Method for adapting BICM scheme to amplitude shaping in conjunction with puncturing, data transmitter and computer program

Abstract

The present invention relates to a method for transmitting symbols. A first signal comprising a sequence of bits representing a first data stream and a second data stream is obtained. The first data stream includes shaped bits. The second data stream includes unshaped bits including quantization bits and / or symbol bits. At least a portion of the unshaped bits of the second data stream are punctured, thereby obtaining an incomplete bit stream. The symbols are obtained based at least on the incomplete bitstream and based on the first data stream. The invention also relates to a corresponding data transmitter and a corresponding computer program.

Description

Technical Field

[0001] The present disclosure relates to the field of telecommunications. More specifically, the present disclosure relates to a method for transmitting symbols, a data transmitter, and a computer program. Background Art

[0002] In a communication system, for a given communication channel, the channel capacity characterizes the highest information rate that can be achieved for a fixed average transmission power while maintaining a small error probability.

[0003] Generally, the channel inputs transmitted by a transmitter are symbols of a finite set. This finite set is called a constellation. For example, it can be a one-dimensional amplitude shift keying (ASK) constellation or a two-dimensional quadrature amplitude modulation (QAM) constellation. The latter can be regarded as the Cartesian product of two ASK constellations.

[0004] Generally, if the symbols of the constellation are transmitted with equal probability, the channel capacity cannot be achieved. As a result, the transmitter should process the data such that the symbols of the constellation are transmitted with a probability that can approach the capacity. This operation is called shaping.

[0005] In addition to shaping, error correction codes should also be used to protect the message. The 5G New Radio (NR) standard specifies a coding scheme called bit-interleaved coded modulation (BICM). This coding scheme does not implement shaping.

[0006] Combining shaping and coding is not easy and requires specific algorithms, especially if the 5G NR coding scheme is to be adhered to.

[0007] Therefore, there is a need for a coding scheme that is suitable as a BICM scheme, preferably suitable as a 5G NR coding scheme, which allows providing symbols that comply with the shaping performed by a distribution matcher (DM) as output. Summary of the Invention

[0008] The present disclosure improves this situation.

[0009] A method for transmitting k” symbols in a data transmitter is proposed, where k” is a positive integer, and the method includes the following steps:

[0010] - Obtaining input bit sequences representing a first data stream and a second data stream,

[0011] The first data stream includes at least k’×(m - q) shaping bits representing m - q input marker bit streams, where k’ is a positive integer greater than or equal to k”, m is the number of bit streams to be output by a demultiplexer, and q is a positive integer,

[0012] The second data stream includes c' non-integer bits, where c' is a positive integer less than or equal to (q - 1)k', and the c' non-integer bits include at most q - 1 quantization and / or symbol bits.

[0013] - Puncture at least some of the non-integer bits of the second data stream, thereby obtaining at most q - 1 incomplete bitstreams, and

[0014] - Obtain k'' symbols based at least on the at most q - 1 incomplete bitstreams and based on the m - q input marker bitstreams of the first data stream.

[0015] In other words, a technique for puncturing non-integer bits is proposed. According to this technique, when the input bit sequence includes c' non-integer bits, c of the c' non-integer bits can be punctured after encoding.

[0016] The proposed technique can be implemented as a minor modification to the specification to improve the existing 5G NR coding scheme (more generally, any BICM scheme) such that the symbols at the coding output comply with the shaping performed by the distribution matcher. In particular, the proposed technique allows some systematic bits to be punctured without changing the target shaping distribution, for example, during rate matching (RM) and hybrid automatic repeat request (HARQ).

[0017] Optionally, the method may further include sorting the input bit sequence by placing c of the c' non-integer bits at systematic puncture positions, where c is a positive integer less than or equal to c', and puncturing at least some of the non-integer bits of the second data stream may include puncturing at least the c non-integer bits at the systematic puncture positions.

[0018] Alternatively, c non-integer bits may be received at default positions in the input bit sequence, and the systematic puncture positions may be selected to correspond to these default positions, so that it is not necessary to sort the input bit sequence before puncturing. In other words, the method may further include designating the positions of at least c of the c' non-integer bits in the input bit sequence as systematic puncture positions, and puncturing at least some of the non-integer bits of the second data stream may include puncturing at least the c non-integer bits at the systematic puncture positions.

