APPARATUS AND METHOD FOR ENCODING A MESSAGE HAVING A TARGET PROBABILITY DISTRIBUTION OF CODE SYMBOLS TECHNICAL FIELD

In general, the present invention relates to encoding in communication systems. More specifically, the present invention relates to an apparatus and a method for encoding a message using a precoder.

BACKGROUND

In order to achieve the capacity of a transmission channel in communication systems, the channel input symbols should have a certain probability distribution. For example, a

Gaussian distribution can be used in order to achieve the capacity of an additive white Gaussian noise (AWGN) channel. However, in many practical communication systems, uniformly distributed channel input symbols are used, which can cause a gap to the capacity. This loss is also called shaping loss and can be up to 1 .53 dB on AWGN channels, if uniformly distributed quadrature amplitude modulation (QAM) symbols are used.

The shaping loss can become significant especially with high order modulation. A common approach used for transmission with high order modulation is the so-called bit-interleaved coded modulation (BICM), wherein the message to be transmitted is first encoded by a channel encoder to a code word, which is interleaved, and, then, mapped to channel input symbols via a symbol mapper. In many systems, binary channel codes are used in such a way that the code words are binary vectors. In general, the distribution of one and zeros in a code word is uniform and this causes the channel input symbols to have a uniform distribution, too. In the prior art, different approaches are proposed in order to reduce the shaping loss for high order modulation, as listed in the following.

In the so-called non-uniform constellations (NUC) approach, a symbol mapper with nonuniform constellations is used. In this approach, the output of the channel encoder is mapped to symbols that do not have a regular structure like QAM symbols, but have an optimized structure that helps to reduce the shaping loss. This approach does not have any constraints on the used channel code. This approach is also called geometric shaping. However, due to the non-regular constellation structure, the standard QAM symbol mapper and QAM demapper should be replaced by more complex symbol mappers and symbol demappers, respectively. In the so-called probabilistic amplitude shaping (PAS), a shaping encoder is used prior to the channel encoder, which converts the uniformly distributed input message to a non-uniformly distributed sequence. Then, this sequence is encoded by a systematic channel encoder (i.e., the output of the channel encoder contains the input of the channel encoder as a subvector), which is then fed to a QAM symbol mapper. At the receiver, a QAM demapper can be used. After decoding the channel code, the shaping decoder should process the output of the channel code in order to retrieve the message. This approach reduces the shaping loss. However, this approach requires a shaping encoder and shaping decoder, which can increase the complexity at the transmitter and at the receiver. Moreover, the information is retrieved after being processed by two decoders in serial, which is suboptimal compared to a joint decoder. Furthermore, this approach poses a constraint on the used channel code, since the channel encoder has to be a systematic encoder, which is not always favorable.

Thus, there is a need for an improved communication apparatus and a method for encoding a message which allow to reduce the gap to the capacity of the transmission channel.

SUMMARY

It is an object of the invention to provide for an improved communication apparatus and a method for encoding a message which allow to reduce the gap to the capacity of the transmission channel.

The foregoing and other objects are achieved by the subject matter of the independent claims. Further implementation forms are apparent from the dependent claims, the description and the figures.

According to a first aspect, the invention relates to a communication apparatus for encoding a message to be transmitted over a communication channel, wherein the communication apparatus comprises a precoder configured to generate on the basis of the message and a channel code a pre-coded message, and a channel encoder configured to encode the pre- coded message based on the channel code into a code word, wherein the code word comprises a plurality of bits and/or symbols which have a probability distribution, wherein the precoder is configured to generate the pre-coded message such that the channel encoder generates the plurality of bits and/or symbols with the probability distribution matching a target probability distribution.

Matching the probability distribution to a target probability distribution can comprise that the precoder generates the bits and/or symbols based on the target probability distribution. Further, this can comprise that the bits and/or symbols generated by the precoder (or the channel encoder that processes the output of the precoder) have a probability distribution that is substantially equal to the target distribution, in particular that the probability distribution has substantially the same mean and/or variance as the target distribution. For example, the distance between the probability distribution of the plurality of bits of the code word and the target probability distribution can be given by the Kullback-Leibler distance.

