WO2019197037A1

WO2019197037A1 - Multi-level encoder and decoder with shaping and methods for multi-level encoding and decoding with shaping

Info

Publication number: WO2019197037A1
Application number: PCT/EP2018/059538
Authority: WO
Inventors: Onurcan ISCAN; Ronald BOEHNKE; Wen Xu
Original assignee: Huawei Technologies Duesseldorf GmbH
Current assignee: Huawei Technologies Duesseldorf GmbH
Priority date: 2018-04-13
Filing date: 2018-04-13
Publication date: 2019-10-17
Anticipated expiration: 2020-10-13
Also published as: CN111954990B; CN111954990A

Abstract

An encoder is proposed for encoding a message into channel input symbols. The encoder is configured to divide the message for obtaining message parts, encode the message parts into encoded parts such that at least one encoded part has a non-uniform distribution, map the encoded parts into the channel input symbols. A channel input symbol is based on a plurality of encoded parts.

Description

TITLE

MULTI-LEVEL ENCODER AND DECODER WITH SHAPING AND METHODS FOR MULTI-LEVEL ENCODING AND DECODING WITH SHAPING

TECHNICAL FIELD

The present invention generally relates to the field of communication network technology.

Particularly, the present invention relates to an encoder for encoding a message into channel input symbols, and to a corresponding encoding method. Furthermore, the present invention relates to a decoder for decoding channel symbols into a message, and to a corresponding decoding method. Furthermore the present invention relates to a corresponding computer program.

BACKGROUND

A transmission channel or communications channel of e.g. a telecommunications network can be characterized by its channel capacity, which e.g. reflects the highest information rate that can be achieved on the transmission channel, and which particularly reflects the highest information rate that can be achieved at an arbitrarily small error probability.

In order to reach the capacity of a transmission channel, the channel input symbols need to have a certain probability distribution. For example, a Gaussian distribution is required to reach the capacity of an Additive white Gaussian noise (AWGN) channel. However, in most known systems, the distribution of the channel input symbols is not optimized because uniformly distributed channel input symbols are used. This uniform distribution is disadvantageous because the capacity cannot be reached in general, and because there is a gap to the capacity. The loss with regard to the capacity is called the shaping loss and can be up to 1.53dB on AWGN channels for uniformly distributed channel input symbols. The shaping loss can become significant especially with higher order modulation. There are two known approaches for reducing the shaping loss for high order modulation. A first approach, referred to as probabilistic shaping (PS), is illustrated by the encoder 100 of Fig. 1. The input of the encoder 100 is a message 101 to be transmitted over a transmission channel. The message, which comprises uniformly distributed bits, is transformed by a shaping encoder 102 into a shaped message 103 with a non-uniform distribution. A channel encoder 104 then encodes the shaped message 103 so as to output non-uniformly distributed bits in the form of binary codewords 105. A codeword 105 is divided by a demultiplexer 106 into codeword parts 107a, 107b, 107c. The codeword parts 107a, 107b, 107c are mapped to channel input symbols 109 by means of a symbol mapper 108, which can be a conventional symbol mapper like a regular Quadrature Amplitude Modulation (QAM) or Amplitude-Shift Keying (ASK) symbol mapper, where each codeword part may correspond to a different bit-level of the QAM or ASK symbols. The shaping encoder 102 causes differing probabilities per constellation point, so that by adjusting the probability distribution, the channel input symbols 109 can have a capacity approaching distribution. This in turn results in a shaping gain at the receiver.

A second known approach is referred to as non-uniform constellations (NUC) or geometrical shaping, see Loghin, Nabil Svenh, et al. "Non-uniform constellations for ATSC 3.0.", IEEE Transactions on Broadcasting 62.1 (2016), pages 197-203. An encoder according to this approach comprises a symbol mapper with non-uniform constellations. Such a symbol mapper maps binary codewords to channel input symbols that do not have a regular structure like QAM symbols. Rather, the channel input symbols have an optimized structure that helps to reduce the shaping loss. The probability distribution of the channel input symbols is uniform, but the distance between the constellation points is optimized, i.e. the constellation points are non-uniformly spaced.

In general, the PS scheme implemented in the encoder 100 of Fig. 1 performs better than the NUC approach. The reason is that on AWGN channels, PS can remove the shaping loss, and can also compensate for the demapping loss incurred due to single stage demapping. However, while the PS of the encoder 100 works almost optimally on AWGN channels, it is not capacity approaching when fading channels are considered. SUMMARY

Having recognized the above-mentioned disadvantages and problems, the present invention aims to improve the state of the art. In particular, an object of the present invention is to address the above-mentioned issues and to provide an improved encoding scheme. It is particularly an object of the present invention to reduce the shaping loss, particularly on fading channels.

The above-mentioned object is achieved by the features of the independent claims. Further embodiments of the invention are apparent from the dependent claims, the description and the figures.

According to a first aspect, the invention relates to an encoder for encoding a message into channel input symbols. The encoder is configured to divide the message for obtaining message parts. The encoder is configured to encode the message parts into encoded parts such that at least one encoded part has a non-uniform distribution. The encoder is configured to map the encoded parts into the channel input symbols. A channel input symbol is based on a plurality of encoded parts.

