output symbol sequences.

In a further implementation form, the non-uniform distribution defines the occurrence of symbols according to their power in line with a Maxwell-Boltzmann distribution.

The Maxwell-Boltzmann distribution limits the occurrence of high-power signal points with large amplitude.

In a further implementation form, the first component is an in-phase, I, component and the second component is a quadrature, Q, component.

The disclosed method enables an independent and improved (i.e., optimal) demapping of the in-phase component (I) and the quadrature-phase (Q) component. In a further implementation form, the first and second symbol sequences have distinct signaling intervals.

The distinct signaling intervals of the first symbol sequence and the second symbol sequence enables digital-to-analog conversion (DAC) and analog-to-digital conversion (ADC) with an ease.

In a further implementation form, the first symbol sequence is transmitted in a first slot of a plurality of slots, and the second symbol sequence is transmitted in a second slot of the plurality of slots.

In a further implementation form, the first and second slots are transmitted in a repeating pattern, and a ratio between the occurrence of first and second slots is 1 : 1 or 2: 1.

In a further implementation form, the plurality of slots are time slots or frequency slots.

In a further implementation form, one of M and P is an even number, and further comprises encoding a sequence of binary forward error correction, FEC, parity bits onto a sign of the even set of symbols.

By virtue of encoding the sequence of binary FEC parity bits onto the sign of the even set of symbols, more reliable communication is obtained.

In a further implementation form, the FEC parity bits are generated by a FEC encoder based on the first component and the second component.

In a further implementation form, the method further comprises rotating a constellation of the M x P symbols by 90 degrees for each successively mapped symbol.

The constellation of the M*P symbols is rotated by 90 degrees for each successively mapped symbol, in order to avoid an imbalance between quadratures.

In a further implementation form, in an initial configuration, the M x P symbols are at 0 and 90 degrees, respectively, or -45 and 45 degrees, respectively.

The M*P symbols are rotated between 0 and 90 degrees or -45 and 45 degrees, respectively, in order to reduce number of minimum required levels per quadrature for conversion between digital-to-analog (DAC) and analog-to-digital (ADC). In a further implementation form, the digital message for transmission further comprises one or more additional components, and where the method further comprises mapping the one or more additional components onto respective sets of real symbols in one or more additional carrier signals.

In an implementation, the digital message may have one or more components in addition to the first component and the second component. The additional one or more components can be mapped to different ASK constellations of real symbols in different quadratures in order to reduce PAPR value.

In another aspect, the present disclosure provides a digital transmitter device. The digital transmitter device comprises a processing module configured to map a first component of a digital message to a first symbol sequence, the first symbol sequence consisting of symbols from a constellation of M real symbols. The processing module is further configured to map a second component of the digital message to a second symbol sequence, the second symbol sequence consisting of symbols from a constellation of P real symbols, where at least one of M and P is an odd number. The digital transmitter device further comprises a communication module configured to transmit the first symbol sequence and the second symbol sequence.

The digital transmitter device achieves all the advantages and technical effects of the disclosed method of the present disclosure, after execution of the method.

In yet another aspect, the present disclosure provides a digital receiver device. The digital receiver device comprises a communication module configured to receive a first symbol sequence and a second symbol sequence, the first symbol sequence consisting of symbols from a constellation of M real symbols and the second symbol sequence consisting of symbols from a constellation of P real symbols, where at least one of M and P is an odd number. The digital receiver device further comprises a processing module configured to map the first symbol sequence to a first component of a digital message, and map the second symbol sequence to a second component of the digital message.

The digital receiver device achieves all the advantages and technical effects of the disclosed method of the present disclosure, after execution of the method.

It has to be noted that all devices, elements, circuitry, units and means described in the present application could be implemented in the software or hardware elements or any kind of combination thereof. All steps which are performed by the various entities described in the present application as well as the functionalities described to be performed by the various entities are intended to mean that the respective entity is adapted to or configured to perform the respective steps and functionalities. Even if, in the following description of specific embodiments, a specific functionality or step to be performed by external entities is not reflected in the description of a specific detailed element of that entity which performs that specific step or functionality, it should be clear for a skilled person that these methods and functionalities can be implemented in respective software or hardware elements, or any kind of combination thereof. It will be appreciated that features of the present disclosure are susceptible to being combined in various combinations without departing from the scope of the present disclosure as defined by the appended claims.

Additional aspects, advantages, features and objects of the present disclosure would be made apparent from the drawings and the detailed description of the illustrative implementations construed in conjunction with the appended claims that follow.

BRIEF DESCRIPTION OF THE DRAWINGS

The summary above, as well as the following detailed description of illustrative embodiments, is better understood when read in conjunction with the appended drawings. For the purpose of illustrating the present disclosure, exemplary constructions of the disclosure are shown in the drawings. However, the present disclosure is not limited to specific methods and instrumentalities disclosed herein. Moreover, those in the art will understand that the drawings are not to scale. Wherever possible, like elements have been indicated by identical numbers.

Embodiments of the present disclosure will now be described, by way of example only, with reference to the following diagrams wherein:

FIG. 1 is a flowchart of a method of transmitting a digital message, in accordance with an embodiment of the present disclosure;

FIG. 2 is a block diagram that illustrates various exemplary components of a digital transmitter device, in accordance with an embodiment of the present disclosure; FIG. 3 is a block diagram that illustrates various exemplary components of a digital receiver device, in accordance with an embodiment of the present disclosure;

FIG. 4 illustrates an odd-even quadrature amplitude modulation (QAM) constellation with a modified probabilistic amplitude shaping (PAS), in accordance with an embodiment of the present disclosure;

FIG. 5 A illustrates one real dimension of an odd constellation and an even constellation, in accordance with an embodiment of the present disclosure;

FIG. 5B illustrates distributions of various symbols of an odd constellation and an even constellation according to different entropy values, in accordance with an embodiment of the present disclosure;

FIG. 5C is a graphical representation that illustrates peak-to-average-power-ratio (PAPR) obtained by an even constellation and an odd constellation, in accordance with an embodiment of the present disclosure;

FIG. 6A is a graphical representation that illustrates achievable spectral efficiency per QAM symbol for different forward error correction (FEC) overheads, in accordance with an embodiment of the present disclosure;

FIG. 6B is a graphical representation that illustrates variation of bit error rate (BER) with respect to signal -to-noise-ratio (SNR) for different QAM constellations, in accordance with an embodiment of the present disclosure;

FIG. 7A is a graphical representation that illustrates variation of peak-to-average- power-ratio (PAPR) with respect to a FEC overhead for different QAM constellations, in accordance with an embodiment of the present disclosure;

FIG. 7B is a graphical representation that illustrates variation of peak-to-average-power- ratio (PAPR) with respect to different PAPR types, in accordance with an embodiment of the present disclosure;

FIG. 8A is a graphical representation that illustrates variation of achievable spectral efficiency for different QAM constellations with respect to SNR, in accordance with an embodiment of the present disclosure; FIG. 8B is a graphical representation that illustrates variation of achievable spectral efficiency for different QAM constellations with respect to peak-SNR, in accordance with an embodiment of the present disclosure;

FIG. 9A illustrates a scatter plot of a rectangular QAM constellation, in accordance with an embodiment of the present disclosure;

FIG. 9B illustrates a scatter plot of an odd-even QAM constellation, in accordance with an embodiment of the present disclosure;

FIG. 10A illustrates a scatter plot of an even-even QAM constellation, in accordance with an embodiment of the present disclosure; and

FIG. 10B illustrates a scatter plot of an odd-odd QAM constellation, in accordance with an embodiment of the present disclosure.