Thus, an improved communication apparatus is provided, since the shaping gap of the bits and/or symbols produced by the precoder is reduced, and, therefore, the transmission performance is improved.

In a possible implementation form of the communication apparatus according to the first aspect, the precoder is a systematic precoder. Thus, an improved communication apparatus is provided, since the output of the precoder contains the input, i.e., the message to be transmitted, and, thus, making the process of decoding at the receiver side easier.

In a further possible implementation form of the communication apparatus according to the first aspect, the channel encoder is a non-systematic encoder. In a further possible implementation form of the communication apparatus according to the first aspect, the communication apparatus further comprises an interleaver configured to interleave the plurality of bits and/or symbols of the code word and/or a modulator, in particular a symbol mapper configured to map the code word to one or more symbols for transmission over the communication channel. Thus, an improved communication apparatus is provided, since a modulator which is easy to implement, e.g. a QAM symbol mapper, can be used.

In a further possible implementation form of the communication apparatus according to the first aspect, the channel encoder is configured to encode the pre-coded message on the basis of a polar transform into the code word, wherein the polar transform is applied to the pre-coded message and a sequence of frozen bits and wherein the precoder is configured to generate the pre-coded message on the basis of the message and the sequence of frozen bits. This provides the advantage of making use of the polarisation effects of the polar transform, which allows to approach the capacity of the transmission channel.

As used herein, the polar transform can be based on the Arikan kernel corresponding to the

In a further possible implementation form of the communication apparatus according to the first aspect, the message is a vector u and wherein the precoder is configured to generate a vector of shaping bits s on the basis of the message vector u and the target probability distribution and to generate the pre-coded message by concatenating the vector of shaping bits s with the message vector u such that the probability distribution of the plurality of bits of the code word matches the target probability distribution. This provides the advantage of generating a code word having substantially the desired target probability distribution, and, thus, of reducing the gap to the capacity of the transmission channel due to the shaping loss.

In a further possible implementation form of the communication apparatus according to the first aspect, the precoder comprises a channel decoder based on the channel code.

In a further possible implementation form of the communication apparatus according to the first aspect, the precoder is configured to generate an auxiliary channel decoder input sequence y on the basis of the target probability distribution.

In a further possible implementation form of the communication apparatus according to the first aspect, the precoder is configured to generate a channel decoder a priori information sequence based on the message vector u.

In a further possible implementation form of the communication apparatus according to the first aspect, the channel decoder of the precoder is configured to generate the pre-coded message on the basis of the auxiliary channel decoder input sequence y and the channel decoder a priori information sequence.

In a further possible implementation form of the communication apparatus according to the first aspect, the channel decoder of the precoder is a channel decoder using log-likelihood ratios. In a further possible implementation form of the communication apparatus according to the first aspect, the target probability distribution is non-uniform. This provides the advantage that the plurality of bits and/or symbols of the code word can have the desired probability distribution.

In a further possible implementation form of the communication apparatus according to the first aspect, the channel code is a polar code, a binary LDPC code, a non-binary LDPC code or a convolutional code. According to a second aspect, the invention relates to a method for encoding a message to be transmitted over a communication channel. The method comprises the steps of:

generating on the basis of the message and a channel code a pre-coded message, and encoding the pre-coded message based on the channel code into a code word, wherein the code word comprises a plurality of bits and/or symbols which have a probability distribution, wherein the pre-coded message is generated in such a way that the plurality of bits and/or symbols are generated with the probability distribution matching a target probability distribution.

According to a third aspect, the invention relates to a computer program comprising program code for performing the method of the second aspect, when executed on a computer or a processor.

According to a fourth aspect, the invention relates to a communication apparatus for decoding a message received over a communication channel, wherein the communication apparatus comprises: a channel decoder configured to generate a vector [it's'], wherein the estimate vector it' comprises an estimate of a vector of information bits it and the estimate vector s' comprises an estimate of a vector of shaping bits s, and wherein the communication apparatus is configured to discard the estimate vector s'. In a possible implementation form of the communication apparatus according to the fourth aspect, the communication apparatus is further configured to generate a sequence s" on the basis of the estimate vector it' and to output an error message, in case the sequence s" is not equal to the estimate vector s'. In a further possible implementation form of the communication apparatus according to the fourth aspect, the channel decoder comprises a list decoder configured to select a respective code word from a list of code words by selecting the code word, for which the sequence s" is equal to the estimate vector s'.

