Field

The invention relates to a method, system and apparatus for optical communications, and more particularly, but not exclusively to a method, system and apparatus for optical communications with encoded phase-conjugated twin wave or optical variant dual polarization optical signals through non-linear optical channels.

Background

Signal distortions generated by, for example the fiber Kerr nonlinearity, impose a significant limitation on the achievable capacity and transmission reach in optical communications. Various investigations have been attempted to mitigate such effects, such as digital back propagation , optical phase conjugate, and nonlinear Fourier transform. However, these attempts exhibit either limited performance improvement and/or high complexity, and may require strict design of the optical fiber link. Recently, another attempt named phase-conjugate twin wave (PCTW) has been proposed in United States patent application publication number 2013/0070786 that exhibits some improvements, but reduces the spectral efficiency (SE) by a factor of two.

Despite the recent attempts to mitigate such signal distortions in non-linear optical communications, additional improvements and/or alternative solutions may be needed in the spectral efficiency (SE) and transmission performance of optical signals of optical communication channels that address or at least alleviate the problems associated with prior attempts.

An object of the invention is to mitigate or obviate to some degree one or more problems associated with known optical fiber nonlinearity mitigation technology schemes.

The above object is met by the combination of features of the main claims ; the sub-claims disclose further advantageous embodiments of the invention .

One skilled in the art will derive from the following description other objects of the invention. Therefore, the foregoing statements of object are not exhaustive and serve merely to illustrate some of the many objects of the present invention. Summary

In a first main aspect, the invention provides, as defined in the appended claims, an apparatus comprising an optical transmitter, the optical transmitter comprising a transmitter processor to generate at least two digital representations of at least two phase-conjugated optical variants carrying the same data payload for transmission ; an encoder for encoding one of the at least two phase-conjugated optical variants with additional information (E _a ) to the data payload; an electrical to optical converter modulating the digital electrical signal into at least two phase conjugated optical variants.

In a second main aspect, the invention provides an apparatus comprising an optical receiver, the optical receiver comprising an optical to electrical converter for receiving at least two phase-conjugated optical variants with modulated data payloads, and one of the at least two phase- conjugated optical variants having a modulated data payload with additional information, and converting into corresponding digital representations of the at least two phase-conjugated optical variants; a receiver processor arranged to map onto a constellation corresponding digital representations of the at least two phase-conjugated optical variants and to select for de-mapping and determining the data payload.

In a third main aspect, the invention provides an optical communication system for transmitting through an optical transmission link, comprising an optical transmitter, the optical transmitter comprising a transmitter processor to generate at least two digital representations of at least two phase-conjugated optical variants carrying the same data payload for transmission; an encoder for encoding one of the at least two phase-conjugated optical variants with additional information (E _a ) to the data payload; an electrical to optical converter modulating the digital electrical signal into at least two phase conjugated optical variants; and an optical receiver, the optical receiver comprising an optical to electrical converter for receiving the at least two phase- conjugated optical variants with modulated data payloads, and converting into corresponding digital representations of the at least two phase-conjugated optical variants; a receiver processor arranged to map onto a constellation corresponding digital representations of the at least two phase-conjugated optical variants and selecting for de-mapping and determining the data payload.

In a fourth main aspect, the invention provides a method of optical communication comprising the steps of generating, at a transmitter processor, at least two digital representations of at least two phase-conjugated optical variants carrying the same data payload for transmission ; encoding, at an encoder, one of the at least two phase-conjugated optical variants with additional information (E _a ) to the data payload; modulating, at an electrical to optical converter, the digital electrical signal into at least two phase conjugated optical variants.

In a fifth main aspect, the invention provides a method of optical communication comprising the steps of receiving, at an optical to electrical converter, at least two phase-conjugated optical variants with modulated data payloads, and one of the at least two phase-conjugated optical variants having a modulated data payload with additional information; and converting into corresponding digital representations of the at least two phase-conjugated optical variants; mapping, at a receiver processor, onto a constellation corresponding digital representations of the at least two phase-conjugated optical variants and selecting for de-mapping and determining the data payload.

In one embodiment there is provided apparatus comprising an optical transmitter, the optical transmitter comprising:

a transmitter processor to generate at least two constellation representations of at least two phase-conjugated optical variants carrying the same data payload for transmission ;

an encoder for encoding one of the at least two phase-conjugated optical variants with additional information (E _a ) to the data payload;

an electrical to optical converter modulating an electrical signal into at least two phase conjugated optical variants.

In another embodiment there is provided apparatus comprising an optical receiver, the optical receiver comprising:

an optical to electrical converter for receiving at least two phase-conjugated optical variants with modulated data payloads, and one of the at least two phase-conjugated optical variants having a modulated data payload with additional information, and converting into corresponding constellation representations of the at least two phase-conjugated optical variants;

a receiver processor arranged to de-map the constellation to a corresponding digital representation of the at least two phase-conjugated optical variants and to determine the data payload.