The encoding also comprises a direct mapping such that the message part equals the encoded part.

Thereby, an encoded part obtained by encoding a message part has a non-uniform distribution of bits, wherein this encoded part is referred to as non-uniform encoded part. The non-uniform distribution of bits means that the probability of 0 and 1 in the encoded part is not equal. The non-uniformity of the bit distribution of this non-uniform encoded part advantageously allows for the channel input symbols to present a non-uniform distribution. When transmitting the channel input symbols over the transmission channel, shaping gain can then be achieved. Particularly, the channel capacity can be approached. Particularly, one or more of the message parts can be encoded into non-uniform encoded parts having a non-uniform distribution of bits. In other words, one or more of the encoded parts can have a non-uniform distribution of bits.

According to a further implementation of the first aspect, the non-uniform encoded part is obtained by means of a constituent encoder comprising a non-linear encoder.

Thereby, the non-linear encoder can advantageously generate a non-uniformity in the bit distribution of the non-uniform encoded part. Accordingly, the channel capacity can be approached.

A constituent encoder describes generally an encoder that is a part of a larger encoder. The constituent encoder, which comprises the shaping encoder for obtaining the non-uniform encoded part, is a part of the larger encoder that is configured to encode the message parts into encoded parts.

A non-linear encoder generally describes an encoder that maps an input sequence to an output sequence, where the mapping is one-to-one (for each input sequence there is a unique and different output sequence) and the relation between input and output sequence is not linear.

A shaping encoder generally describes an encoder that maps an input sequence to a (possibly longer) output sequence, where the elements of the output sequence has a target probability distribution.

According to a further implementation of the first aspect, the non-linear encoder is a shaping encoder.

Thereby, the shaping encoder generates a sequence so that it is possible to advantageously generate a non-uniformity in the bit distribution of the non-uniform encoded part. According to a further implementation of the first aspect, the constituent encoder comprises the non-linear encoder and, in particular in series with, a channel encoder.

Thereby, it is possible to add redundant bits to the bits generated by the non-linear encoder, so that a decoder or receiver can advantageously correct errors due to e.g. channel noise.

Particularly, the channel encoder can be configured so that it does not modify the non- uniform bit distribution obtained by the non-linear encoder. Alternatively, the channel encoder can be configured so that it only slightly modifies the non-uniform bit distribution obtained by the non-linear encoder. An example of a channel encoder carrying out no change or only a slight change in the bit distribution is a systematic encoder. Advantageously, since the impact of the channel encoder on the bit distribution of the non- uniform encoded part is null or very limited, it is only necessary to configure the non-linear encoder so as to achieve a desired non-uniform bit distribution of the non-uniform encoded part.

According to a further implementation of the first aspect, the constituent encoder comprises the non-linear encoder without a channel encoder.

Thereby, the non-uniformity bit distribution of the non-uniform encoded part can advantageously be obtained without using extra redundancy for error correction.

According to a further implementation of the first aspect, the non-linear encoder is a polar precoder. The constituent encoder comprises the polar precoder in series with a polar encoder.

A polar precoder generally describes an invertible operation that takes place prior to a polar encoding operation. The polar precoder takes as input a precoder input sequence and generates a precoder output sequence, wherein the input of the polar encoding operation is based on the precoder output sequence. A polar precoder can for example be a systematic precoder, where the precoder output sequence contains the precoder input sequence, and additional bits that are based on the precoder input sequence. The relation between the precoder input sequence and the precoder output sequence in general can be linear or non-linear (in this invention, the considered polar precoder is non-linear).

Thereby, the shaping gain can advantageously be further improved by using a polar precoder, i.e. by using polar codes. The non-uniform encoded part can have a desired or target probability distribution of bits so as to advantageously achieve shaping gain.

According to a further implementation of the first aspect, the polar precoder comprises a polar decoder.

Thereby, the shaping gain can be advantageously implemented. The polar decoder can be e.g. a successive cancellation decoder or a successive cancellation list decoder.

According to a further implementation of the first aspect, the encoder is configured to encode one message part into the non-uniform encoded part having a non-uniform distribution. The encoder is configured to encode the remaining message parts into uniform encoded part, in particular having a uniform distribution.

Thereby, it is only necessary to have a non-uniform bit distribution for a single message part in order to obtain a shaping gain. The encoder can then be advantageously simplified.

A uniform distribution in the sense of this invention also comprises distributions which are close to uniform distributions. In particular because exact uniform distributions are difficult to measure.

According to a further implementation of the first aspect, the encoded parts mapped into the channel input symbols correspond to bit-levels of the channel input symbols. A non- uniform encoded part corresponds to the bit-level that determines whether the channel input symbols have a low magnitude or a high magnitude. Thereby, it can be advantageously ensured that the channel input symbols have a non- uniform distribution of bits. Particularly, each encoded part can correspond to a different bit-level of the channel input symbols.

According to a further implementation of the first aspect, the non-uniform distribution of a non-uniform encoded part is configured so as to obtain a desired non-uniform probability distribution of the channel input symbols.