The invention can be implemented in hardware and/or software.

BRI EF DESCRIPTION OF THE DRAWINGS

Further embodiments of the invention will be described with respect to the following figures, wherein:

Fig. 1 shows a schematic diagram illustrating a communication system comprising a communication apparatus for encoding a message according to an embodiment, and a communication apparatus for decoding the message according to an embodiment; Fig. 2 shows a schematic diagram illustrating a communication system comprising a communication apparatus for encoding a message according to an embodiment and a communication apparatus for decoding the message according to an embodiment;

Fig. 3 shows a schematic diagram of a channel encoder and channel decoder implemented in a communication apparatus according to an embodiment;

Fig. 4 shows a schematic diagram of a precoder implemented in a communication apparatus according to an embodiment; and Fig. 5 shows a schematic diagram of a method for encoding a message to be transmitted over a communication channel according to an embodiment.

In the various figures, identical reference signs will be used for identical or at least functionally equivalent features.

DETAI LED DESCRI PTION OF EMBODIMENTS

In the following description, reference is made to the accompanying drawings, which form part of the disclosure, and in which are shown, by way of illustration, specific aspects in which the present invention may be placed. It is understood that other aspects may be utilized and structural or logical changes may be made without departing from the scope of the present invention. The following detailed description, therefore, is not to be taken in a limiting sense, as the scope of the present invention is defined by the appended claims.

For instance, it is understood that a disclosure in connection with a described method may also hold true for a corresponding device or system configured to perform the method and vice versa. For example, if a specific method step is described, a corresponding device may include a unit to perform the described method step, even if such unit is not explicitly described or illustrated in the figures. Further, it is understood that the features of the various exemplary aspects described herein may be combined with each other, unless specifically noted otherwise.

Fig. 1 shows a schematic diagram illustrating a communication system 100 comprising a communication apparatus 110 for encoding a message u according to an embodiment, and a communication apparatus 120 for decoding the message according to an embodiment.

The communication apparatus 1 10 comprises a precoder 102 configured to generate on the basis of the message u and a channel code a pre-coded message u _s , and a channel encoder 104 configured to encode the pre-coded message u _s based on the channel code into a code word u _c , wherein the code word u _c comprises a plurality of bits and/or symbols which have a probability distribution P, wherein the precoder 102 is configured to generate the pre-coded message u _s such that the channel encoder 104 generates the plurality of bits and/or symbols with the probability distribution P matching a target probability distribution P _t .

This provides the advantage of reducing the shaping loss for high order modulation encoding schemes, since the plurality of bits and/or symbols of the code word u _c can have a an appropriate probability density distribution allowing to reduce the shaping loss. Therefore, the transmission performance of the communication apparatus 110 is improved.

The communication apparatus 1 10 can send the code word u _c to the communication apparatus 120 over a communication channel.

The communication apparatus 120 for decoding the message received over the

communication channel, comprises: a channel decoder 120a configured to generate a vector [uV], wherein the estimate vector u' comprises an estimate of a vector of information bits u and the estimate vector s' comprises an estimate of a vector of shaping bits s, and wherein the communication apparatus 120 is configured to discard the estimate vector s'. Furthermore, the communication apparatus 120 is configured to generate a sequence s" on the basis of the estimate vector u' and to output an error message, in case the sequence s" is not equal to the estimate vector s'. Figure 2 shows a schematic diagram of a communication system 100 comprising the communication apparatus 1 10 according to an embodiment and the communication apparatus 120 according to an embodiment.

In the embodiment shown in figure 2, the communication system 100 comprises the communication apparatus 1 10 and the communication apparatus 120 or receiver, wherein the communication apparatus 120 can be configured to receive the encoded message, namely the code word u _c , via the communication channel.

In this embodiment, the communication apparatus 1 10 comprises the precoder 102, in particular a systematic precoder, the channel encoder 104, and a symbol mapper 202, in particular a QAM mapper.