In one embodiment there is provided an optical communication system for transmitting through an optical transmission link, comprising:

an optical transmitter, the optical transmitter comprising:

a transmitter processor to generate at least two constellation representations of at least two phase-conjugated optical variants carrying the same data payload for transmission ;

an encoder for encoding one of the at least two phase-conjugated optical variants with additional information (E _a ) to the data payload;

an electrical to optical converter modulating electrical signals into at least two phase conjugated optical variants; and

an optical receiver, the optical receiver comprising:

an optical to electrical converter for receiving the at least two phase-conjugated optical variants, and one of the at least two phase-conjugated optical variants having a modulated data payload with additional information, and converting into corresponding constellation representations of the at least two phase-conjugated optical variants; a receiver processor arranged to de-map the constellation to the corresponding digital representations of the at least two phase-conjugated optical variants and to determine the data payload.

In another embodiment there is provided a method of optical communication comprising the steps of:

generating, at a transmitter processor, at least two constellation representations of at least two phase-conjugated optical variants carrying the same data payload for transmission ;

encoding, at an encoder, one of the at least two phase-conjugated optical variants with additional information (E _a ) to the data payload;

modulating, at an electrical to optical converter, an electrical signal into at least two phase conjugated optical variants.

In a further embodiment there is provided a method of optical communication comprising the steps of:

receiving, at an optical to electrical converter, at least two phase-conjugated optical variants with modulated data payloads, and one of the at least two phase-conjugated optical variants having a modulated data payload with additional information ; and

converting into corresponding constellation representations of the at least two phase- conjugated optical variants;

de-mapping, at a receiver processor, from the constellation to a corresponding digital representation of the at least two phase-conjugated optical variants and to determine the data payload.

There is also provided a computer program comprising program instructions for causing a computer program to carry out the above method which may be embodied on a record medium, carrier signal or read-only memory.

The summary of the invention does not necessarily disclose all the features essential for defining the invention ; the invention may reside in a sub-combination of the disclosed features.

Brief Description of the Drawings

The foregoing and further features of the present invention will be apparent from the following description of preferred embodiments which are provided by way of example only in connection with the accompanying figures, of which:

Figure 1 is a block diagram of a system in accordance with an embodiment of the invention ;

Figure 2 is a block diagram of the system of FIG. 1 shown in more detail in accordance with an embodiment of the invention; Figure 3 is a diagram showing the principle of the generalized encoded PCTW in accordance with an embodiment of the invention;

Figure 4 is a diagram showing the principle of the generalized encoded PCTW in accordance with another embodiment of the invention ;

Figure 5 is a table showing an example to illustrate the encoding of E _y in accordance with an embodiment of the invention;

Figure 6 is a constellation diagram of a path when E _x is a quadrature phase shift keying (QPSK) signal, and E _a is 1 or -1 in accordance with an embodiment of the invention ;

Figure 7 is a constellation diagram of a path when E _x is a quadrature phase shift keying (QPSK) singal and is 1 , -1 , y or -j in accordance with an embodiment of the invention;

Figure 8 is a table showing the two receiver paths when E _x is a quadrature phase shift keying (QPSK) signal and E _a is 1 or -1 in accordance with an embodiment of the invention ;

Figure 9 is a diagram showing the principle of the generalized encoded PCTW in accordance with an another embodiment of the invention;

Figure 10 is a diagram showing the principle of the generalized encoded PCTW showing

0/E conversion, processing unit 1 and processing unit 2 in accordance with an another embodiment of the invention ;

Figure 1 1 is a receiver processing unit shown in Figure 10 in more detail in accordance with an embodiment of the invention;

Figure 12 is a constellation diagram of a QPSK for E (N=2) in accordance with an embodiment of the invention;

Figure 13 is a constellation diagram of a 16-star QAM for E (N=4) in accordance with an embodiment of the invention;

Figure 14 is a diagram showing the principle of the generalized encoded PCTW showing 0/E conversion, pre-processing unit, processing unit 1 and processing unit 2 in accordance with an another embodiment of the invention ;

Figure 15 is a method of optical communication at a transmitter in accordance with an embodiment of the invention;

Figure 16 is a method of optical communication at a receiver in accordance with an embodiment of the invention;

Figure 17 is a graph that shows Q factor versus signal launch power for the conventional PDM QPSK, PCTW, and M-PCTW-1 in accordance with an embodiment of the invention ;

Figure 18 depicts the constellation diagrams of the conventional PDM QPSK, PCTW, and M-PCTW-1 in accordance with an embodiment of the invention Figure19 illustrates optical variants for two time slots in two polarizations ;

Figure 20 illustrates optical variants for two time slots in two polarizations; and

Figure 21 illustrates optical variants for two time slots in two polarizations. Description of Preferred Embodiments

The following description is of preferred embodiments by way of example only and without limitation to the combination of features necessary for carrying the invention into effect.

Reference in this specification to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the invention . The appearances of the phrase "in one embodiment" in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments. Moreover, various features are described which may be exhibited by some embodiments and not by others. Similarly, various requirements are described which may be requirements for some embodiments but not other embodiments.

It should be understood that the elements shown in the figures, may be implemented in various forms of hardware, software or combinations thereof. Preferably, these elements are implemented in a combination of hardware and software on one or more appropriately programmed general-purpose devices, which may include a processor, memory and input/output interfaces.

The present description illustrates the principles of the present invention . It will thus be appreciated that those skilled in the art will be able to devise various arrangements that, although not explicitly described or shown herein , embody the principles of the invention and are included within its spirit and scope.