[0019] Optionally, the method may further include the following steps:

[0020] - Use a systematic error correction coding scheme and receive the bits associated with the input bit sequence as input to obtain the output of the encoder, where the output of the encoder includes qk' - d parity bits, where d = c' - c, and d is a positive integer or zero, and

[0021] - Use (qk’ - d) - k’ out of the qk’ - d parity check bits to complete at most q - 1 incomplete bitstreams, thus obtaining at most q - 1 completed bitstreams, and

[0022] Obtaining k” symbols can be based on

[0023] The m - q input marked bitstreams of the first data stream,

[0024] At most q - 1 completed bitstreams, and

[0025] The parity check bits output by the encoder and not used to complete at most q - 1 incomplete bitstreams.

[0026] It is not required that the data transmitter itself obtains the output of the encoder, complete the incomplete bitstreams and / or determine k” symbols. According to an alternative possibility, the method may include sending q - 1 incomplete bitstreams to an entity separate from the data transmitter. Such a separate entity may further be adapted to determine k” symbols based on the q - 1 incomplete bitstreams and provide the determined k” symbols to the data transmitter in return. The data transmitter that thus obtains k” symbols from the separate entity can then send them via an appropriate channel.

[0027] Optionally, c’ = k′.

[0028] Optionally, c = c’.

[0029] Optionally, obtaining k” symbols based on the m original marked bitstreams includes:

[0030] - Sorting the output bit sequence including the m original marked bitstreams by placing x bits in additional puncturing positions, where x is a positive integer and the x bits include x / m bits of each of the m original marked bitstreams,

[0031] - Puncturing the x bits placed in the additional puncturing positions to obtain m punctured marked bitstreams, and

[0032] - Using one bit of each punctured marked bitstream to label the corresponding input symbol to obtain k” symbols.

[0033] In other words, a technique for puncturing shaping bits is also proposed. An input bit sequence can be provided to an encoder, and then the input bit sequence can be concatenated with the output of the encoder to obtain an output bit sequence. Sorting the output bit sequence can include placing all the bits to be punctured at additional puncturing positions (e.g., the end of the output bit sequence) by using a second interleaver. In a first example, the input bit sequence includes only shaping bits. In this case, no "first interleaver" is required before encoding, and the bits to be punctured are x bits, where each of the x bits is x / m bits of each of the m original labeled bit streams. In a second example, the input bit sequence includes both shaping bits and non-shaping bits. In this case, puncturing can be performed on only the shaping bits, only the non-shaping bits, or both the shaping bits and the non-shaping bits. In the latter case, the two techniques can be combined, and then the bits to be punctured can include not only the x bits, where each of the x bits is x / m bits of each of the m original labeled bit streams, but also c bits out of c' non-shaping bits.

[0034] The combined technique of puncturing both shaping bits and non-shaping bits can achieve a rate where:

[0035] The rate of the code is

[0036] c is the number of systematic non-shaping bits to be punctured (and c' = c + d), and

[0037] x is the number of bits to be punctured under the constraint that the bits in each original labeled bit stream are punctured.

[0038] Optionally, the additional puncturing positions correspond to the end of the output bit sequence after sorting the output bit sequence.

[0039] Then, a rate matcher (such as in the 5G NR LDPC coding scheme) that punctures the last encoded bits can discard the bits to be punctured.

[0040] In another example, obtaining k'' symbols includes:

[0041] - Labeling corresponding input symbols using one bit from each original labeled bit stream, thus obtaining k'' symbols and additional symbols, and

[0042] - Using a rate matcher to discard the additional symbols.

[0043] Then, compared with the previous example, no interleaver is required before the rate matcher.

[0044] Optionally, the method further includes: after transmitting k' symbols, transmitting a symbol having c punctured non-shaping bits and x punctured bits as flag bits separately.

[0045] A data transmitter configured to transmit k'' symbols is also proposed, where k'' is a positive integer, by at least the following steps:

[0046] - Obtaining input bit sequences representing a first data stream and a second data stream,

[0047] The first data stream includes at least k'×(m - q) shaping bits representing at least m - q input flag bit streams, where k' is a positive integer greater than or equal to k'', m is the number of bit streams to be output by the demultiplexer, and q is a positive integer.

[0048] The second data stream includes c' non-shaping bits, where c' is a positive integer less than or equal to (q - 1)k', and the c' non-shaping bits include at most q - 1 quantization and / or symbol bits.

[0049] - Puncturing at least part of the non-shaping bits of the second data stream to obtain at most q - 1 incomplete bit streams, and

[0050] - Obtaining k'' symbols based at least on the at most q - 1 incomplete bit streams and on the m - q input flag bit streams of the first data stream.

[0051] A computer program including instructions is also proposed, which when executed by a computer causes the computer to execute the above method.

[0052] Other features, details, and advantages will be shown in the following detailed description and the drawings. Description of the Drawings

[0053] Figure 1 Figure 1 Shows a 5G NR LDPC coding scheme known in the prior art.