The channel encoder 104 can be seen as a one-to-one mapper, namely for each input, a unique output is generated. For example, if the message or message vector u is encoded with the channel encoder 104, then a code word u _c can be obtained. However, the precoder 102 can be configured to extend the message vector u by concatenating the message vector u with a vector of shaping bits s, e.g., 10 bits. Moreover, the channel encoder 104 can be configured to encode the resulting pre-coded message u _s — [u s], such that a different code word u _c for each different choice of the vector of shaping bits can be obtained. The s symbols of the vector of shaping bits 5 can be selected depending on the target probability distribution P _t and the values of the message vector u.

In the above mentioned example, the vector of shaping bits s has 10 bits, therefore 2 ¹⁰ different code words u _c can be generated by the channel encoder 104 depending on the choice of the vector of shaping bits s. The set of 2 ¹⁰ code words in this example can be seen as a subset of code words in a code book. All the code words in the subset represent the message vector , but only one of them, namely the code word u _c is transmitted. The selection from the subset can be done according to the target probability distribution P _t at the output of the channel encoder 104. In an embodiment, the vector of shaping bits s is chosen depending on the message vector , such that the resulting code word u _c has the desired characteristics in terms of the probability distribution P. The s symbols forming the vector of shaping bits s can also be called shaping bits or shaping symbols.

As already mentioned above, the precoder 102 can be a systematic precoder, as the input of the precoder 102, namely the message to be transmitted u, is included in the output of the precoder 102, namely in the pre-coded message u _s = [u s]. Moreover, the precoder 102 can be configured to a generate channel decoder a priori information sequence based on the message vector u.

The symbol mapper 202 can be configured to map the code word u _c to one or more symbols for transmission over the communication channel. In an embodiment, the communication apparatus 1 10 comprises further an interleaver (not shown in figure 2) configured to interleave the plurality of bits and/or symbols of the code word u _c .

Differently from the conventional PAS systems, the channel encoder 104 may not be a systematic channel encoder, making the channel encoder 104 according to the present invention more suitable for many applications, wherein a non-systematic channel encoder may be required.

In the embodiment shown in figure 2, the communication apparatus 120, which receives the noisy symbols representing the code word u _c , comprises a demapper 206, in particular a QAM demapper, the channel decoder 120a, and an error detection unit 210. The demapper 206 can be configured to take the a priori probabilities of the transmitted symbols of the message vector u into account. At the receiver or communication apparatus 120, the channel decoder 120a can be configured to decode the received signal comprising the message vector , and estimate the message vector u. Moreover, the channel decoder 120a can be configured to output a vector [u' s'], wherein the estimate vector u' represents an estimate of the transmitted message vector u. The channel decoder 120a can be configured to discard the estimate vector s' in order to obtain the transmitted message vector u. Thus, another advantage of embodiments of the invention is to provide a receiver, which can decode the encoded code word in a simple and efficient way, namely by using a one-step decoder, and not a two-step decoder like in conventional PAS approaches, in which an additional shaping decoder is required, which aims to extract the message.

Moreover, since the precoding operation can be systematic, the output of the channel decoder 120a [ιι' s'] already contains an estimate vector u' of the message vector u, and, therefore, the estimate vector s' can easily be discarded. Moreover, the communication apparatus 120 can comprise an error detection unit 210. In an embodiment, after the channel decoder 120a obtains an estimate for the pre-coded message u _s — [u s], the error detection unit 210 can be configured in order to check, if the estimated vector of shaping bits s' is the same as the received one.

This additional error detection is similar to a cyclic redundancy check (CRC) check. In particular, the channel decoder 120a can use the estimate vector ' to produce a sequence s" by using the precoder 102, and, if the sequence s" is not equal to the estimate vector s', the channel decoder 120a can declare an error.

Figure 3 shows a schematic diagram of a channel encoder 104 and a channel decoder 120a.

In this embodiment, the channel encoder 104 can be configured to take the message sequence input d (corresponding to the pre-coded vector u _s = [u s] of figure 2) and generate the code word u _c . In an embodiment, the channel decoder 120a takes as input the noisy observation input sequence y, namely the code word u _c affected by noise due to the transmission over the communication channel, and estimates the transmitted message sequence input d.