Thereby, the channel capacity can be approached.

According to a further implementation of the first aspect, the non-uniform distribution of a non-uniform encoded part is configured so that channel input symbols with a low magnitude have an equal or higher probability than channel input symbols with a high magnitude.

Thereby, a non-uniform distribution of the channel input symbol can be achieved. Accordingly, shaping gain can be advantageously obtained.

According to a further implementation of the first aspect, the encoded parts mapped into the channel input symbols correspond to bit-levels of the channel input symbols. A non- uniform encoded part corresponds to the bit-level that causes a symmetric distribution of the channel input symbols.

According to a second aspect, the invention relates to a method for encoding a message into channel input symbols. The method comprises dividing the message for obtaining message parts. The method comprises encoding the message parts into encoded parts such that at least one encoded part has a non-uniform distribution. The method comprises mapping the encoded parts into the channel input symbols. A channel input symbol is based on a plurality of encoded parts.

Thereby, the channel capacity can be approached.

According to a further implementation of the second aspect, the non-uniform encoded part is obtained by means of a constituent encoder comprising a non-linear encoder.

According to a further implementation of the second aspect, the non-linear encoder is a shaping encoder.

Thereby, the shaping encoder has a non-uniform probability distribution so that it is possible to advantageously generate a non-uniformity in the bit distribution of the non- uniform encoded part.

According to a further implementation of the second aspect, the constituent encoder comprises the non-linear encoder and, in particular in series with, a channel encoder.

According to a further implementation of the second aspect, the constituent encoder comprises the non-linear encoder without a channel encoder.

Thereby, the non-uniformity bit distribution of the non-uniform encoded part can advantageously be obtained without using extra redundancy for error correction. According to a further implementation of the second aspect, the non-linear encoder is a polar precoder. The constituent encoder comprises the polar precoder in series with a polar encoder.

According to a further implementation of the second aspect, the polar precoder comprises a polar decoder.

According to a further implementation of the second aspect, the method comprises encoding one message part into the non-uniform encoded part having a non-uniform distribution. The method comprises encoding the remaining message parts into uniform encoded part, in particular having a uniform distribution.

Thereby, it is only necessary to have a non-uniform bit distribution for a single message part in order to obtain a shaping gain. The encoding method can then be advantageously simplified.

According to a further implementation of the second aspect, the encoded parts mapped into the channel input symbols correspond to bit-levels of the channel input symbols. A non-uniform encoded part corresponds to the bit-level that determines whether the channel input symbols have a low magnitude or a high magnitude.

Thereby, it can be advantageously ensured that the channel input symbols have a non- uniform distribution of bits. Particularly, each encoded part can correspond to a different bit-level of the channel input symbols. According to a further implementation of the second aspect, the non-uniform distribution of a non-uniform encoded part is configured so as to obtain a desired non-uniform probability distribution of the channel input symbols.

Thereby, the channel capacity can be approached.

According to a further implementation of the second aspect, the non-uniform distribution of a non-uniform encoded part is configured so that channel input symbols with a low magnitude have an equal or higher probability than channel input symbols with a high magnitude.

According to a further implementation of the second aspect, the encoded parts mapped into the channel input symbols correspond to bit-levels of the channel input symbols. A non-uniform encoded part corresponds to the bit-level that causes a symmetric distribution of the channel input symbols.

According to a third aspect, the invention relates to a decoder for decoding channel symbols into a message. The decoder is configured to demap the channel symbols into decoder input sequences according to information about a distribution of the channel symbols. The decoder is configured to decode the decoder input sequences into message parts, wherein the decoding is based on a constituent encoder comprising a non-linear encoder. The decoder is configured to concatenate the message parts to the message.

Thereby, a shaping gain can be achieved at the decoder. According to a further implementation of the third aspect, the decoder is configured to perform the demapping step and/or the decoding step in two or more iterations. The result of an earlier iteration is used as an input for one or more succeeding iterations.

Thereby, the decoding can be improved and the shaping gain can be achieved at the decoder.

According to a further implementation of the third aspect, the non-linear encoder is a shaping encoder.

Thereby, the shaping encoder has a non-uniform probability distribution so that it is possible to advantageously obtain a shaping gain.

According to a further implementation of the third aspect, the constituent encoder comprises the non-linear encoder and, in particular in series with, a channel encoder.

Thereby, it is possible to take account of redundant bits with respect to the bits generated by the non-linear encoder, so that the decoder can advantageously correct errors due to e.g. channel noise.

According to a further implementation of the third aspect, the constituent encoder comprises the non-linear encoder without a channel encoder.

Thereby, the shaping gain can be obtained without using extra redundancy for error correction.

According to a further implementation of the third aspect, the non-linear encoder is a polar precoder. The constituent encoder comprises the polar precoder in series with a polar encoder. Thereby, the shaping gain can advantageously be further improved by using a polar precoder, i.e. by using polar codes.

According to a further implementation of the third aspect, the polar precoder comprises a polar decoder.