[0054] Figure 2 Figure 2 Shows the natural bit labeling of a 16-ASK constellation known in the prior art.

[0055] Figure 3 Figure 3 Shows the implementation of a HARQ scheme in 5G known in the prior art.

[0056] Figure 4 Figure 4 Shows a probability amplitude shaping technique known in the prior art.

[0057] Figure 5 Figure 5 ​​​​​​​​​​A system is shown with a distributive matcher (DM) arranged in front of a 5G NR LDPC coding scheme.

[0058] Figure 6 Figure 6 A puncturing scheme in an embodiment is shown.

[0059] Figure 7 Figure 7 An example of a quantization target shaping distribution of a 16-ASK constellation known in the prior art is shown.

[0060] Figure 8 Figure 8 Two sub-constellations of a 16-ASK constellation known in the prior art and their natural labeling according to the main constellation (but without quantization bits) are shown, with the least significant bit on the left.

[0061] Figure 9 Figure 9 An adaptation of a 5G NR LDPC scheme for puncturing system non-shaped bits in an embodiment is shown.

[0062] Figure 10 Figure 10 Another adaptation of a 5G NR LDPC scheme for puncturing system non-shaped bits in another embodiment is shown.

[0063] Figure 11 Figure 11 A system is shown in an embodiment that is different from the system depicted in Figure 5 in that an interleaver is arranged between the system parity encoder and the rate matcher.

[0064] Figure 12 Figure 12 A bit ordering after the interleaver depicted in Figure 11 in an embodiment is shown.

[0065] Figure 13 Figure 13 A system is shown in an embodiment that is different from the system depicted in Figure 5 in that the positions of the rate matcher and the multiplexer are switched.

[0066] Figure 14 Figure 14 A system is shown in an embodiment that is different from the system depicted in Figure 11 in that an additional interleaver is arranged after the multiplexer.

[0067] Figure 15 Figure 15 A bit ordering that is an alternative to the ordering depicted in Figure 12 in an embodiment is shown. ​​​​​​​​​​​​​​​​​​​​

[0068] Figure 16 Figure 16 Illustrates the adaptation of the 5G NRLDPC scheme that punctures both systematic shaped and unshaped bits in an embodiment.

[0069] Figure 17 Figure 17 Illustrates an example of a sequence at the output of parity check encoding in an embodiment Figure 16 before puncturing and interleaving.

[0070] Figure 18 Figure 18 Illustrates the encoded bits at the output of the error correction code in an embodiment Figure 16 wherein.

[0071] Figure 19 Figure 19 Illustrates the adaptation of the HARQ scheme that punctures both systematic shaped and unshaped bits in an embodiment. Detailed Description

[0072] Now refer to the 5G New Radio (NR) Low Density Parity Check (LDPC) coding scheme as described in 3GPP TS 38.212 Figure 1 as shown. An overview can also be found in [DPS2020].

[0073] The 5G NR LDPC coding scheme works as follows. k information bits are used as the input to the systematic parity check encoder (100). n + ∈ - k parity check bits (102) are generated without modifying the information bits since the code is systematic. After encoding, ∈ = 2Z systematic bits are punctured by the puncturer (104). Z is a parameter depending on the code length used. The resulting codeword of size n is called the mother codeword (106). The rate of the mother code is R = k / n. Then, the rate matcher (RM) (108) is responsible for removing (puncturing) some bits of the mother codeword such that only n' bits are output. The effective rate of the system is R = k / n'. Next, the n' bits are provided to the demultiplexer (110) which is combined with the symbol mapper in order to label the symbols to be transmitted over the channel.

[0074] If the modulation used is Binary Phase Shift Keying (BPSK) modulation or Quadrature Phase Shift Keying (QPSK) modulation, bits are transmitted over the channel. If higher order modulation is used, the bits are processed as follows.

[0075] First, is considered as an M-ASK constellation. The symbols of the M-ASK constellation are where m = 2 m ​​​​​​​​Therefore, m bits are required to label the symbols. As an example, the natural labeling (200) of the symbols in an M = 16-ASK constellation is provided by Figure 2 . Here, m = log2(M) = 4 bits are required for the labeling.

[0076] After RM, the demultiplexer (referred to as an interleaver in the standard) outputs m streams, each labeling bit of the modulated symbol (i.e., at the bit level, see Figure 2 ) one stream. Then the symbols at the output of the symbol mapper are sent over the channel.