In the accompanying drawings, an underlined number is employed to represent an item over which the underlined number is positioned or an item to which the underlined number is adjacent. A non-underlined number relates to an item identified by a line linking the nonunderlined number to the item. When a number is non-underlined and accompanied by an associated arrow, the non-underlined number is used to identify a general item at which the arrow is pointing.

DETAILED DESCRIPTION OF EMBODIMENTS

The following detailed description illustrates embodiments of the present disclosure and ways in which they can be implemented. Although some modes of carrying out the present disclosure have been disclosed, those skilled in the art would recognize that other embodiments for carrying out or practicing the present disclosure are also possible.

FIG. 1 is a flowchart of a method of transmitting a digital message, in accordance with an embodiment of the present disclosure. With reference to FIG. 1, there is shown a method 100 of transmitting a digital message. The method 100 includes steps 102, 104, and 106. The method 100 is executed by a digital transmitter device, described in detail, for example, in FIG. 2. The method 100 introduces a beneficial combination of a symbol constellation with a bitmapper and a probabilistic amplitude shaping (PAS) architecture, in order to obtain low number of bits (m) per symbol, low value of peak-to-average-power ratio (PAPR) and low bit error rate (BER) as well. The method 100 is described in detail, in following steps.

At step 102, the method 100 comprises mapping a first component of the digital message to a first symbol sequence, the first symbol sequence consisting of symbols from a constellation of M real symbols. In an example, the first component of the digital message is mapped to the first symbol sequence that may have the symbols from an amplitude shift keying (ASK) constellation in one quadrature. The ASK constellation includes M real symbols in the quadrature, and hence, may be denoted as M ASK constellation.

At step 104, the method 100 further comprises mapping a second component of the digital message to a second symbol sequence, the second symbol sequence consisting of symbols from a constellation of P real symbols, where at least one of M and P is an odd number. Similar to the mapping of the first component of the digital message, the second component of the digital message is mapped to the second symbol sequence that may have the symbols from another ASK constellation in another quadrature. The other ASK constellation includes P real symbols, and hence, may be denoted as P ASK constellation. However, value of M and P is different from each other. After mapping, the first symbol sequence and the second symbol sequence are combined together in order to generate a quadrature amplitude modulation (QAM) constellation that has symbols from different ASK constellations in different quadratures. In an example, an odd value for M ASK constellation and an even value for P ASK constellation is considered, in order to obtain an odd-even QAM constellation (i.e., MxP), such as 3x2 QAM constellation, and the like. Alternatively stated, the odd-even QAM constellation is obtained through Cartesian product of the M ASK constellation in one quadrature and the P ASK constellation in the other quadrature. In another example, an even value for M ASK constellation and an odd value for P ASK constellation is considered, in order to obtain an even-odd QAM constellation (i.e., MxP), such as 2x3 QAM constellation, and the like. Thus, at least one of M and P must be an odd number in both the constellations.

In accordance with an embodiment, mapping the first and second components comprises applying probabilistic amplitude shaping to impose a non-uniform distribution on the output symbol sequences. In an implementation, the M ASK constellation (e.g., an odd ASK constellation with odd ASK bits) and the P ASK constellation (e.g., an even ASK constellation with even ASK bits) are shaped using a modified probabilistic amplitude shaping (PAS) architecture. In PAS, a distribution matcher is used to impose a constraint on bit-sequences, so that the symbol sequence output by a bit-mapper follows a desired non-uniform distribution P _x . The spectral efficiency of PAS, that is the distribution matcher followed by a forward error correction (FEC) encoder followed by the bit-mapper is represented by equation (1) where the entropy of Px is defined by equation (2)

In equations (1) and (2), entropy (P _x ) maybe replaced by the actual rate m ■ R _dm of the distribution matcher approximating P _x , as the actual distribution matcher rate can be slightly lower than the optimal value entropy(Py) in practical implementations.

The odd-even QAM constellation cannot be obtained by merely choosing the support of a distribution on a conventional QAM. In addition, a shift of the odd size quadrature is required.

In accordance with an embodiment, the non-uniform distribution is configured to reduce an average power of the output symbol sequences by reducing an occurrence of symbols having a higher amplitude. For example, suppose the QAM constellation is per real dimension {-3, - 1,1,3}. Then, the signal points {-3,3} with amplitude 3 may be used less often than the signal points {-1,1 } with amplitude 1, resulting in reduced average power of the output symbol sequences. This is due to the non-uniform distribution of the output symbol sequences, which effectively reduces the average power of the output symbol sequences by reducing the occurrence of the symbols (i.e., {-3,3}) having the higher amplitude.

In accordance with an embodiment, the non-uniform distribution defines the occurrence of symbols according to their power in line with a Maxwell-Boltzmann distribution. The probability of occurrence of symbols according to their power in line with the Maxwell- Boltzmann (MB) distribution is given by equation (3) where V is a non-negative parameter that controls the probabilistic amplitude shaping overhead. For instance, for V=0, all signal points are used equally often and the entropy of Px takes its largest value, and for V large, high power signal points with large amplitude are used much less often than low power signal points with low amplitude and the entropy of Px takes a small value. Generally, the Maxwell-Boltzmann (MB) distribution may be defined as a sampled Gaussian density and that performs close to Shannon limit on an additive white Gaussian noise (AWGN) channel. Moreover, the MB distribution maximizes entropy subject to an average power constraint and assigns equal probability to equal amplitudes.

In accordance with an embodiment, the first component is an in-phase, I, component and the second component is a quadrature, Q, component. The first component of the digital message is the in-phase, I, component that may have a phase shift of 0°, and the second component of the digital message is the quadrature-phase, Q, component that may have a phase shift of 90°.

In accordance with an embodiment, the first and second symbol sequences have distinct signaling intervals. For example, the first symbol sequence (e.g., 3 ASK constellation) and the second symbol sequence (e.g., 2 ASK constellation) has signal points {-2, 0, 2} and {-1, 1 }, respectively, that corresponds to five distinct signaling intervals.

At step 106, the method 100 further comprises transmitting the first symbol sequence and the second symbol sequence. Alternatively stated, the QAM constellation (i.e., the odd-even QAM constellation or the even-odd QAM constellation) comprising the symbols from the M ASK constellation and P ASK constellation is transmitted.

In accordance with an embodiment, the first symbol sequence is transmitted in a first slot of a plurality of slots, and the second symbol sequence is transmitted in a second slot of the plurality of slots. For example, the first symbol sequence (e.g., 3 ASK constellation) is transmitted in the first slot of the plurality of slots, and the second symbol sequence (e.g., 2 ASK constellation) is transmitted in the second slot of the plurality of slots. In this way, the two different ASK symbols are transmitted in a successive order.