According to a fourth aspect, the invention relates to a method for decoding channel symbols into a message. The method comprises demapping the channel symbols into decoder input sequences according to information about a distribution of the channel symbols. The method comprises decoding the decoder input sequences into message parts, wherein the decoding is based on a constituent encoder comprising a non-linear encoder. The method comprises concatenating the message parts into the message.

Thereby, a shaping gain can be achieved when applying the decoding method.

According to a further implementation of the fourth aspect, the method performs the demapping step and/or the decoding step in two or more iterations. The result of an earlier iteration is used as an input for one or more succeeding iterations.

Thereby, the decoding can be improved and the shaping gain can be achieved when applying the decoding method.

According to a further implementation of the fourth aspect, the non-linear encoder is a shaping encoder.

Thereby, the shaping encoder has a non-uniform probability distribution so that it is possible to advantageously obtain a shaping gain. According to a further implementation of the fourth aspect, the constituent encoder comprises the non-linear encoder and, in particular in series with, a channel encoder.

Thereby, it is possible to take account of redundant bits with respect to the bits generated by the non-linear encoder, so that the decoding method can advantageously correct errors due to e.g. channel noise.

According to a further implementation of the fourth aspect, the constituent encoder comprises the non-linear encoder without a channel encoder.

According to a further implementation of the fourth aspect, the non-linear encoder is a polar precoder. The constituent encoder comprises the polar precoder in series with a polar encoder.

Thereby, the shaping gain can advantageously be further improved by using a polar precoder, i.e. by using polar codes.

According to a further implementation of the fourth aspect, the polar precoder comprises a polar decoder.

According to a fifth aspect, the invention relates to a computer program having a program code for performing the method according to the second or fourth aspect, when the computer program runs on a computing device. Thereby, the method can be performed in an automatic and repeatable manner. Advantageously, the computer program can be respectively performed by the encoder according to the first aspect or by the decoder according to the third aspect.

More specifically, it should be noted that the above apparatuses may be implemented based on a discrete hardware circuitry with discrete hardware components, integrated chips or arrangements of chip modules, or based on a signal processing device or chip controlled by a software routine or program stored in a memory, written on a computer- readable medium or downloaded from a network such as the internet.

It shall further be understood that a preferred embodiment of the invention can also be any combination of the dependent claims or above embodiments with the respective independent claim.

These and other aspects of the invention will be apparent and elucidated with reference to the embodiments described hereinafter.

BRIEF DESCRIPTION OF THE DRAWINGS

The above aspects and implementation forms of the present invention will be explained in the following description of specific embodiments in relation to the enclosed drawings, in which

Fig. 1 shows a known encoder using probabilistic shaping (PS),

Fig. 2 shows an encoder according to an embodiment of the present invention,

Fig. 3 shows a shifted natural binary labeling according to a further embodiment of the present invention,

Fig. 4 shows an encoder according to a further embodiment of the present invention, Fig. 5 shows a constituent encoder according to a further embodiment of the present invention, and

Fig. 6 shows a decoder according to a further embodiment of the present invention.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

Fig. 2 shows an encoder 200 according to an embodiment of the present invention for encoding a message 201 into channel input symbols 207.

The encoder 200 is configured to divide the message 201 for obtaining message parts 203a, 203b, 203c. The encoder is configured to encode the message parts 203a, 203b, 203c into encoded parts 205a, 205b, 205c, such that at least one encoded part 205c has a non- uniform distribution, i.e. such that at least one encoded part 205c has a non-uniform probability distribution. The encoder is configured to map the encoded parts 205a, 205b, 205c into the channel input symbols 207. A channel input symbol 207 is based on a plurality of encoded parts 205a, 205b, 205c.

The message 201 is typically formed of a plurality of bits or other symbols. The channel input symbols 207 obtained from the message 201 are to be transmitted over a transmission channel.

Those bits or symbols forming the message 201 are usually taken from an alphabet that defines the available bits or symbols. For example, a binary alphabet is the set {0, 1}. The "distribution" or "probability distribution" of a bit sequence defines the relative proportions of the different alphabet members that the sequence contains. So, for example, the probability distribution of a binary sequence refers to its relative proportions of 'l's and O's. The distribution of the message 201 and of the message parts 203a, 203b, 203c may be uniform, i.e. the relative proportions of the alphabet members in the message 201 and in the message parts 203a, 203b, 203c may be the same. The encoded parts 205a, 205b, 205c are encoded such that at least one encoded part 205c has a non-uniform distribution. In other words at least one encoded part 205c presents a probability of 'l's and '0's that is not uniform. This advantageously allows for the channel input symbols 207 to present a non-uniform distribution. When transmitting the channel input symbols over the transmission channel, shaping gain can then be achieved and the channel capacity can be approached.

The encoder 200 may comprise a splitter 202 that is configured to receive the message 201 and divide it into the plurality of separate message parts 203a, 203b, 203c. The splitter may be a switch but could also be implemented by any suitable means for separating the message 201, including e.g. a demultiplexor as shown in Fig. 2.