Moreover, all statements herein reciting principles, aspects, and embodiments of the invention , as well as specific examples thereof, are intended to encompass both structural and functional equivalents thereof. Additionally, it is intended that such equivalents include both currently known equivalents as well as equivalents developed in the future, i.e., any elements developed that perform the same function, regardless of structure.

In the claims hereof, any element expressed as a means for performing a specified function is intended to encompass any way of performing that function including, for example, a) a combination of circuit elements that performs that function or b) software in any form, including, therefore, firmware, microcode or the like, combined with appropriate circuitry for executing that software to perform the function. The invention as defined by such claims resides in the fact that the functionalities provided by the various recited means are combined and brought together in the manner which the claims call for. It is thus regarded that any means that can provide those functionalities are equivalent to those shown herein.

The invention aims to provide a system to mitigate signal distortions generated by the fiber Kerr nonlinearity and improve spectral efficiency (SE) and extend transmission reach and/or system capacity. Signal distortions generated by the fiber Kerr nonlinearity in optical communication systems impose a significant limitation on the achievable capacity and transmission reach in optical communications. Embodiments of the invention address this issue, and through the transceiver and receiver design, exhibits better tolerance to fiber nonlinearity and therefore extends the transmission reach and/or system capacity.

Referring to the figures, Figure 1 is a block diagram of a system 10 in accordance with an embodiment of the invention . The encoded phase-conjugated twin wave (PCTW) system 10 comprises an optical transmitter 12 in optical communication with an optical fiber transmission link 14 and encoded PCTW optical receiver 16. The optical transmitter is configured to transmit optical variants that differ from each other in polarization or time, or both, and the optical receiver is configured to receive the optical variants.

It will be appreciated that an optical transport link is typically configured to support multiple degrees of freedom, such as time, space, carrier frequency (wavelength) , and polarization . This is discussed in United States patent publication number 2013/0070786 published 21 March 2013, and which is incorporated herein by reference in its entirety. Each of these degrees of freedom can be used for optical-signal multiplexing. Multiplexing techniques corresponding to these four different individual degrees of freedom are referred to in the literature as time-division multiplexing, space-division multiplexing, wavelength-division multiplexing, and polarization-division multiplexing.

In addition to or instead of using the various degrees of freedom supported by an optical transport link for multiplexed transmission of independent optical signals, various embodiments of the invention employ these degrees of freedom for the transmission of correlated optical signals, referred to as optical variants. I n a representative embodiment, two optical variants are two optical signals that carry the same piece of payload data, bit-word, or bit sequence, but differ from each other in the way they carry the payload data: these two optical variants are complex conjugates. Assuming that the E-field of an optical signal intended for transmission is E, the E-field of one of the two optical variants can be E, and the other can be E*, where "*" denotes complex conjugate. Here, introduced is a more general term "phase-conjugated optical variants", which refers to two optical variants that are complex conjugates after removing a constant phase offset and/or time delay between them. By complex conjugates is meant a pair of complex numbers, both having the same real part, but with imaginary parts of equal magnitude and opposite signs. The principles of the conventional phase conjugated twin wave (PCTW) scheme are based on the x-polarization and y-polarization optical signals at the transmitter are phase conjugated. Assuming the signals of these two polarizations at the distance L are E _x (L,t) and E _y (L,t)), respectively, we have E _y (0,f) = (E _x (0,f)) ^* with ( ^■ ) ^* referring as the complex conjugation operation. These two signals are launched into the fiber, and the nonlinear distortions on the two polarization signals in the frequency domain, 5E _x (L,iy) and 5E _y (L,aj), are:

9

y ₎ (. aj) = i- P ₀ L _ff \_ ⁺ Zdo \_ ⁺ Ζάω ₂ η{ο ω ₂ ) ,)( ⁰ ' ^iy + ^iy 2 ,)( ⁰ ' ^iy + ⁱ ¾ + ^iy 2) (1)

+ ^E _y (0, ® + fl¾ )E _{X (or y)} (0, ® + t¾ )E _{y (or x)} (Ο,ω + fl¾ + t¾ )] where

Left, γ, and are the effective length, the fiber nonlinear Kerr coefficient, and the dimensionless nonlinear transfer function, respectively. For a symmetric dispersion and power map along the link, is real-valued. Given E _y (0,f) = (E _x (0,f))) ^* or Ε _¥ (0,(ή = (Ε _χ (0,-ω))) ^* , we can derive from Eq. (1):

dE _y (L,C0) = -SE δΕ _y (L,t) = -δΕ _x (L,t)" (3)

Consequently, at the receiver, the first-order nonlinear distortions can be cancelled and the original signal can be recovered by using:

E _r (t) = E L,t) + E _y (L,t ' = 2E( ,t) (4)

However, as discussed, the conventional PCTW scheme reduces the spectral efficiency by a factor of two.

Figure 2 is a block diagram 20 of the system 10 of FIG. 1 shown in more detail in accordance with an embodiment of the invention. An input stream payload data or net information 22 is received at a transmitter processor 24. An electrical to optical (E/O) converter (front end circuit) 26 receives the net information from the transmitter processor. An encoder 28 is in communication with the transmitter processor 24. The E/O converter 26 comprises a digital to analog converter (DAC) 30, an in-phase (I) component/quadrature-phase (Q) component modulator 32, and a polarization beam combiner 34. The combiner 34 combines modulated optical signals and generates the optical output signal. An optical add/drop multiplexer (OADM) 40 receives the optical output signal from the E/O converter, and adds the optical output signal from transmitter 12 to the optical fibre transmission link 14.