In accordance with an embodiment, the plurality of slots are time slots or frequency slots. In an implementation, the plurality of slots may be time slots. In another implementation, the plurality of slots may be frequency slots. In accordance with an embodiment, the first and second slots are transmitted in a repeating pattern, and a ratio between the occurrence of first and second slots is 1 : 1 or 2: 1 or r:s, where r and s are integers. In an implementation, the first slot for transmitting the first symbol sequence and the second slot for transmitting the second symbol sequence may be repeated one after another or in the ratio of 1 : 1. In another implementation, the first slot for transmitting the first symbol sequence may be used two times and the second slot for transmitting the second symbol sequence may be used one time. Alternatively stated, the ratio of occurrence of the first slot and the second slot may be 2: 1 in the other implementation.

In accordance with an embodiment, one of M and P is an even number, and the method 100 further comprises encoding a sequence of binary forward error correction, FEC, parity bits onto a sign of the even set of symbols. For example, in the odd-even QAM constellation (e.g., 3^2 QAM constellation), M is the odd number and P is the even number. Moreover, in the evenodd constellation (i.e., 2x3 QAM constellation), M is the even number and P is the odd number. Therefore, in both of the odd-even QAM and the even-odd QAM constellations, one of the M and P is the even number. Additionally, the method 100 includes mapping of the sequence of binary FEC parity bits onto the sign of the even ASK bits.

In accordance with an embodiment, the FEC parity bits are generated by a FEC encoder based on the first component and the second component. The FEC parity bits are generated by the FEC encoder depending on the first component and the second component of the digital message.

In accordance with an embodiment, the method 100 further comprises rotating a constellation of the M x P symbols by 90 degrees for each successively mapped symbol. For example, the odd-even QAM constellation (i.e., 3x2 QAM constellation) is rotated by 0 degree and 90 degrees for two successive QAM symbols (i.e., MxP symbols) in order to avoid imbalance between the quadratures, if any.

In accordance with an embodiment, in an initial configuration, the M x P symbols are at 0 and 90 degrees, respectively, or -45 and 45 degrees, respectively. In an example, in the odd-even QAM constellation, the MxP symbols may be initially rotated at 0 and 90 degrees, respectively. In another example, in the odd-even QAM constellation, the MxP symbols may be initially rotated at -45 and 45 degrees, respectively. The rotation of the M x P symbols between -45 and 45 degrees manifests the advantage of a reduced number of minimum required levels per quadrature for converting digital -to-analog (DAC) and analog-to-digital (ADC).

In accordance with an embodiment, the digital message for transmission further comprises one or more additional components, and where the method 100 further comprises mapping the one or more additional components onto respective sets of real symbols in one or more additional carrier signals. In an implementation, the digital message may have one or more components in addition to the first component and the second component. The additional one or more components can be mapped onto the respective sets of real symbols (i.e., QAM symbols) in one or more additional carrier signals.

Thus, the method 100 enables an integration of the first symbol sequence comprising the symbols from an odd amplitude shift keying (ASK) constellation and the second symbol sequence comprising the symbols from an even ASK constellation. The method 100 enables an integration of an odd-even quadrature amplitude modulation (QAM) constellation or an evenodd QAM constellation. Moreover, the method 100 integrates the odd-even QAM constellation with binary FEC using probabilistic amplitude shaping (PAS). The proposed integration supports using low number of bits per QAM symbol, which further results in low PAPR value.

Conventionally, in order to achieve a flexibility in spectral efficiency, either modulation order of a conventional QAM constellation (e.g., a square or a rectangular QAM constellation) is changed or entropy is decreased. Increasing the modulation order requires a conventional transceiver application specific integrated circuit (ASIC) to transport more number of bits per symbol. Decreasing entropy (i.e., shaping more) increases PAPR value which further results in amplified quantization noise. Consequently, shaping overhead is not preferable for achieving varying spectral efficiency. However, the method 100 supports a varying spectral efficiency by reducing the required ASIC throughput. For instance, constellation A is preferable over constellation B where, and mg are the number of bits required to index the signal points in A and B, respectively. For example, a 32QAM constellation requires 5 bits per symbol and 64 QAM requires 6 bits per symbol.

In order to reduce the required effective number of bits (ENOB) of the DAC for achieving a target quantization error after transmitter amplification, modulation format A is preferable over modulation format B if A has lower PAPR than B. The method 100 supports a beneficial combination of the symbol constellation with the bit-mapper (i.e., Gray mapping) and the probabilistic amplitude shaping architecture, in order to obtain low number of bits (m) per symbol, low value of peak-to-average-power ratio (PAPR) and low bit error rate (BER) as well.

The steps 102-to-106 are only illustrative, and other alternatives can also be provided where one or more steps are added, one or more steps are removed, or one or more steps are provided in a different sequence without departing from the scope of the claims herein.

FIG. 2 is a block diagram that illustrates various exemplary components of a digital transmitter device, in accordance with an embodiment of the present disclosure. FIG. 2 is described in conjunction with elements from FIG. 1. With reference to FIG. 2, there is shown a block diagram of a digital transmitter device 200 that includes a processing module 202, a communication module 204 and a memory 206. The memory 206 is configured to store a digital message 206A.

The digital transmitter device 200 may include suitable logic, circuitry, interfaces, or codes that is configured to map and transmit the digital message 206A to a symbol constellation, such as an odd-even QAM constellation, and the like. The digital transmitter device 200 is configured to execute the method 100 (of FIG. 1). The digital transmitter device 200 may also be referred to as a transmitter or a transmitting unit that is configured for use in 5G or beyond 5G networks. Alternatively, the digital transmitter device 200 may be a part of another optical communication device or other portable or non-portable communication device used for optical communication. Examples of the digital transmitter device 200 may include, but are not limited to, a base station, user equipment, and the like.

The processing module 202 may include suitable logic, circuitry, interfaces, or codes that is configured to map a first component and a second component of the digital message 206A to a first symbol sequence and a second symbol sequence, respectively. Moreover, the processing module 202 is configured to execute the instructions stored in the memory 206. In an example, the processing module 202 may be a general-purpose processor. Other examples of the processing module 202 may include, but are not limited to, a central processing unit (CPU), a digital signal processor (DSP), a microprocessor, a microcontroller, a complex instruction set computing (CISC) processor, an application-specific integrated circuit (ASIC) processor, a reduced instruction set (RISC) processor, a very long instruction word (VLIW) processor, a data processing unit, and other processors or control circuitry. The communication module 204 may include suitable logic, circuitry, interfaces, or codes that is configured to transmit the first symbol sequence and the second symbol sequence. Moreover, the communication module 204 is configured to communicate with each of the memory 206, and the processing module 202. Examples of the communication module 204 may include, but are not limited to, a radio frequency transceiver, a network interface, a telematics unit, or any other communication module suitable for use in the digital transmitter device 200, or other portable or non-portable communication devices. The communication module 204 may comprise an optical transmitter. In an embodiment, the communication module 204 supports various optical communication protocols to execute optical communication.

The memory 206 may include suitable logic, circuitry, interfaces, or codes that is configured to store data and the instructions executable by the processing module 202. Examples of implementation of the memory 206 may include, but are not limited to, an Electrically Erasable Programmable Read-Only Memory (EEPROM), Random Access Memory (RAM), Read Only Memory (ROM), Hard Disk Drive (HDD), Flash memory, Solid-State Drive (SSD), or CPU cache memory. The memory 206 may store an operating system, or the digital message 206A or other program products (including one or more operation algorithms) to operate the digital transmitter device 200.