The encoder 200 may comprise constituent encoders 204a, 204b, 204c. Each of the constituent encoders 204a, 204b, 204c is configured to receive one of the separate message parts 203a, 203b, 203c and encode it to generate one of the encoded parts 205a, 205b, 205c. The message 201 is divided into m message parts 203a, 203b, 203c, wherein each of them is encoded with a different constituent encoder 204a, 204b, 204c. The term constituent encoders refers to multiple smaller encoders in a larger encoder and applies to Fig. 2 since the constituent encoders 204a, 204b, 204c are part of the encoder 200.

The message parts 203a, 203b, 203c may all have the same length. Similarly, the encoded parts 205a, 205b, 205c may all have the same length. Moreover, the length of a message part may be the same as the length of the corresponding encoded part.

The encoder 200 is based on a multi-level coding (MLC). Accordingly, each channel input symbol 207 may be based on all the encoded parts 205a, 205b, 205c. In other words, each channel input symbol 207 contains bits from each encoded part 205a, 205b, 205c.

Furthermore, the encoder 200 is based on a multi-level coding (MLC) with m bit-levels, wherein m>l. In Fig. 2, the 1^st bit-level may refer to the constituent encoder 204a that generates the encoded part 205a of 1^st bit-level. Similarly, the 2^nd bit-level may refer to the constituent encoder 204b that generates the encoded part 205b of 2^nd bit-level, etc., and the m^th bit-level may refer to the constituent encoder 204c that generates the encoded part 205c of m^th bit-level. A bit-level with a constituent encoder configured to generate a non-uniform encoded part is referred to as a shaped bit-level.

The encoder 200 may comprise a symbol mapper 206 for mapping the encoded parts 205a, 205b, 205c into the channel input symbols 207. The symbol mapper 206 may map the encoded parts according to a constellation having m bit-level. Particularly, the symbol mapper 206 may map bits from the encoded part of i^th bit-level to the i^th bit-level of the constellation for i=l,..,m. Each encoded part 205a, 205b, 205c may correspond to a different bit-level of the channel input symbols 207.

Particularly, the non-uniform encoded part 205c may be obtained by means of a constituent encoder 204c comprising a non-linear encoder 211. Accordingly, the channel capacity can be approached. Particularly, the non-linear encoder 211 may be a shaping encoder. A shaping encoder aims to produce a sequence of bits or symbols with a desired probability distribution given a sequence of symbols as an input. The input symbols often have a uniform probability distribution.

According to the embodiment of Fig. 2, the constituent encoder 204c generating the encoded part 205c having a non-uniform distribution comprises a serial concatenation of the non-linear encoder 211 and a channel encoder 212. Alternatively, the non-uniform encoded part may be obtained by a constituent encoder comprising a serial concatenation of a precoder - e.g. a shaping encoder or another linear or non-linear processing block - and a channel encoder.

The encoder 200 may comprise one or more constituent encoders 204a, 204b that are configured to generate encoded parts 205a, 205b with a uniform probability distribution. Such constituent encoders 204a, 204b may comprise a channel encoder such as turbo encoder, polar encoder, low-density parity-check (LDPC) encoder, convolutional encoder, etc. Advantageously, at least one of the constituent encoders 204a, 204b, 204c produces an encoded part with a non-uniform distribution of bits, which may be obtained with the help of precoders or shaping encoders. The channel input symbols 207 after the symbol mapper 206 have a non-uniform distribution that results in a shaping gain.

Depending on the required output distribution, the number of constituent encoders generating an encoded part with non-uniform distribution can change:

- For example, if no shaping is necessary, all the constituent encoders may be configured to generate an encoded part with uniform distribution.

- If a symmetric distribution of the channel input symbols 207 is desired, at least one of the constituent encoders may be configured to generate an encoded part with uniform distribution. This guarantees symmetry of the distribution. The remaining constituent encoders of the encoder may be configured to generate encoded parts with non-uniform distribution. Examples of such symmetric distributions of the channel input symbols 207 include discrete Gaussian distribution or Maxwell-Boltzmann distribution.

- For many cases, using only a single constituent encoder with non-uniform output distribution is enough to have a shaping gain. The constituent encoder with non-uniform output may be used for a single bit-level. Such an embodiment wherein only a single bit- level is shaped is referred to as Single Bit-Level Shaping.

Fig. 3 shows a shifted natural binary labeling 500 according to a further embodiment of the present invention.

In this embodiment, only a single bit-level (j^th bit-level) is shaped, i.e. the probability of 'l's and O's for this bit-level is not uniform. In this embodiment, the symbol mapper 206 maps the encoded parts 205a, 205b to transmit channel input symbols 207 according to a bit labeling. The j^th bit-level may decide whether the channel input symbols 207 are chosen from a set of high energy or low energy symbols. The embodiment of Fig. 3 shows the bit-levels bl, b2, b3, b4 of the channel input symbols 207. The non-uniform encoded part 205c corresponds to the bit-level b4 that determines whether the channel input symbols 207 have a low magnitude or a high magnitude.

In the embodiment of Fig. 3, m=4 and j=4, and the bit-labeling is a shifted natural binary labeling. Particularly, the 4^th bit-level 'l's correspond to symbols with low energy (i.e. channel input symbols have low absolute values), and '0's correspond to symbols with high energy (i.e., channel input symbols have high absolute values). Accordingly, if the bits in the 4^th bit-level have a higher probability of being a 1, the resulting distribution of the channel input symbols are non-uniform.