An optical add/drop multiplexer (OADM) 42 drops the transmitted optical signal from the optical fibre transmission link 14 to the optical receiver 16. The optical receiver comprises receiver processor 50 and optical to electrical (O/E) converter (front end circuit) 60. The O/E converter comprises an analog to digital converter (ADC) 62, modulator polarization diverse photo detectors (PDOH) 64, and optical local oscillator 66. A signal selector 70 and decoder 72 are in communication with the receiver processor. The processer then provides the output stream payload 78 net information . The transmitter processor is arranged to generate the constellation representations by mapping from a digital representation, and the encoder is arranged to encode the additional information to either the digital representation or the constellation representation of one of the at least two phase-conjugated optical variants, described in more detail below.

Embodiments of the invention propose an improved PCTW scheme, named modified PCTW method I I (M-PCTW-I I) to improve the spectral efficiency while maintaining the performance benefits of the conventional PCTW method. To reach the ultimate M-PCTW-I I , there are two intermediate schemes, named generalized PCTW (G-PCTW) and M-PCTW-I schemes.

Figure 3 is a diagram 1 00 showing the principle of the generalized encoded PCTW in accordance with an embodiment of the invention . The x-polarization and y-polarization optical signals 102 at the transmitter are shown with complex conjugation encoded E _y with constant electric field E _a that are launched into the fibre optic transmission link and the receiver 104 de-mapping to output Ex.

In conventional PCTW, E _y (0, f) = (E _x (0, f))\ In fact, observation of the principle shows that if E _y (0, f) = E _a x(Ex(0, f))) ^* , where E _a is a constant optical field, we have:

dE _y (L, co) = -dE _x (L -co) ^* E _a , SE _y (L, t) = -SE _x (L, t)' x E _a (5) At the receiver, the original optical signal is recovered by using :

E _r (t) = E _x (L, t) + (E _y (L, t) l E _a )' = [E _x ( , t) + SE _x (L, t)] + [E _x ( , t) - δΕ _x (L, t)] = 2E ( , t) (6)

Eq. (6) implies that when there is a constant field multiplied to E _y (0, f), the fiber nonlinearity can still be cancelled. However, E _a does not add additional information. It is possible to also encode E _a to increase the spectral efficiency. Figure 4 depicts the principle of M-PCTW-I scheme. Additional information is encoded in E _a before it multiplies to Ex ^* so that E _a is not a constant anymore. Figure 5 shows an example when Ex is a QPSK signal with the symbol period of 7. I n this example, E _a is encoded as either 1 or -1 in each 7 so that 1 /7 additional bits are encoded in E _a and the total transmission rate increases from 2/7to 3/ 7compared to the conventional PCTW method. Similarly, when E _a is encoded as 1 , -1 , y ^' or -j, the spectral efficiency is 4/7, the same as that of the dual- polarization QPSK signal. Without the loss of generality, we define the / ^h signal levels in E _a as Eu, 1 ≤ i≤ N, with being the bit number encoded in E _a . At the receiver, after coherent detection and analogue-to-digital conversion with the sampling rate of T, the received signals are split into N paths, with the / ^h path performing the operation of:

E _{r l} (t) = E _x ( L, t) + ( E _y (L, t) l E _{a l} )' , l≤ i≤ N ( ⁷ )

Figure 4 is a diagram 120 showing the principle of the encoded PCTW (M-PCTW-I) in accordance with another embodiment of the invention . The x-polarization and y-polarization optical signals 122 at the transmitter are shown with complex conjugation encoded E _y with electric field Ea that are launched into the fibre optic transmission link and the receiver 124 selection for decision of Ea. I n this embodiment E _a is independent of E _x .

Figure 5 is a table 130 showing an example to illustrate the encoding of E _y in accordance with an embodiment of the invention.

Figure 6 is a constellation diagram 140 of a path at the receiver when E _x is a QPSK signal and Ea is 1 or -1 in accordance with an embodiment of the invention, and Figure 7 is a constellation diagram 146 of a path when E _x is a QPSK signal and E _a is 1 , -1 , j, or -y in accordance with an embodiment of the invention. More specifically, Figure 6 and Figure 7 show the constellation of E,i when Ex is a QPSK signal and E _a is encoded as 1 or -1 in Figure 6, and 1 , -1 , y ^' or -y in Figure 7.