In operation, the processing module 202 is configured to map a first component of the digital message 206A to a first symbol sequence, the first symbol sequence consisting of symbols from a constellation of M real symbols. In an implementation, the processing module 202 is configured to map the first component of the digital message 206A to the first symbol sequence that may have the symbols from an amplitude shift keying (ASK) constellation in one quadrature. The ASK constellation includes M real symbols in the quadrature.

The processing module 202 is further configured to map a second component of the digital message 206A to a second symbol sequence, the second symbol sequence consisting of symbols from a constellation of P real symbols, wherein at least one of M and P is an odd number. The processing module 202 is further configured to map the second component of the digital message 206A to the second symbol sequence that may have the symbols from another ASK constellation in another quadrature. The other ASK constellation includes P real symbols, which may be denoted as P ASK constellation. However, value of M and P is different from each other and at least one of M and P is an odd number. For example, an odd-even QAM constellation, such as 3x2 QAM constellation, or an even-odd QAM constellation (i.e., M*P), such as 2x3 QAM constellation, and the like. Thus, at least one of M and P must be an odd number in both the constellations.

The communication module 204 is configured to transmit the first symbol sequence and the second symbol sequence. After mapping of the first component and the second component of the digital message 206A to the first symbol sequence and the second symbol sequence, respectively, the communication module 204 is configured to transmit the first symbol sequence and the second symbol sequence to a digital receiver device, described in detail, for example, in FIG. 3.

The digital transmitter device 200 achieves all the advantages and technical features of the method 100 by executing the method 100. Thus, the digital transmitter device 200 supports varying spectral efficiency in terms of varying baud rates and net rates. The digital transmitter device 200 may be configured for use in optical communication systems (or optical transceivers) used for 5G or beyond 5G networks.

FIG. 3 is a block diagram that illustrates various exemplary components of a digital receiver device, in accordance with an embodiment of the present disclosure. FIG. 3 is described in conjunction with elements from FIGs. 1, and 2. With reference to FIG. 3, there is shown a block diagram of a digital receiver device 300 that includes a communication module 302, a processing module 304 and a memory 306.

The digital receiver device 300 may include suitable logic, circuitry, interfaces, or codes that is configured to receive a first symbol sequence and a second symbol sequence of a digital message (e.g., the digital message 206A) transmitted by the digital transmitter device 200 (of FIG. 2). The digital receiver device 300 may also be referred to as a receiver or a receiving unit that is configured for use in 5G or beyond 5G networks. Alternatively, the digital receiver device 300 may be a part of another optical communication device or another portable or nonportable communication device used for optical communication. Examples of the digital receiver device 300 may include, but are not limited to, a base station, user equipment, and the like.

The communication module 302 may include suitable logic, circuitry, interfaces, or codes that is configured to receive the first symbol sequence and the second symbol sequence of the digital message 206A (of FIG. 2) transmitted by the communication module 204 of the digital transmitter device 200 (of FIG. 2). Moreover, the communication module 302 is configured to communicate with each of the memory 306, and the processing module 304. Examples of the communication module 302 may include, but are not limited to, a radio frequency transceiver, a network interface, a telematics unit, or any other communication module suitable for use in the digital receiver device 300, or other portable or non-portable communication devices. The communication module 302 may comprise an optical receiver. In one embodiment, the communication module 302 supports various optical communication protocols to execute optical communication.

The processing module 304 may include suitable logic, circuitry, interfaces, or codes that is configured to map the first symbol sequence and the second symbol sequence of the digital message 206A to a first component and a second component, respectively. Moreover, the processing module 304 is configured to execute the instructions stored in the memory 306. In an example, the processing module 304 may be a general-purpose processor. Other examples of the processing module 304 may include, but are not limited to, a central processing unit (CPU), a digital signal processor (DSP), a microprocessor, a microcontroller, a complex instruction set computing (CISC) processor, an application-specific integrated circuit (ASIC) processor, a reduced instruction set (RISC) processor, a very long instruction word (VLIW) processor, a data processing unit, and other processors or control circuitry.

The memory 306 may include suitable logic, circuitry, interfaces, or codes that is configured to store data and the instructions executable by the processing module 304. Examples of implementation of the memory 306 may include, but are not limited to, an Electrically Erasable Programmable Read-Only Memory (EEPROM), Random Access Memory (RAM), Read Only Memory (ROM), Hard Disk Drive (HDD), Flash memory, Solid-State Drive (SSD), or CPU cache memory. The memory 306 may store an operating system, or the digital message 206A or other program products (including one or more operation algorithms) to operate the digital receiver device 300.

In operation, the communication module 302 is configured to receive the first symbol sequence and the second symbol sequence, the first symbol sequence consisting of symbols from a constellation of M real symbols and the second symbol sequence consisting of symbols from a constellation of P real symbols, wherein at least one of M and P is an odd number. In an implementation, the communication module 302 is configured to receive the first symbol sequence and the second symbol sequence of the digital message 206 A (of FIG. 2) transmitted by the communication module 204 of the digital transmitter device 200 (of FIG. 2). The first symbol sequence comprises the symbols from an amplitude shift keying (ASK) constellation of M real symbols in one quadrature and the second symbol sequence comprises the symbols from another amplitude shift keying (ASK) constellation of P real symbols in another quadrature. However, at least one of M and P is an odd number.

The processing module 304 is configured to map the first symbol sequence to a first component of a digital message, and map the second symbol sequence to a second component of the digital message. After receiving the first symbol sequence and the second symbol sequence of the digital message 206A, the processing module 304 is configured to map the first symbol sequence to the first component and the second symbol sequence to the second component of the digital message 206A.

The digital receiver device 300 achieves all the advantages and technical features of the method 100 by executing the method 100. Thus, the digital receiver device 300 supports varying spectral efficiency in terms of varying baud rates and net rates. The digital receiver device 300 may be configured for use in optical communication systems (or optical transceivers) used for 5G or beyond 5G networks.

FIG. 4 illustrates an odd-even quadrature amplitude modulation (QAM) constellation with a modified probabilistic amplitude shaping (PAS), in accordance with an embodiment of the present disclosure. FIG. 4 is described in conjunction with elements from FIGs. 1, 2 and 3. With reference to FIG. 4, there is shown a sequence diagram 400 that illustrates an odd-even QAM constellation with modified probabilistic amplitude shaping. The sequence diagram 400 includes a plurality of information bits 402, a demultiplexer 404, a distribution matcher for odd- ASK bits 406A, another distribution matcher for even- ASK bits 406B, a first multiplexer 408A, a forward error correction (FEC) encoder 410, a second multiplexer 408B, a Gray mapper for odd-ASK bits 412A, another Gray mapper for even ASK bits 412B, and a combiner 414.