The shifted natural binary labeling is a shifted version of the natural binary labeling that corresponds to 000, 001, 010, Oil, 100, ..., Ill for three bit-levels. In Fig. 3, the channel input symbols are denoted by -15, -13, -11, -9 ..., 9, 11, 13, 15, but a scaled version (multiplied with a scalar constant) of these symbols can also be considered. It can be observed that bits defining neighboring channel input symbols correspond to binary representation of subsequent integers in rnod(2^m).

Fig. 4 shows an encoder 400 according to a further embodiment of the present invention.

Similarly to the encoder 200 of Fig. 2, the encoder 400 comprises a splitter 402 like a demultiplexor for receiving a message 401 and dividing it into separate message parts 403, 412. The encoder 400 comprises a constituent encoder 413 that, similarly to the constituent encoder 204c of Fig. 2, generates from a message part 412 an encoded part 414 having non-uniform distribution.

The embodiment of Fig. 4 proposes to replace the constituent encodes 204a, 204b of Fig. 2 that generate uniformly distributed encoded parts 205a, 205b by a single channel encoder 404. This channel encoder 404 uses a Bit-Interleaved coded modulation (BICM) approach to obtain multiple encoded parts 409a, 409b from the message part 403. Accordingly, the channel encoder 404 encodes the message part 403 to a codeword 405, which is interleaved by an interleaver 406 and then divided by a splitter 408 into the encoded parts 409a, 409b.

Like in Fig. 2, a symbol mapper 410 is configured to map the encoded parts 409a, 409b, 414 into the channel input symbols 411.

While in the embodiment of Fig. 2 each of the encoded parts 203a, 203b, 203c is encoded with a different constituent encoder 204a, 204b, 204c, the embodiment of Fig. 4 shows an encoder 400 with multiple bit-levels being generated jointly by the channel encoder 404.

Fig. 5 shows a constituent encoder 500 according to a further embodiment of the present invention.

The constituent encoder 500 is configured to generate an encoded part with a non-uniform distribution. It may replace e.g. the constituent encoder 204c in the encoder 200 of Fig. 2 or the constituent encoder 413 in the encoder 400 of Fig. 4. Accordingly, the transmission scheme of Fig. 2 or Fig. 4 with m bit-levels may be used in combination with at least one constituent encoder 500.

The constituent encoder 500 takes as input a sequence b 501 corresponding to a message part obtained from the message. The sequence b 501 is first processed by a polar precoder 502 to generate a sequence s 503, wherein the sequence s 503 may contain b as a subsequence. Then, the sequence s 503 is encoded to a codeword c 505 by a polar encoder 504. The codeword c 505 is the encoded part obtained by the constituent encoder.

The codeword c 505 is obtained by the polar encoder 504 as explained in E. Arikan, "Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels", IEEE Transactions on Information Theory, vol. 55, No. 7, pp. 3051-3073, July 2009. The task of the polar precoder 502 is to generate the sequence s 503, such that after polar encoding the codeword c i.e. the encoded part 505 has a target probability distribution of bits that is non-uniform.

As shown in Iscan, Boehnke, Xu, "Shaped Polar Codes for Higher Order Modulation", IEEE Communication Letters, Vol. 22, No. 2, Feb. 2018, pages 252-255, the polar precoder 502 may be implemented by using a polar decoder. Particularly, the polar decoder may be a successive cancellation decoder as known from E. Arikan, "Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels", IEEE Transactions on Information Theory, vol. 55, No. 7, pp. 3051-3073, July 2009. Alternatively, the polar decoder may be a successive cancellation list decoder as known from Tal, I., and Vardy, A., "List decoding of polar codes", Information Theory Proceedings (ISIT), 2011.

According to an embodiment (not shown in the Figs.), the constituent encoder generating the encoded part having a non-uniform distribution is a shaping encoder without a channel encoder. Such a shaping encoder without a channel encoder may be e.g. an encoder based on m-out-of-n codes according to Tenkasi V. Ramabadran, "A Coding Scheme for m-out-of- n Codes", IEEE Transactions on Communications, Vol. 38, No. 8, August 1990, pages 1156- 1163. Alternatively, such a shaping encoder without a channel encoder may be e.g. an encoder based on Constant Composition Distribution Matching (CCDM) according to Patrick Schulte and Georg Bocherer, "Constant Composition Distribution Matching", IEEE Transactions on Information Theory, Vol. 62, No. 1, January 2016, pages 430-434.

Such an embodiment with one of the constituent encoders containing only a shaping encoder without a channel encoder - i.e. the constituent encoder causing a non-uniform distribution of the encoded part - is based on the m bit-levels transmission scheme of the embodiment of Fig. 2 or Fig. 4 and may use any channel coding scheme. Preferably, the bit- level with this constituent encoder is selected in a way, such that this bit-level is decoded last during the successive decoding process at the receiver. In general, the last decoded bit- level in an MLC system is the most robust bit-level against channel errors, and hence may not require any extra protection. Hence, selecting a constituent encoder using no channel code for the last decoded bit-level ensures that the desired distribution is obtained without using extra redundancy for error correction.