Figure 8 is a table 150 showing the two receiver paths when E _x is a quadrature phase shift keying (QPSK) signal and E _a is 1 or -1 in accordance with an embodiment of the invention . The table of Figure 8 analyses the outputs of different paths for the case of Figure 6. It can be seen that the constellation of each path in the case of Figure 6 and Figure 7 is no longer the same as that of Ex, and has five and nine points, respectively. I n the case of Figure 6 (or the Table of Figure 8) , when Ea = 1 , the output of path 1 , E _r ,i , is equal to the transmitted QPSK signal Ex while E,2 = 0. Conversely, when E _a = -1 , E,2 gives the QPSK signal E _x while E,i = 0. A selection module compares the outputs of these two paths and select the larger one. This selection process operates every symbol period 7 and decides either 1 or -1 is transmitted in Ea. The selected path is then sent to the next de-mapping module to decide E _x . I n Figure 6, the points are marked, which represents that when those points occur at the output of a path, this path is the selected one to decode E _x and the index of this path can be used to decode E _a . Similarly, the points are marked in Figure 7 and it can be seen that in this case, a path can also be selected if the absolute value of the output of this path is larger than that of the other three paths. It is clear that M-PCTW-I can improve the spectral efficiency but the key question is if this scheme can maintain certain performance benefits of the conventional PCTW scheme. We find that, once the information of E _a , which is either a constant (G-PCTW) or an encoded field (M- PCTW-I), is given , Ex can maintain the same performance as that in the conventional PCTW method. On the other hand, E _a does not have the performance benefits in Ex and is the main source limiting the system performance. This is seen more clearly in the numerical analysis. Furthermore, it can be seen that in M-PCTW-I , the decoding of Ex is dependent on the correct selection of paths and improper decoding of E _a also increases the errors in Ex. Therefore, redundancy is added in E _a to mitigate this dominant performance limiting source. In practice, this redundancy can be realized in different ways, by using, for example, error correction code, reducing the symbol rate of E _a from 1 /Tto 1 /(27), or the like. I n this embodiment, without the loss of generality, we use the BCH code in E _a . Figure 9 shows the setup of the proposed M-PCTW-I I scheme.

Figure 9 is a diagram 160 showing the principle of the encoded PCTW (M-PCTW-I I) in accordance with another embodiment of the invention . The x-polarization and y-polarization optical signals 162 at the transmitter are shown with complex conjugation encoded E _y with electric field E _a and added redundancy when encoding E _a , that are launched into the fibre optic transmission link and the receiver 1 64 selection for decision of E _a . I n this embodiment E _a has redundancy to improve the correct reading of E _a . E _a can be independent or dependent of Ex. The de-mapping to output Ex is processed in the receiver 164 in the digital domain, and not in the receiver front end circuit.

Figure 10 is a diagram 1 70 showing the principle of the generalized encoded PCTW showing a transmitter section 172 and a receiver section 1 74 showing O/E conversion , processing unit 1 and processing unit 2 in accordance with an another embodiment of the invention. Figure 1 1 is a receiver processing unit (1 ) 180 shown in more detail in accordance with an embodiment of the invention. It will be appreciated that the optical system in accordance with an embodiment of the invention is configured to transmit 2 Optical signals, where ^" is an integer, /^signals (named as the signals of group 1 ) are independently encoded by data streams into formats such as single- carrier formats such as quadrature phase shift keying (QPSK) , 8 quadrature amplitude modulation (QAM) , 1 6QAM , and the like, and multi-carrier formats such as orthogonal frequency-division multiplexing (OFDM) and the like. For clarity the embodiments discussed herein refer to data streams with single-carrier formats, however, it will be appreciated that data streams with multi- carrier formats may also be used in embodiments of the invention . For multi-carrier formats such as OFDM , Ex can be one of subcarriers in the x-polarization signal, and E _y is one of subcarriers in the y-polarization signal. For each of these /^signals, E, there is a signal, E, in the rest /^signals (named as the signals of group 2) . Assume in this embodiment that the data encoded in E are {a , a≥, a3...aw), E can be expressed as Px E _a , where * represents the conjugate, and E _a is a signal encoded using data of (aN+i, aN+2,...aN+Mi) and can be independent or dependent on the value of E. Additional error correction code is applied to (aN+i, aN+2,...aN+Mi) so that the correctness of aN+2,...aN+Mi) in the system has higher priority than that for (ai, a≥, as...aw). This design is based on the finding that more errors may occur in aN+2,...aN+Mi) due to fiber nonlinearity than in (ai, a2, a3...aw), and the incorrect decoding of aN+2,...aN+Mi) also degrades that of (at, a≥, 33...aw). The data after the error correction coding are represented by (0N+I, 0N+2,...0N+M2), M2>MI. Note that M2 and Mi here are not necessarily an integer. The presentations such as (a +t, aN+2,...aN+Mi) are used for simple illustration. In fact, it means that Mi-bit net or Λfc-bit raw (with error correction code) information is transmitted in E when the information of E* is known. This can be seen more clearly in the examples of Figures 12-14. Similarly, Λ/is not necessarily an integer either.

At the receiver, the received signal in group 1 , E, and its associated signal in group 2, Ex, are processed jointly. The receiver consists of but is not limited to the following two processing units. In processing unit 1, the data (a +t, aN+2,...aN+M2) are decided. The error correction code in aN+2,...aN+M2) is employed in this process to reduces the errors of (a +t, aN+2,...aN+M2). Processing unit 2 is after the unit 1, where (at, ai, a3...aw) is decided.

Embodiments of the invention are based on the finding that more errors may occur in (an+t , aN+2,...aN+Mi) due to fiber nonlinearity than in (at, a≥, as...aw), and the incorrect decoding of aN+2,...aN+Mi) also degrades that of (at, a≥, as...aw). Therefore, the correctness of aN+2,...aN+Mi) in the system has higher priority than that for (at, a≥, 33...aw) so that redundancy is added in (aN+i, aN+2,...aN+Mi) to improve its and hence the overall system performance. E _a here can be independent or dependent on the value of E.