The plurality of information bits 402 may be a number of bits and may be represented as nSE (bits/s/Hz/QAM symbol). The plurality of information bits 402 are demultiplexed into one bit stream of odd ASK bits 402A and another bit stream of even ASK bits 402B, by use of the demultiplexer 404. After demultiplexing, the distribution matcher for odd-ASK bits 406A is applied on the bit stream of odd ASK bits 402A, in order to generate shaped information bits from Bi ^dd to B° ^dd . Similarly, the other distribution matcher for even- ASK bits 406B is applied on the other bit stream of even ASK bits 402B, in order to generate shaped information amplitude bits from to Bp ^ven . The distribution matcher for odd-ASK bits 406A, and the other distribution matcher for even- ASK bits 406B impose a constraint on the bit stream of odd ASK bits 402A, and the other bit stream of even ASK bits 402B, respectively, so that the symbols output by the Gray mapper for odd-ASK bits 412A, and the other Gray mapper for even ASK bits 412B, follow a desired non-uniform distribution P _x . For example, an odd-even QAM constellation is a M*P QAM constellation where M is odd and P is even, and consists of the Cartesian product of the M ASK constellation in one quadrature and the P ASK constellation in another quadrature. Normalized, the M ASK constellation has signal points {0, ±2, . . ., ±(M- 1)}, for instance 3 ASK = {-2, 0, 2}, and the P ASK constellation has signal points {0, ±3, . . ., ±(P-1)}, for instance 4 ASK = {-3, -1, 1, 3}. The ASK constellation are each Gray labelled, with m = [log ₂ M] and p = log ₂ P bits, respectively. In an example, a 3^2 QAM constellation includes Cartesian product of an odd 3ASK constellation in one quadrature and an even 2ASK constellation in the other quadrature. The odd 3 ASK constellation with m=2 bits per symbol is specified in Table 1.

The binary label is a Gray label which means that the label of neighboring points differ in exactly one bit because in Gray mapping the binary m-tuples of any two neighboring symbols differ in only one bit. Also, the binary 2 tuples are constrained, i.e., the 2-tuple, 10, is forbidden. The even 2ASK constellation with p=l bits per symbol is specified in Table 2.

Trivially, the label is Gray label and the bits are unconstrained. Each of the odd 3ASK constellation, and the even 2ASK constellation is shaped by use of the distribution matcher for odd-ASK bits 406A (also represented as DM Odd), and the other distribution matcher for even- ASK bits 406B (also represented as DM Even), respectively. An input and output of the distribution matcher for odd-ASK bits 406A (i.e., DM Odd) is specified in Table 3. The distribution matcher for odd-ASK bits 406A has a binary input alphabet {0, 1 } and a ternary output alphabet {00, 01, 11 }, corresponding to the 3ASK symbols {-2, 0, 2}. The distribution matcher for odd-ASK bits 406A maps input sequences of length j _n , for example, several hundred bits, to output sequences of length Tldim,out using a distribution matcher (DM) algorithm, for example, a constant composition DM (CCDM) algorithm. Other DM algorithms already available may also be used. The rate of the distribution matcher for odd-ASK bits 406A is

_D 3ASK ⁿ dim,in “dm ⁿ (4) dim,out where the super ³ refers to 3ASK, R is data rate, number of dimensions. An example of the distribution matcher for odd-ASK bits 406A (i.e., DM Odd) is specified in Table 3.

The binary DM output is mapped to 3 ASK symbols. The rate of the distribution matcher (DM) for odd-ASK bits 406A is

The maximum rate of the DM for odd-ASK bits 406A is ³ = 0.7925 and is achieved by mapping long input sequences to long output sequences and results in the symbols -2, 0, 2 occurring equally often, i.e., with a uniform distribution. By letting the DM for odd-ASK bits 406A choose sequences where 0 occurs more often than -2 and 2 results in non-uniform distribution P _x , the highest rate with this distribution will be according to the equation (5).

The DM for even- ASK bits 406B (i.e., DM even) trivially copies input to output for 2 ASK with p=l. After shaping by use of the DM for odd- ASK bits 406 A and the DM for even- ASK bits 406B, the shaped information bits, the shaped information amplitude bits and the unshaped information sign bits ([ 1 — (1 — R _FEC )(m + p) bits) from the demultiplexer 404 are multiplexed by use of the first multiplexer 408 A and then, passed to the FEC encoder 410. The FEC encoder 410 is configured to generate additional parity bits which are mapped to the sign bit of even ASK bits 402B in order to generate unshaped parity sign bits ((1 — R _FEC )(m + p^nbits). The unshaped parity sign bits are passed to the second multiplexer 408B. Thereafter, the shaped information bits are mapped to Gray labels by use of the Gray mapper for odd-ASK bits 412A in order to generate n odd ASK symbols. Similarly, the shaped information amplitude bits and the sign bits consisting of information sign bits and parity sign bits are mapped to the Gray labels by use of the other Gray mapper for even ASK bits 412B in order to generate n even ASK symbols. The n odd ASK symbols and the n even ASK symbols are combined by use of the combiner 414 in order to generate n QAM symbols. In some examples, the combiner 414 may be an adder. Alternatively, in some examples, combiner 414 may be a multiplexer, where the n odd ASK symbols and the n even ASK symbols may be multiplexed to generate n QAM symbols. The spectral efficiency of n QAM symbols can be computed this way. For n QAM symbols, the total number of label bits is (m + p)n = 3n, of which (1 bits are used for FEC parities. Thus, the spectral efficiency is computed according to equation (6)

From the equation (6), the DM rate R _m SE, /? _dm ) ^can be calculated as a function of the required SE and R _ec , and since, according to the equation (5), the corresponding distribution Px(SE, Rf _ec on the odd 3 ASK constellation can be computed.

Moreover, the operation of the bit stream of odd ASK bits 402A require probabilistic amplitude shaping (PAS), since no odd number is a power of two, so bit-sequences are required that are constrained such that the bit-mapper maps to odd ASK symbols, even when a uniform distribution on the odd ASK symbols is required. Therefore, the modified PAS is required for practical operation of the odd size constellations. Additionally, in order to avoid imbalance between the quadratures, the 3^2 QAM constellation is rotated alternatively, between 0 and 90 degrees for two successive QAM symbols, or by -45 degree and 45 degree.

The data rate (R) in bits per second may be defined as, R = B • SE • n _{d m} . For instance, in a coherent dual polarization optical communication system, the spectral efficiency (SE) is usually measured in bits per complex symbol. However, in a case, the — 2 is the number of polarizations. Alternatively stated, the spectral efficiency could be measured in bits per real symbol, in which case = 4 would be the number of real dimensions, counting the I and Q components in two polarizations. Usually, the desired data rate (R) is required to be equal to some nominal value (e.g., 200Gbit/s) as defined in some communication standard. The baudrate (B) is usually determined by bandwidth supported by an employed hardware and therefore, the equation of the data rate (R) results in a required spectral efficiency, that further depends on a suitable choice of transceiver configuration.

FIG. 5A illustrates one real dimension of an odd constellation and an even constellation, in accordance with an embodiment of the present disclosure. FIG. 5A is described in conjunction with elements from FIGs. 1, 2, 3 and 4. With reference to FIG. 5 A, there is shown an even constellation 502 and an odd constellation 504.

The even constellation 502 (e.g., 4 ASK constellation) includes 4 ASK symbols, which are represented as {-3, -1, 1, 3}, comprising m=2 bits per ASK symbol. Similarly, the odd constellation 504 (e.g., 3 ASK constellation) includes 3 ASK symbols, which are represented as {-3, 0, 3}, comprising m=2 bits per ASK symbol.