This embodiment with the constituent encoder generating the non-uniformly distributed encoded part being a shaping encoder without a channel encoder, may also be combined with the shifted natural binary labeling 500 according to the embodiment of Fig. 2. The shifted natural binary labeling may be adapted in such a way that the last bit-level decides whether the transmitted symbols are selected from a set of high or low energy channel input symbols.

Fig. 6 shows a decoder 600 according to a further embodiment of the present invention.

The decoder 600 for decoding channel symbols 601 into a message 616 is configured to perform the following steps:

- demap the channel symbols 601 into decoder input sequences 604, 608, 613 according to information 602 about a distribution of the channel symbols 601,

- decode the decoder input sequences 604, 608, 613 into message parts 606, 610, 615, wherein the decoding is based on a constituent encoder 605, 609, 614 comprising a non linear encoder, and

- concatenate the message parts 606, 610, 615 to the message 616.

The information 602 about a distribution of the channel symbols 601 may be the probability distribution Px of the received channel symbols 601. This probability distribution Px is used as a parameter during demapping. In known decoders, this parameter Px is not used during demapping.

The decoder 600 is particularly configured to decode the channel input symbols 207, 411. Each bit-level is demapped and decoded successively, using the information obtained from decoding of the previous bit-levels. The decoder is configured to perform the demapping step and/or the decoding step in two or more iterations, wherein the result of an earlier iteration is used as an input for one or more succeeding iterations. The decoder 600 of an MLC system generally comprises m bit- levels, m demappers 603, 607, 612 and m decoders 605, 609, 614, working in succeeding iterations or a successive fashion. Particularly, the decoder 600 of Fig. 6 is a 3 bit-levels decoder comprising a number of m= 3 demappers 603, 607, 612 and constituent decoders 605, 609, 614, working in 3 successive iterations.

For each iteration a different constituent decoder 605, 609, 614 can be defined. Preferably, the different constituent decoder of at least one bit-level comprises a non-linear encoder (not shown in Fig. 6).

Preferably, the non-linear encoder may be a shaping encoder. Preferably, the constituent encoder comprising the non-linear encoder comprises a channel encoder that may be in in series with the non-linear encoder. Alternatively, the constituent encoder comprising the non-linear encoder does not comprises a channel encoder.

Particularly, the non-linear encoder may be a polar precoder. The constituent encoder may comprise the polar precoder in series with a polar encoder. Particularly, the polar precoder may comprise a polar decoder.

The received symbols 601 are decoded in multiple iterations in a successive fashion, wherein the output of each constituent decoder is used for demapping the next bit levels. In other words, the constituent decoder 605 of the 1^st bit-level is used for demapping the 2^nd and 3^rd bit-levels. Moreover, the constituent decoder 609 of the 2^nd bit-level is used for demapping the 3^rd bit-level.

According to the iterative process implemented in the decoder 600, the 1^st bit-level is demapped and decoded using the 1^st bit-level symbol demapper 603 and constituent decoder 605 to obtain the estimate of the first message part 606. This is followed by a second iteration for the 2^nd bit-level: the symbol demapper 607 and the constituent decoder 609 assigned to the 2^nd bit-level obtain the estimate of the second message part 610. In a third iteration, the symbol demapper 612 and the constituent decoder 614 assigned to the 3^rd bit-level obtain the estimate of the third message part 615.

The task of the /^h symbol demapper 603, 607, 612 is to extract the information about the /^h bit-level from the received symbols 601 and generate the decoder input sequence 604, 608, 613, which is used by the corresponding constituent decoder 605, 609, 614 to obtain the estimate of the corresponding message part 606, 610, 615. The extracted information about the /^h bit-level can be in form of the probability of each bit on the /^h bit-level being 0 or 1, or in form of a likelihood or log-likelihood ratio.

Moreover, each symbol demapper 603, 607, 612 also uses the output of the decoders in the previous interation steps to extract the information.

An idea of the invention is to use an MLC transmission scheme, wherein instead of using conventional channel codes, constituent encoders are used. At least one of the constituent encoders consists of a (non-linear) precoder that generates the output of the channel encoder to have a non-uniform probability distribution. Combined with a symbol mapper, the channel output symbols have a desired target probability distribution.

The invention is advantageous because significant performance improvements can be obtained, particularly with polar codes.

Depending on the required distribution of the channel input symbols, it is possible to use shaping in several bit-levels. Therefore, the complexity increase compared to known systems can be kept manageable according to the needs.

While the invention has been illustrated and described in detail in the drawings and the foregoing description, such illustration and description are to be considered illustrative or exemplary and not restrictive. The invention is not limited to the disclosed embodiments. From reading the present disclosure, other modifications will be apparent to a person skilled in the art. Such modifications may involve other features, which are already known in the art and may be used instead of or in addition to features already described herein.