In another embodiment, the channel decoder 120a can also take as input the a priori probabilities of the bits p _d (or the channel decoder a priori information sequence) of the transmitted message sequence input d, i.e., the probabilities of the transmitted bits to be zero or one.

In an embodiment, the channel decoder 120a uses log-likelihood ratios (LLR). In an embodiment, the channel coding schemes, such as LDPC, turbo, polar, or

convolutional codes can be realized by a LLR-based channel decoder.

Figure 4 shows a schematic diagram of the precoder 102 according to an embodiment.

As explained in the context of figure 2, in an embodiment, the precoder 102, which in this embodiment comprises a first processing unit 400 and a second processing unit 402, is configured to find the pre-coded message u _s = [u s] in such a way that, after channel encoding of the pre-coded message u _s , the resulting code word u _c has a probability distribution P which matches the target probability distribution P _t . To this aim, a channel decoder 102a (similar or identical to the channel decoder 120a of the communication apparatus 120) with modified inputs as shown in figure 4 can be used, as will be described in more detail in the following. In an embodiment, the first processing unit 400 is configured to generate the noisy observation sequence or the auxiliary channel decoder input sequence y according to the target probability distribution P _t . For example, if the channel decoder 102a of the precoder 102 accepts LLR-based inputs, and the target probability distribution is 0.1 (the probability of zeros in the code word is 0.1 ), then, the first processing unit 400 can be configured to generate an input containing the value log(0.1/(l - 0.1)) at each position.

In an embodiment, if the channel decoder 102a of the precoder 102 accepts LLR-based inputs, then, the second processing unit 402 can be configured to generate a sequence p _{u s} , where at the positions corresponding to the transmitted message vector u the values +infinity/-infinity can be used (depending on whether the elements of the transmitted message vector u are zero or one), and at the positions corresponding to the shaping bits s the value 0 can be used.

This provides the advantage that the channel decoder 102a of the precoder 102 can be configured to generate the pre-coded message u _s = [u, s] in such a way that the probability distribution of the bits and/or symbols P of the generated code word u _c matches the desired target probability distribution P _t .

Figure 5 shows a schematic diagram of a corresponding method 500 for encoding a message to be transmitted over a communication channel according to an embodiment. The method 500 comprises the steps of: generating 502 on the basis of the message and a channel code a pre-coded message, and encoding 504 the pre-coded message based on the channel code into a code word, wherein the code word comprises a plurality of bits and/or symbols which have a probability distribution, wherein the pre-coded message is generated in such a way that the plurality of bits and/or symbols are generated with the probability distribution matching a target probability distribution.

While a particular feature or aspect of the disclosure may have been disclosed with respect to only one of several implementations or embodiments, such feature or aspect may be combined with one or more other features or aspects of the other implementations or embodiments as may be desired and advantageous for any given or particular application. Furthermore, to the extent that the terms "include", "have", "with", or other variants thereof are used in either the detailed description or the claims, such terms are intended to be inclusive in a manner similar to the term "comprise". Also, the terms "exemplary", "for example" and "e.g." are merely meant as an example, rather than the best or optimal. The terms "coupled" and "connected", along with derivatives may have been used. It should be understood that these terms may have been used to indicate that two elements cooperate or interact with each other regardless whether they are in direct physical or electrical contact, or they are not in direct contact with each other.

Although specific aspects have been illustrated and described herein, it will be appreciated by those of ordinary skill in the art that a variety of alternate and/or equivalent

implementations may be substituted for the specific aspects shown and described without departing from the scope of the present disclosure. This application is intended to cover any adaptations or variations of the specific aspects discussed herein.

Although the elements in the following claims are recited in a particular sequence with corresponding labeling, unless the claim recitations otherwise imply a particular sequence for implementing some or all of those elements, those elements are not necessarily intended to be limited to being implemented in that particular sequence.

Many alternatives, modifications, and variations will be apparent to those skilled in the art in light of the above teachings. Of course, those skilled in the art readily recognize that there are numerous applications of the invention beyond those described herein. While the present invention has been described with reference to one or more particular embodiments, those skilled in the art recognize that many changes may be made thereto without departing from the scope of the present invention. It is therefore to be understood that within the scope of the appended claims and their equivalents, the invention may be practiced otherwise than as specifically described herein.