FIG. 5B illustrates distributions of various symbols of an odd constellation and an even constellation according to different entropy values, in accordance with an embodiment of the present disclosure. FIG. 5B is described in conjunction with elements from FIGs. 1, 2, 3, 4, and 5 A. With reference to FIG. 5B, there is shown a first plurality of binary plots 506 and a second plurality of binary plots 508.

The first plurality of binary plots 506 illustrates distributions of 4 ASK symbols of the even constellation 502 (of FIG. 5A) according to different entropy values. According to the equation (1), in order to compare the even constellation 502 (i.e., 4 ASK constellation) and the odd constellation 504 (i.e., 3 ASK constellation) at the same spectral efficiency (SE), same entropy value should be considered for the same number of bit levels (m) and the same FEC rate Rf _ec - Therefore, 4 entropy values between log 2 2 and lo 2 3 are considered for the first plurality of binary plots 506 as well as for the second plurality of binary plots 508. For each entropy value, the distributions of ASK symbols of the even constellation 502 (i.e., 4 ASK constellation) and the odd constellation 504 (i.e., 3 ASK constellation) that have the corresponding entropy value, are represented in the first plurality of binary plots 506 and the second plurality of binary plots 508, respectively. The resulting peak-to-average-power-ratio (PAPR) corresponding to the even constellation 502 (i.e., 4 ASK constellation) and the odd constellation 504 (i.e., 3 ASK constellation), is described in detail, for example, in FIG. 5C.

FIG. 5C is a graphical representation that illustrates peak-to-average-power-ratio (PAPR) obtained by an even constellation and an odd constellation, in accordance with an embodiment of the present disclosure. FIG. 5C is described in conjunction with elements from FIGs. 1, 2, 3, 4, 5A, and 5B. With reference to FIG. 5C, there is shown a graphical representation 500C that illustrates PAPR reduction imposed by the odd constellation 504 (i.e., 3 ASK constellation) over the even constellation 502 (i.e., 4 ASK constellation). The graphical representation 500C includes a X-axis 510 that represents entropy and a Y-axis 512 that represents PAPR in decibels (dB).

With reference to the graphical representation 500C, there is shown a first curve 514 that represents PAPR obtained by using the even constellation 502 (i.e., 4 ASK constellation). There is further shown a second curve 516 that represents PAPR obtained by using the odd constellation 504 (i.e., 3 ASK constellation). The second curve 516 illustrates that the odd constellation 504 (i.e., 3 ASK constellation) has a PAPR that is about 3 dB lower than the PAPR of the even constellation 502 (i.e., 4 ASK constellation), at all considered entropy values. Hence, the odd-even constellation (e.g., 3^2 QAM constellation) has 3 dB lower PAPR in comparison to rectangular constellation (e.g., 3x2 QAM constellation).

FIG. 6A is a graphical representation that illustrates achievable spectral efficiency per QAM symbol for different forward error correction (FEC) overheads, in accordance with an embodiment of the present disclosure. FIG. 6A is described in conjunction with elements from FIGs. 1, 4, 5 A, 5B, and 5C. With reference to FIG. 6A, there is shown a graphical representation 600A that illustrates achievable spectral efficiency per QAM symbol for different forward error correction (FEC) overheads. The graphical representation 600A includes a X-axis 602 that represents signal -to-noise-ratio (SNR) in decibels (dB) and a Y-axis 604 that represents achievable spectral efficiency per QAM symbol. For the SNR, the AWGN noise is added with increasing noise power to a transmitted signal prior to detection.

With reference to the graphical representation 600A, there is shown a first curve 606 that illustrates achievable spectral efficiency according to Shannon’s theorem (i.e., Iog2 (1+SNR)). A second curve 608 represents achievable spectral efficiency for quadrature phase shift keying (QPSK) symbols. A third curve 610 represents required spectral efficiency (e.g., 1.8 bits/QAM symbol). There is further shown a fourth curve 612 (i.e., solid line) that represents achievable spectral efficiency for a rectangular QAM constellation (e.g., 4x2 QAM constellation) with a FEC overhead of 15%. A fifth curve 614 (i.e., dashed line) represents achievable spectral efficiency for an odd even QAM constellation (e.g., 3x2 QAM constellation) with the FEC overhead of 15%. Similarly, there is further shown a sixth curve 616 (i.e., solid line) and a seventh curve 618 (i.e., solid line) that represents achievable spectral efficiency for the rectangular QAM constellation (i.e., 4x2 QAM constellation) with the FEC overhead of 21% and 27%, respectively. An eighth curve 620 (i.e., dashed line) represents achievable spectral efficiency for the odd even QAM constellation (i.e., 3x2 QAM constellation) with the FEC overhead of 27%. Each of the rectangular QAM constellation (i.e., 4x2 QAM constellation) and the odd even QAM constellation (i.e., 3x2 QAM constellation) is probabilistically shaped. The graphical representation 600A illustrates that the achievable spectral efficiency is virtually same for the rectangular QAM constellation (i.e., 4x2 QAM constellation) and the odd even QAM constellation (i.e., 3x2 QAM constellation) over the three considered FEC overheads of 15%, 21%, and 27%. However, there is an improvement over the QPSK symbols by 0.6 dB to 1.1 dB and this improvement is achieved by the rectangular QAM constellation (i.e., 4x2 QAM constellation) as well as the odd even QAM constellation (i.e., 3x2 QAM constellation).

FIG. 6B is a graphical representation that illustrates variation of bit error rate (BER) with respect to signal -to-noise-ratio (SNR) for different QAM constellations, in accordance with an embodiment of the present disclosure. FIG. 6B is described in conjunction with elements from FIGs. 1, 4, 5 A, 5B, and 5C. With reference to FIG. 6B, there is shown a graphical representation 600B that illustrates variation of bit error rate (BER) with respect to signal-to-noise-ratio (SNR) for different QAM constellations. The graphical representation 600B includes a X-axis 622 that represents signal-to-noise-ratio (SNR) in decibels (dB) and a Y-axis 624 that represents bit error rate (BER). With reference to the graphical representation 600B, there is shown a first curve 626, a second curve 628 and a third curve 630 that represents required BER at the FEC overheads of 15%, 21%, and 27%, respectively. There is further shown a fourth curve 632 (i.e., a solid line), a fifth curve 634 (i.e., a solid line), and a sixth curve 636 (i.e., a solid line) that represents variation of BER with respect to signal -to-noise-ratio (SNR) for the rectangular QAM constellation (i.e., 4x2 QAM constellation), also referred as hybrid 8QAM constellation at the FEC overheads of 15%, 21%, and 27%, respectively. There is further shown a seventh curve 638 (i.e., a dashed line), an eighth curve 640 (i.e., a dashed line), and a ninth curve 642 (i.e., a dashed line) that represents variation of BER with respect to signal-to-noise-ratio (SNR) for the odd even QAM constellation (i.e., 3x2 QAM constellation) over the three considered FEC overheads of 15%, 21%, and 27%, respectively. Moreover, the graphical representation 600B illustrates that the BER is virtually same for the rectangular QAM constellation (i.e., 4x2 QAM constellation) and the odd even QAM constellation (i.e., 3x2 QAM constellation) over the three considered FEC overheads of 15%, 21%, and 27%.

In difference to the odd even QAM constellation (i.e., 3^2 QAM constellation), the odd 3 ASK is replaced by the 4ASK in the rectangular QAM constellation (i.e., 4x2 QAM constellation). The even 4ASK constellation is specified in Table 4.