The two signals E and E, defined here, can be signals directly modulated on optical carriers such as optical QPSK/16QAM signals, or signals on an electric subcarrier of two optical multicarrier signals (or two electric subcarriers of an optical multicarrier signal). For example, E and E can be two optical signals at different wavelengths, at the same wavelength but with different polarizations, or two subcarriers of an optical orthogonal frequency division multiplexing signal. In particular, the signals of group 1 and group 2 are in two different optical polarizations. That is, for each signal E in one polarization, there is a signal E (= Px£ _a ) in another polarization. There is no limitation on which type of error correction code is applied to (a +t, 3Ν+2,...3Ν+ΜΙ). When E _a is independent on the value of E, the typical configuration of the processing unit 1 , as shown in Figure 11 , where Eu, 1< /< 2 ^M2 , presents the / ^h format level of E _a mapped from (£>N+I, 0N+2,...0 +M2).

Figure 12 is a constellation diagram 184 of a QPSK for E (N=2) in accordance with an embodiment of the invention, and Figure 13 is a constellation diagram 188 of a 16-star QAM for E (N=4) in accordance with an embodiment of the invention. In Figure 12, E _a is encoded independent of E, with the values of 1 , -1 , j, and -j. At the receiver, the four paths as shown in Fig. 1 1 are: E,i

= Er + (Er')*, E,2 = Er + (-Er')*, E,3 = Er + (jx Er')*, Er,4 = Er + (-jx Er')*.

When Λ/>2, E _a can be dependent on E. As an example, when E is a 16-star QAM with the constellation shown in Figure 13. Referring to Figure 13, E _a is encoded as 1 , -1 , j, and -j when E is on the inner circle. When E is on the outer circle, E _a is encoded as exp(j-O) , exp(j-7t/6) , exp(j-27t/6) , exp(j-37t/6) , exp(j-47t/6) , exp(j-57t/6) , exp(j-67t/6) , exp(j-77t/6), exp(j-87t/6), exp(j-9n/6) , exp(j-107t/6) , exp(j- 1 17c 6). The transmitted bit number in E is log2(1 6)=4 while the bit information jointly in E and E' (including the FEC in E _a ) is log2(4x4+12x12)=7.3. That is M2=3.3. At the receiver, when E _a is dependent on E, a pre-processing unit is used before processing unit (1 ) of Figure 1 1 . I n the above example, the pre-decision module decides whether E is on the inner or the outer circles. When E, is on the inner circle, processing unit 1 can decide E _a using the setup of Figure 1 1 , where E _a ,i, 1 < / < 4, are 1 , -1 , j, or -j. When E is on the outer circle, processing unit 1 can decide E _a also with the setup of Figure 1 1 but Eg, 1 < / < 12, are exp(j-O) , exp(j-7t/6) , exp(j-27t/6), exp(j-37t/6) , exp(j-47t/6) , exp(j-57t/6) , exp(j-67t/6) , exp(j-77t/6) , exp(j-87t/6) , exp(j-97t/6) , exp(j-1 07t/6), or exp(j- 1 1 π/6) . Figure 14 shows the diagram when E _a is dependent on E.

Figure 14 is a diagram 1 90 showing the principle of the generalized encoded PCTW showing a transmitter section 191 and receiver section with O/E conversion 192, pre-processing unit 194, processing unit (1 ) 196, and processing unit (2) 1 98 in accordance with an another embodiment of the invention.

Commonly, E and E are verified to be effective when they have the same modulation formats with the same constellation profile. For example, if E is a QPSK signal with format levels of (1 +j), (1 -j) , (-1 +j), (-1 -j) , E is also a QPSK signal with format levels of (1 +j), (1 -j) , (-1 +j) , (-1 -j) . In particular, the proposed scheme is verified to be effective while exhibiting good spectral efficiency for E _a with constant intensity and M≥ > 1 . For example, E _a is a 4-PSK signal in the example of Fig. 3 with format shape of 1 , -1 , j, -j or any phase-rotation form of this constellation (such as (1 +j) , (1 - j). (" ¹ +j) _> (" ¹ -j)) ^{or an} y constant scaling form of this constellation (such as 2, -2, 2j, -2j) . I n particular, Λ/ can be larger than 2, representing high-level formats such as 8-PSK and 16QAM. I n particular, the scheme is shown to be more effective when E is a multi-phase signal with a constant intensity (e.g. 8-PSK) or a star-QAM signal with several intensity circles (e.g. 1 6-star QAM). The case that E _a can be dependent on E commonly occurs for a star-QAM signal with several intensity circles. E _a is a function of intensity circles and the pre-processing at the receiver is used to decide which intensity circle the received signal is on. Once the intensity circle is decided, the processing for each circle is similar to the case where E _a is independent on E (e.g. Figure 13 and 14). Finally, the proposed scheme only defines that from the perspective of fiber nonlinearity tolerance, , aN+2, . . . aN+Mi ) in the system is more vulnerable to fiber nonlinearity and is more important than (ai , a≥, 33... in data decoding, and so require additional redundancy to improve the overall system performance. This does not place any limitation that another one or more error correction codes can be applied at higher layers to the net information of the proposed scheme, (a , a≥, a3...aw,aN+i , 3 +2, . . .3

Figure 15 is a method 200 of optical communication at a transmitter in accordance with an embodiment of the invention. The phase-conjugate twin wave optical signals 202 are generated, and additional information is encoded 204 with optical field (E _a ) 204. In an embodiment, error redundancy 206 is provided. The encoded phase-conjugate twin wave optical signals are modulated 208 and transmitted through nonlinear fibre optical channel 210 to the receiver.