[0077] Define the labeling bit stream as a subset of the coded bits at the bit level used to label the symbols before the demultiplexer. For example, Figure 1 B1 on is the labeling bit stream, and i where k' is the number of symbols transmitted over the channel. In this document, when the bit stream B i contains k' shaping bits b Figure 1 representing the unique data stream among the k input bits, it is called "original". Therefore,

[0078] Now refer to the hybrid automatic repeat request (HARQ) scheme implemented in 5G. This scheme belongs to the category of incremental redundancy schemes. In each round, a subset of the mother codeword is selected (by RM) and then transmitted.

[0079] Figure 3 Illustrates how HARQ is implemented in 5G. First, the bits of the mother codeword are placed in a circular buffer (300). Then, in each of the possible four rounds (RV0, RV1, RV2, and RV3), a different subset of the coded bits is transmitted. For example, in the RV2 round (302), only the parity bits are transmitted.

[0080] Now refer to the probability amplitude shaping (PAS) scheme disclosed in [BSS2015], which is a popular technique that combines shaping and coding. Figure 4 The principle of PAS shown on i is as follows: The distribution matcher (DM) (400) outputs symbols according to the positive side of the target shaping distribution, where each symbol is labeled using multiple bits. The function b() (402) outputs the labeling bits of a given symbol x i . The bits corresponding to the labeling of the symbol are used as the input to the systematic error correction code. These bits are called shaping bits. The block "P" (404) calculates and outputs a parity bit, one parity bit per symbol, which determines the sign of the symbol to be transmitted. The function s() (406) outputs the symbol corresponding to the bit The corresponding symbols. These bits are referred to as symbol bits.

[0081] The core idea of the PAS underlying layer is as follows:

[0082] - Since systematic coding is used, the error correction code does not change the distribution of the shaping bits. Therefore, they can be non-equiprobable.

[0083] - It is widely accepted that the parity check bits of the error correction code have an equiprobable distribution. This is suitable for a symmetric shaping distribution because the probability of the symbol being positive and negative is the same, and the symbol bits should therefore remain equiprobable.

[0084] Therefore, PAS successfully combines shaping and coding.

[0085] Using this scheme, the baseline rate of the code is R = (m - 1) / m. The rate can be easily increased by using some of the symbol bits as systematic bits. However, the rate cannot be reduced using this standard scheme.

[0086] As will be described below, problems are encountered when attempting to combine a shaping scheme such as PAS with a 5G NR LDPC coding scheme.

[0087] Regarding puncturing of the shaping bits, ideally, the shaping scheme (500) is "inserted" into the 5G NR LDPC coding scheme (510), as shown in the system depicted, for example Figure 5 In this example, m = 4 bits are used per symbol, including three shaping bits. For simplicity, in this example, puncturing of both the systematic bits and the non-systematic bits is the responsibility of the RM.

[0088] However, the above combination of the shaping scheme and the coding scheme cannot achieve the desired shaping distribution. In fact, if the shaping bits used as systematic bits are not carefully punctured, the resulting symbol distribution changes significantly.

[0089] Regarding puncturing of the HARQ scheme, as Figure 3 shown, some rounds of the HARQ scheme do not include systematic bits (e.g., Figure 3 RV2 on

[0090] Therefore, only parity check bits are included. Since the parity check bits have an equiprobable independent and identical distribution, it is impossible to achieve shaping using only these bits. Figure 2 ) corresponding to a given bit level, the bits are non-shaping bits. The bits corresponding to a given bit level are shaping bits if they are not non-shaping bits.

[0091] For the puncturing of systematic bits, two cases are distinguished: the case where the punctured systematic bits are shaping bits and the case where the punctured systematic bits are non-shaping bits.

[0092] Now, a technique focusing on the puncturing of systematic non-shaping bits is proposed.

[0093] To this end, the quantization target shaping distribution is first reviewed. Figure 7 An example of the quantization target shaping distribution (1200) of 16-ASK is shown, which meets the requirements set forth in European patent application EP22305529.4. As shown in the simulation results depicted in [CG2022], Figure 4 this distribution can achieve near-optimal performance. Therefore, this distribution can be used as the target shaping distribution.

[0094] Figure 8 Two sub-constellations of 16-ASK are represented. Their natural labeling according to the main constellation is also shown, with the least significant bit on the left. The bits on the figure correspond to bit levels 2 / 3 / 4. The first sub-constellation (1300) corresponds to bit level 1 = 0, and the second sub-constellation (1302) corresponds to bit level 1 = 1.

[0095] Therefore, the constellation can be represented as the union of two shifted versions of a reference sub-constellation (referred to as ): for example where α = {0, 2}. In addition, the transmitted symbols belong to one of the two sub-constellations with equal probability.