In the claims, the word "comprising" does not exclude other elements or steps, and the indefinite article "a" or "an" does not exclude a plurality. A single processor or other unit may fulfil the functions of several items recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage. A computer program may be stored/distributed on a suitable medium, such as an optical storage medium or a solid- state medium supplied together with or as part of other hardware, but may also be distributed in other forms, such as via the Internet or other wired or wireless telecommunication systems.

Claims

1. Encoder (200, 400) for encoding a message (201, 401) into channel input symbols (207, 411), the encoder (200, 400) being configured to:

- divide the message (201, 401) for obtaining message parts (203a, 203b, 203c, 403, 412),

- encode the message parts (203a, 203b, 203c, 403, 412) into encoded parts (205a, 205b, 205c, 409a, 409b, 414) such that at least one encoded part (205c, 414) has a non-uniform distribution,

- map the encoded parts (205a, 205b, 205c, 409a, 409b, 414) into the channel input symbols (207, 411),

wherein a channel input symbol (207, 411) is based on a plurality of encoded parts (205a, 205b, 205c, 409a, 409b, 414).

2. Encoder (200, 400) according to claim 1,

wherein the non-uniform encoded part (205c, 414) is obtained by means of a constituent encoder (204c, 413) comprising a non-linear encoder (211).

3. Encoder (200, 400) according to claim 2,

wherein the non-linear encoder (211) is a shaping encoder.

4. Encoder (200, 400) according to claim 2 or 3,

wherein the constituent encoder (204c, 413) comprises the non-linear encoder (211) and, in particular in series with, a channel encoder (212).

5. Encoder (200, 400) according to claim 2 or 3,

wherein the constituent encoder (204c, 413) comprises the non-linear encoder (211) without a channel encoder.

6. Encoder (200, 400) according to claim 2,

wherein the non-linear encoder is a polar precoder (502), and wherein the constituent encoder (204c, 413, 500) comprises the polar precoder (502) in series with a polar encoder (504).

7. Encoder (200, 400) according to claim 6,

wherein the polar precoder (502) comprises a polar decoder.

8. Encoder (200, 400) according to any of the preceding claims,

wherein the encoder (200, 400) is configured to:

- encode one message part (203c, 412) into the non-uniform encoded part (205c, 414) having a non-uniform distribution, and

- encode the remaining message parts (203a, 203b, 403) into uniform encoded part (205a, 205b, 409a, 409b), in particular having a uniform distribution.

9. Encoder (200, 400) according to any of the preceding claims,

wherein the encoded parts (205a, 205b, 205c, 409a, 409b, 414) mapped into the channel input symbols (207, 411) correspond to bit-levels (bl, b2, b3, b4) of the channel input symbols (207, 411),

wherein a non-uniform encoded part (205c, 414) corresponds to the bit-level (b4) that determines whether the channel input symbols (207, 411) have a low magnitude or a high magnitude.

10. Encoder (200, 400) according to any of the preceding claims,

wherein the non-uniform distribution of a non-uniform encoded part (205c, 414) is configured so as to obtain a desired non-uniform probability distribution of the channel input symbols (207, 411).

11. Encoder (200, 400) according to any of the preceding claims,

wherein the non-uniform distribution of a non-uniform encoded part (205c, 414) is configured so that channel input symbols (207, 411) with a low magnitude have an equal or higher probability than channel input symbols (207, 411) with a high magnitude.

12. Encoder (200, 400) according to any of the preceding claims,

wherein a non-uniform encoded part (205c, 414) corresponds to the bit-level (b4) that causes a symmetric distribution (500) of the channel input symbols (207, 411).

13. Method for encoding a message (201, 401) into channel input symbols (207, 411), the method comprising:

14. Decoder (600) for decoding channel symbols (601) into a message (616),

the decoder (600) being configured to perform the following steps:

- demap the channel symbols (601) into decoder input sequences (604, 608, 613) according to information (602) about a distribution of the channel symbols (601),

- decode the decoder input sequences (604, 608, 613) into message parts (606, 610, 615), wherein the decoding is based on a constituent encoder comprising a non-linear encoder,

- concatenate the message parts (606, 610, 615) to the message (616).

15. Decoder according to the previous claim, configured to perform the demapping step and/or the decoding step in two or more iterations, wherein the result of an earlier iteration is used as an input for one or more succeeding iterations.

16. Decoder (600) according to claim 14 or 15,

wherein the non-linear encoder is a shaping encoder.

17. Decoder (600) according to any of the claims 14 to 16,

wherein the constituent encoder comprises the non-linear encoder and, in particular in series with, a channel encoder.

18. Decoder (600) according to any of the claims 14 to 16,

wherein the constituent encoder comprises the non-linear encoder without a channel encoder.

19. Decoder (600) according to claim 14 or 15,

wherein the non-linear encoder is a polar precoder, and

wherein the constituent encoder comprises the polar precoder in series with a polar encoder.

20. Decoder (600) according to the preceding claim,

wherein the polar precoder comprises a polar decoder.

21. Method for decoding channel symbols (601) into a message (616),

the method comprising:

- concatenate the message parts (606, 610, 615) into the message (616).

22. Computer program having a program code for performing the method according to claim 13 or 21, when the computer program runs on a computing device.