Figure 16 is a method 230 of optical communication at a receiver in accordance with an embodiment of the invention. The receiver receives the transmitted encoded phase conjugate twin wave optical signals 232 and split to multiple paths with the operation similarly as Figure 10 or the like 234. The path is selected 236 and the additional information in the optical field (E _a ) is decoded 238. The selected path undergoes de-mapping to decide Ex 240.

A 25-Gbaud PDM QPSK signal was applied to verify the advantage of the scheme of an embodiment of the invention. A pseudo-random bit sequence (PRBS) with length of 2 ²³ -1 was used to generate the binary bits, which were mapped to the PDM QPSK signal. The fiber link consisted of spans of 80-km standard single-mode fiber with a loss parameter of 0.2 dB/km, a nonlinear coefficient of 1 .31 /W/km, and a dispersion coefficient of 16 ps/km/nm. At the end of each span, an optical amplifier with 16-dB gain and 4.5-dB noise figure was used to compensate the loss in the fiber. The total simulated fiber length was 15,200 km. In-line dispersion compensation was not used and a symmetric dispersion map was adopted by adding dispersion compensating fibers after the transmitter and before the receiver. At the receiver, the signal was coherently detected. Laser linewidth was set to be zero but the Viterbi-Viterbi algorithm was still used to compensate the nonlinearity induced phase rotation. The simulated number of symbols (or bits) was 2 ¹⁶ (or 2 ¹⁸ ). This simulation was iterated three times with different PRBS patterns and the bit error rate (BER) was averaged and used to obtain the Q factor.

Figure 17 is a graph 270 that shows Q factor versus signal launch power for the conventional PDM QPSK, PCTW, and M-PCTW-1 in accordance with an embodiment of the invention (Ex is a QPSK signal and E _a is 1 or -1 ). Figure 15 shows Q factor versus launch power at 15,200 km for 25- and 18.75-Gbaud conventional QPSK (empty and solid circles), 25-Gbaud PCTW (50% net data rate) (triangles), 25-Gbaud M-PCTW-1 (75% net data rate) (squares) and M- PCTW-1 assuming a3 are correctly decoded (diamonds). The 18.75-Gbaud conventional QPSK has better OSNR requirement than the 25-Gbaud signal, but exhibits only slight improvement in the optimal Q factor due to the fiber nonlinearity. As expected, PCTW can improve the optimal Q factor significantly (>3 dB at -1 dBm launch power) but at the expense of 50% net data rate. M- PCTW-1 improves the SE to 75% but reduces the Q factor improvement by ~ 1 .5 dB compared to the PCTW method. It is desirable to understand the reason for this performance degradation.

Figure 18 depicts the constellation diagrams of the conventional PDM QPSK, PCTW, and

M-PCTW-1 in accordance with an embodiment of the invention. Figure 18 shows constellation diagrams of (a) conventional QPSK, (b) PCTW, (c)&(d) outputs of the add/subtract paths in M- PCTW-1 , (e)&(f) output of the selection unit in M-PCTW-1 with conventional decoding and assuming a are correctly decoded. Rectangular symbols represent the errors. The rectangular symbols represent the constellation of the incorrectly decoded data. As described previously, the output of each path in M-PCTW-1 shows a five-point constellation. Ideally, when the output of one path is a QPSK data value, another path should give a zero value, so that by selecting the path that has a larger intensity, the decision unit can give the constellation diagram of {a , as). However, in practice, if a is wrongly decoded due to the nonlinearity-induced distortion and/or the noise, {a , as) would also be decoded incorrectly although the constellation at the output of the decision unit is still clear as shown in Figure 18(e). It implies that the decoding of as is more important than that of a and a≥. More importantly, it is found that the occurrence of errors is more frequent in as. It may be because nonlinearity induced polarization scattering is the main physical mechanism limiting the performance of the system. In Figure 18(f), once a can be correctly decoded, the number of errors in a and a≥ is significantly reduced to a value similar to the PCTW method, implying that M- PCTW-1 can suppress nonlinear distortions for {a ,as) in a similar manner as the conventional PCTW method.

It will be appreciated that embodiments of the invention significantly improve the SE while maintaining the performance benefits when compared to the conventional PCTW method. Simulation results show that for QPSK, the SE can be extended to greater than 80%, which is a substantial improvement from 50% of conventional PCTW scheme, while still maintaining the performance benefit. The scheme of embodiments of the invention is also different from other conventional prior attempts such as a dual-PCTW scheme. For example, the QPSK of the scheme of an embodiment of the invention still transmits a QPSK signal without increasing the signal level in the transmission and this spectral efficiency is tunable by changing the overhead in E _a .