To realize shaping, the first bit-level decides for the sign and the second bit-level B decides for the amplitude. Consequently, only the second bit-level is shaped and the parity bits of the FEC encoder 410 (of FIG. 4) can be mapped to bit-level 1, following a conventional PAS. For ease of comparison, the rectangular QAM constellation (i.e., 4x2 QAM constellation) is parameterized similar to the odd even QAM constellation (i.e., 3 x2 QAM constellation). The equation (6) of spectral efficiency applies to the rectangular QAM constellation (i.e., 4x2 QAM constellation) with a difference that the term R^ _m is replaced by Rdm ^ which is specified in equation (7) where super ⁴ refers to 4 ASK and where in the numerator, is the rate contribution of the shaped bit-level 2 and where 1 is the rate contribution of the unshaped bitlevel 1, which is copied through. The spectral efficiency for the rectangular QAM constellation (i.e., 4x2 QAM constellation) can be computed according to equation (8)

Therefore, R^m ^{K can} be calculated as a function of required SE and R _ec and consequently, also the corresponding distribution (SE, Rf _ec ) of the shaped bit-level 2 of 4ASK can be computed. For a target SE of 1.8 bits/QAM symbol and FEC overheads of 15%, 21% and 27%, the odd even QAM constellation (i.e., 3x2 QAM constellation) and the rectangular QAM constellation (i.e., 4x2 QAM constellation) can be compared with each other. The corresponding system parameters are calculated using the equation (5), the equation (6), the equation (7), and the equation (8) and are listed in Table 5.

FIG. 7A is a graphical representation that illustrates variation of peak-to-average-power-ratio (PAPR) with respect to a FEC overhead for different QAM constellations, in accordance with an embodiment of the present disclosure. FIG. 7A is described in conjunction with elements from FIGs. 1, 4, 5 A, 5B, and 5C. With reference to FIG. 7A, there is shown a graphical representation 700A that illustrates variation of PAPR with respect to a FEC overhead for different QAM constellations. The graphical representation 700A includes a X-axis 702 that represents FEC overhead and a Y-axis 704 that represents PAPR in decibels (dB).

With reference to the graphical representation 700A, there is shown a first curve 706 (i.e., solid line) that represents PAPR for the rectangular QAM constellation (i.e., 4x2 QAM constellation or 8QAM constellation). Similarly, there is further shown a second curve 708 (i.e., dashed line) that represents PAPR for the odd even QAM constellation (i.e., 3x2 QAM constellation). The second curve 708 has 3dB lower PAPR than the first curve 706 that means the odd even QAM constellation (i.e., 3x2 QAM constellation) has a PAPR reduction of 3dB over the rectangular QAM constellation (i.e., 4x2 QAM constellation or 8QAM constellation).

FIG. 7B is a graphical representation that illustrates variation of peak-to-average-power-ratio (PAPR) with respect to different PAPR types, in accordance with an embodiment of the present disclosure. FIG. 7B is described in conjunction with elements from FIGs. 1, 4, 5 A, 5B, 5C, and 7A. With reference to FIG. 7B, there is shown a graphical representation 700B that illustrates variation of PAPR with respect to different PAPR types, such as PAPR for two dimensions (also represented as PAPR2D), PAPR for mix dimensions (also represented as PAPRmix) and PAPR for one dimension (also represented as PAPRID). The graphical representation 700B includes a X-axis 710 that represents PAPR types and a Y-axis 712 that represents PAPR in decibels (dB).

With reference to the graphical representation 700B, there is shown a first curve 714 and a second curve 716 that represents PAPR for an even-odd QAM constellation (e.g., 2x3 QAM constellation) and another even-odd QAM constellation (e.g., 2x3 QAM constellation) which is rotated by 45 degrees, respectively, at the FEC overhead of 15% and a spectral efficiency of 1.78 bits/s/Hz/pol. There is further shown a third curve 718 that represents PAPR for a rectangular QAM constellation (e.g., 2x4 QAM constellation). The first curve 714 and the second curve 716 have significantly lower PAPR than the third curve 718 for all considered PAPR types. That means the even-odd QAM constellation (i.e., 2x3 QAM constellation) and the other even-odd QAM constellation (i.e., 2x3 QAM constellation) rotated by 45 degrees, have significantly lower PAPR than the rectangular QAM constellation (i.e., 2x4 QAM constellation) for considered PAPR types. Moreover, the even-odd QAM constellation (i.e., 2x3 QAM constellation) and the other even-odd QAM constellation (i.e., 2x3 QAM constellation) rotated by 45 degrees or the odd-even QAM constellation (i.e., 3x2 QAM constellation) or the odd-even QAM constellation (i.e., 3x2 QAM constellation) rotated by 45 degrees, offers a PAPR reduction which is not limited to a particular PAPR type including PAPR2D, PAPRmix, and PAPRID. Therefore, all the three types of PAPR are evaluated in this way. For instance, Pi, PQ, P represents peak powers in in-phase, quadrature, and two- dimensions (2D), respectively. For example, for {-2, 0,2} x {-1,1 } 3x2 QAM constellation, values of Pi, PQ, P are

Pi = 2 ² = 4, PQ = 1 ² = 1, P = 4+1=5

Accordingly, represent corresponding average powers in in-phase, quadrature and 2D, respectively. The average powers depend on the distribution imposed by a DM (e.g., the DM for odd-ASK bits 406A, and the other DM for even- ASK bits 406B of FIG. 4) and therefore, the average powers vary with the considered entropies listed in the Table 5. The three considered PAPR types, such as PAPR2D, PAPRmix, PAPRID are specified according to equation (9).

The PAPR _{m x} seems most appropriate for the electrical signals when the rectangular QAM constellations are alternatively rotated by 90 degrees.

FIG. 8A is a graphical representation that illustrates variation of achievable spectral efficiency for different QAM constellations with respect to SNR, in accordance with an embodiment of the present disclosure. FIG. 8 A is described in conjunction with elements from FIGs. 1, 4, 5 A, 5B, 5C, and 6A. With reference to FIG. 8A, there is shown a graphical representation 800A that illustrates variation of achievable spectral efficiency for different QAM constellations with respect to SNR. The graphical representation 800A includes a X-axis 802 that represents signal- to-noise-ratio (SNR) in decibels (dB) and a Y-axis 804 that represents achievable spectral efficiency in bits/pol.

With reference to the graphical representation 800A, there is shown a first curve 806, a second curve 808 and a third curve 810 that represents achievable spectral efficiency in bits/pol for a 32QAM constellation, a 16QAM constellation and a 4*5QAM constellation, respectively, at a FEC overhead of 15% and probabilistic shaping (PS) overhead by required spectral efficiency. There is further shown a fourth curve 812, a fifth curve 814 and a sixth curve 816 that represents achievable spectral efficiency in bits/pol for a 4*6QAM constellation, a 4*7QAM constellation and Shannon’s spectral efficiency, respectively, at a FEC overhead of 15% and probabilistic shaping (PS) overhead by required spectral efficiency. There is further shown a seventh curve 818 that represents required spectral efficiency (i.e., 1.8bits/QAM symbol). Moreover, the third curve 810 for the 4*5QAM constellation includes 5 bits per QAM symbol according to 5= log ₂ 20] and represents 0.25% application specific integrated circuit (ASIC) throughput increase in comparison to the second curve 808 for 16QAM constellation. However, the third curve 810 for the 4*5QAM constellation achieves ASIC throughput increase same as that of the first curve 806 for the 32QAM constellation. The third curve 810 for the 4*5QAM constellation represents 0.75 dB SNR gain over the second curve 808 for 16QAM constellation and 0.22 dB SNR loss in comparison to the first curve 806 for the 32QAM constellation.