In another embodiment when the signal dimension is higher than 2 (e.g. there are more than two optical variants in the time, space, polarization, frequency (wavelength) domain or any combination of these domains), the two encoded phase conjugated optical variants can be combined with other pairs of encoded phase conjugated optical variants, or other pairs of conventional phase conjugated optical variants. For example, assuming the optical variants are Ei , E2, E3, E4, where Ei, i=1 ,2, ... are an optical variant in any of time, space, polarization , and frequency domains, an embodiment is that Ei and E2 are a pair of encoded phase conjugated optical variants (i.e. , _a , where Ei , _a is the encoded additional information) , while E3 is the conjugated of Ei (i.e. d E4 is the conjugate of E2 (i.e. E4=E2*). In another embodiment of the invention is Ei and E3 are a pair of encoded phase conjugated optical variants (i.e. , _a ), while E2 and E4 are another pair of encoded phase conjugated optical variants (i.e. E4=E2*xE2, _a , where E2, _a is another encoded additional information) .

Figures 19 and 20 shows the constellation of the transmitted optical variants for the above two embodiments. Note that the four optical variants are not limited to the combination of time domain (time slot 1 and 2) and polarization domain (x and y polarizations) , as illustrated in figure 19.

Figure 19 illustrates optical variants for two time slots in two polarizations (totally 4 dimensions). The circles on the constellation points represent that when the x polarization in time slot 1 , Ei , is the marked point, E2 is the encoded phase conjugate of , _a , where Ei , _a in this example is 0 or π), E3 is the conventional phase conjugate of Ei E4 is the phase conjugate of E2 (E4=E2*).

Figure 20 illustrates optical variants for two time slots in two polarizations (totally four dimensions). The circles on the constellation points represent that when the x polarization in time slot 1 , Ei , is the marked point, E3 is the encoded phase conjugate of Ei , _a , where Ei , _a in this example is 0 or π) ; E2 and E4 is another pair of encoded phase conjugated optical variants (E4=E2*xE2, _a , where E2, _a in this example is π/2 or 3π/2).

In another embodiment of the invention it will be appreciated that the additional information E2, _a can be independent or dependent on the additional information Ei , _a . The case that E2, _a is independent on Ei , _a has been illustrated in Figure 20. For the case that E2, _a is independent on Ei , _a , Ei , _a in Fig. 2 can be 0, π/2, π, and 3π/2 ; when Ei , _a is 0 or π, E2, _a is π/2 or 3π/2; when Ei , _a is π/2 or 3π/2, E2, _a is 0 or π. Figure 21 shows this embodiment.

Figure 21 illustrates optical variants for two time slots in two polarizations (totally four dimensions). The circles on the constellation points represent that when the x polarization in time slot 1 , Ei , is the marked point, E3 is the encoded phase conjugate of Ei , _a , where Ei , _a in this example is 0, π/2, π, or 3π/2) ; E2 and E4 is another pair of encoded phase conjugated optical variants (E4=E2*xE2, _a , where E2, _a is dependent on Ei , _a : when Ei , _a is 0 or π, E2, _a is π/2 or 3π/2; when Ei , _a is π/2 or 37t/2, E2, _a is 0 or π.).

The above analysis can be extended to higher dimensions : assuming the optical variants are Ei , E2, E3, E4, Es, Ee, E7, Es, where Ei, i=1 ,2, ... are an optical variant in any of time, space, polarization, and frequency domains, Ei and E3 are a pair of encoded phase conjugated optical variants (i.e. where Ei , _a is the encoded additional information) ; E2 and E4 are another pair of encoded phase conjugated optical variants (i.e. E4=E2*xE2, _a , where E2, _a is another encoded additional information) ; Es is the phase conjugate of Ei ; Ee is the phase conjugate of E2 ; E7 is the phase conjugate of E3 ; Es is the phase conjugate of E4.

Similar to the 4-dimension case, in this example, the additional information E2, _a can be independent or dependent on the additional information Ei , _a . For example: Ei , _a can be 0, π/2, π, and 3π/2; when Ei , _a is 0 or π, E2, _a is π/2 or 3π/2; when Ei , _a is π/2 or 3π/2, E2, _a is 0 or π.

While the invention has been illustrated and described in detail in the drawings and foregoing description, the same is to be considered as illustrative and not restrictive in character, it being understood that only exemplary embodiments have been shown and described and do not limit the scope of the invention in any manner. It can be appreciated that any of the features described herein may be used with any embodiment. The illustrative embodiments are not exclusive of each other or of other embodiments not recited herein. Accordingly, the invention also provides embodiments that comprise combinations of one or more of the illustrative embodiments described above. Modifications and variations of the invention as herein set forth can be made without departing from the spirit and scope thereof, and, therefore, only such limitations should be imposed as are indicated by the appended claims.

The embodiments in the invention described with reference to the drawings comprise a computer apparatus and/or processes performed in a computer apparatus. However, the invention also extends to computer programs, particularly computer programs stored on or in a carrier adapted to bring the invention into practice. The program may be in the form of source code, object code, or a code intermediate source and object code, such as in partially compiled form or in any other form suitable for use in the implementation of the method according to the invention. The carrier may comprise a storage medium such as ROM, e.g. CD ROM, or magnetic recording medium, e.g. a memory stick or hard disk. The carrier may be an electrical or optical signal which may be transmitted via an electrical or an optical cable or by radio or other means.

In the specification the terms "comprise, comprises, comprised and comprising" or any variation thereof and the terms include, includes, included and including" or any variation thereof are considered to be totally interchangeable and they should all be afforded the widest possible interpretation and vice versa.

The invention is not limited to the embodiments hereinbefore described but may be varied in both construction and detail.