FIG. 8B is a graphical representation that illustrates variation of achievable spectral efficiency for different QAM constellations with respect to peak-SNR, in accordance with an embodiment of the present disclosure. FIG. 8B is described in conjunction with elements from FIGs. 1, 4, 5 A, 5B, 5C, and 8A. With reference to FIG. 8B, there is shown a graphical representation 800B that illustrates variation of achievable spectral efficiency for different QAM constellations with respect to peak-SNR. The graphical representation 800B includes a X-axis 820 that represents peak-signal-to-noise-ratio (pSNR) in decibels (dB) and a Y-axis 822 that represents achievable spectral efficiency in bits/pol.

With reference to the graphical representation 800B, there is shown a first curve 824, a second curve 826 and a third curve 828 that represents achievable spectral efficiency in bits/pol with respect to pSNR for a 32QAM constellation, a 16QAM constellation and a 4*5QAM constellation, respectively, at a FEC overhead of 15% and probabilistic shaping (PS) overhead by required spectral efficiency. There is further shown a fourth curve 830, and a fifth curve 832 that represents achievable spectral efficiency in bits/pol for a 4/6QAM constellation, and a 4*7QAM constellation, respectively, at a FEC overhead of 15% and probabilistic shaping (PS) overhead by required spectral efficiency. There is further shown a sixth curve 834 that represents required spectral efficiency. Moreover, the third curve 828 for the 4*5QAM constellation represents IdB PAPR increase in comparison to the second curve 826 for 16QAM constellation and 1.5 dB PAPR gain over the first curve 824 for the 32QAM constellation and 1.4 dB PAPR gain over the fourth curve 830 for the 4*6QAM constellation.

FIG. 9A illustrates a scatter plot for a rectangular QAM constellation, in accordance with an embodiment of the present disclosure. FIG. 9A is described in conjunction with elements from FIGs. 1, and 5 A. With reference to FIG. 9A, there is shown a scatter plot 900A that illustrates alignment of different signal points of a rectangular QAM constellation in two real dimensions. The scatter plot 900 A includes a X-axis 902 that represents in-phase (I) components of different signal points and a Y-axis 904 that represents quadrature-phase (Q) components of different signal points of the rectangular QAM constellation (e.g., 4x2 QAM constellation). The rectangular QAM constellation (i.e., 4x2 QAM constellation) is rotated by 0 and 90 degrees.

FIG. 9B illustrates a scatter plot for an odd-even QAM constellation, in accordance with an embodiment of the present disclosure. FIG. 9B is described in conjunction with elements from FIGs. 1, 5 A, and 9 A. With reference to FIG. 9B, there is shown a scatter plot 900B that illustrates alignment of different signal points of an odd-even QAM constellation in two real dimensions. The scatter plot 900B includes a X-axis 906 that represents in-phase (I) components of different signal points and a Y-axis 908 that represents quadrature-phase (Q) components of different signal points of the odd-even QAM constellation (e.g., 3x2 QAM constellation). The odd-even QAM constellation (i.e., 3x2 QAM constellation) is rotated by - 45 and 45 degrees.

The rectangular QAM constellation (i.e., 4x2 QAM constellation) and the odd-even QAM constellation (i.e., 3x2 QAM constellation) has different number of signal points in two real dimensions, which may result in an imbalance between the two dimensions, for instance, the two dimensions see different peak and average powers. In order to mitigate this, the constellations may be alternatively rotated by 0 and 90 degrees for two successive QAM symbols. Equivalently, the 4x2 QAM constellation and 2x4 QAM constellation are used alternatively, and correspondingly, the 3x2 QAM constellation and the 2x3 QAM constellation are alternated. For the 3x2 QAM constellation, the rotation between 0 and 90 degrees may create an issue for digital-to-analog (DAC) and analog-to-digital (ADC) conversion, since each dimension sees both the signal points {-2, 0, 2} and {-1, 1 }, which corresponds to five levels that must be distinguished at least. The issue can be mitigated by rotating the 3x2 QAM constellation between -45 and 45 degrees, and therefore, the DAC and ADC see in each dimension four distinct levels. Moreover, with the rotation between -45 and 45 degrees, the 3 x2 QAM constellation has no disadvantage compared to the 4x2 QAM constellation, in terms of minimum number of distinguishable levels.

FIG. 10A illustrates a scatter plot of an even-even QAM constellation, in accordance with an embodiment of the present disclosure. FIG. 10A is described in conjunction with elements from FIGs. 1, 9A, and 9B. With reference to FIG. 10A, there is shown a scatter plot 1000A that illustrates alignment of different signal points of an even-even QAM constellation 1002 (e.g., 2x2 QAM constellation) in two real dimensions. The even-even QAM constellation 1002 is represented by a dashed box, which is used for illustration purpose only.

FIG. 10B illustrates a scatter plot of an odd-odd QAM constellation, in accordance with an embodiment of the present disclosure. FIG. 10B is described in conjunction with elements from FIGs. 1, 9A, 9B, and 10A. With reference to FIG. 10B, there is shown a scatter plot 1000B that illustrates alignment of different signal points of an odd-odd QAM constellation 1004 (e.g., 3x3 QAM constellation) in two real dimensions. The odd-odd QAM constellation 1004 is represented by a dashed box, which is used for illustration purpose only.

For a certain subset of time or frequency slots, the even-even QAM constellation 1002 (i.e., 2x2 QAM constellation) may be used and for the remaining slots, the odd-odd QAM constellation 1004 (i.e., 3x3 QAM constellation) may be used. In an implementation, the ratio of the even-even slots to the odd-odd slots can be 1 : 1, but it is not limited to this value. In another implementation, the ratio of the even-even slots to the odd-odd slots can be 3: 1, as specified in Table 6. However, other ratios and order of occurrence are possible and can be chosen depending on an application scenario.

Modifications to embodiments of the present disclosure described in the foregoing are possible without departing from the scope of the present disclosure as defined by the accompanying claims. Expressions such as "including", "comprising", "incorporating", "have", "is" used to describe and claim the present disclosure are intended to be construed in a non-exclusive manner, namely allowing for items, components or elements not explicitly described also to be present. Reference to the singular is also to be construed to relate to the plural. The word "exemplary" is used herein to mean "serving as an example, instance or illustration". Any embodiment described as “exemplary” is not necessarily to be construed as preferred or advantageous over other embodiments and/or to exclude the incorporation of features from other embodiments. The word "optionally" is used herein to mean "is provided in some embodiments and not provided in other embodiments". It is appreciated that certain features of the present disclosure, which are, for clarity, described in the context of separate embodiments, may also be provided in combination in a single embodiment. Conversely, various features of the present disclosure, which are, for brevity, described in the context of a single embodiment, may also be provided separately or in any suitable combination or as suitable in any other described embodiment of the disclosure.