[0096] Similarly, considering, for example, the 16-ASK constellation. The natural labeling of the symbols in this constellation is provided in Table 1. We can see that the first bit level distinguishes between the two sub-constellations shown in Figure 7 .

[0097] Therefore, using this distribution, two bits have an equal probability independent distribution: the shaping bit and the bit that distinguishes between the two constellations. This second bit is called the quantization bit.

[0098] In the example, there is only one quantization bit. Instead of having only two adjacent symbols with the same probability, stronger quantization can be used, where 4, 8, etc. adjacent symbols have the same probability. Let q be the number of quantization bits and symbol bits. In the above example, q = 2.

[0099] A technique is also proposed where the quantization bit and / or the symbol bit is used as a punctured systematic bit (independent of other punctured systematic bits).

[0100] The additional bit level with an equal probability distribution enables both the quantization bit and / or the symbol bit to be used as parity check bits. This can reduce the rate of the code to R = (m - q) / m.

[0101] In addition, since these bits have an independent and equiprobable distribution, they can be placed at the systematic puncturing positions of the system and replaced by parity-check bits in the symbol mapping. It should be noted that there are no constraints on puncturing other bits for these bits to be punctured.

[0102] Figure 9 Shows a first example of adaptation of the 5G NR LDPC scheme, where the quantization bit b1 is used as (non-shaped) systematic bits, and the first interleaver π'(1000) places a subset of c of these bits at the puncturing positions. In this example, the code rate is R = ((m - 1)k') / (mk' + c), and the parity-check encoding (100) generates k' + c bits b4. Before the demultiplexer and after the RM, a second interleaver π(1400) is added. This second interleaver places the additional c bits b4 at the positions of the lost punctured bits b1. In Figure 9 , B2 is the original bitstream, which includes k' shaped bits b2 among the k = 3k' bits of the input bit sequence. B3 is also the original bitstream, which includes k' shaped bits b3 among the k = 3k' bits of the input bit sequence. In contrast, as a result of puncturing, B1 only includes k' - c shaped bits b1. B1 does not contain the k' shaped bits b2 among the k = 3k' bits of the input bit sequence, so it is not the original bitstream. B4 only includes parity-check bits that are not part of the input bit sequence. B4 is therefore not the original bitstream.

[0103] Figure 10 Shows a second example of adaptation of the 5G NR LDPC scheme, where only c non-shaped systematic bits are used, where c is the number of punctured systematic bits. Therefore, the rate of the code is reduced to R = ((m - 2)k' + c) / (mk' + c). In Figure 10 , B2 and B3 are the original bitstreams, which remain unchanged throughout the depicted workflow. In contrast, B1 is empty and therefore not the original bitstream. In addition, B1' and B4 only include parity-check bits and are not the original bitstreams.

[0104] It should be noted that c' non-shaped systematic bits can also be used, where c' = c + d, d ≥ 0 (specifically, instead of k' or c as in the example).

[0105] Now a technique focusing on the puncturing of systematic bits including shaped systematic bits is proposed.

[0106] As a note on cyclic redundancy check (CRC): The CRC used by the receiver to check whether the message is decoded correctly is calculated from the information bits before LDPC coding. The generated CRC bits are added to the information bit sequence. The resulting sequence is used as the systematic bits of the channel code. It can be assumed that the CRC bits are equiprobable. Thus, they can be used as non-shaping systematic bits or as the input to the DM together with other information bits.

[0107] The requirement for maintaining shaping in puncturing the systematic shaping bits is that each symbol should be labeled with shaping bits. For example, in Figure 5 above, all symbols should be labeled with the set b1b2b3 (and a non-shaping bit b4). Thus, if a systematic bit b1 is punctured, the corresponding bits b2b3 and a parity check bit b4 should also be punctured.

[0108] Consider Figure 5 the coding scheme where the rate R of the code is R=(m - 1) / m (in the given example, = 3 / 4). At the output of the error correction code, the bits are sorted as the concatenation B1B2B3B4 of three labeled bitstreams B1B2B3 (formed by the systematic bits output by the shaping scheme) and the bitstream B4 (formed by the parity check bits output by the parity check encoder).

[0109] Suppose one wants to achieve a rate R = 6 / 7, i.e., 7k′ / 2 bits, instead of 4k′ = 8k′ / 2 bits, by sending only a subset of the coded bits (and puncturing some parity check bits). Then, a total of k′ / 2 bits should be punctured by the puncturing scheme (600) as shown in Figure 6 : k′ / (2*m) bits (602) of each original labeled bitstream should be punctured.

[0110] This can be achieved by the system depicted in Figure 11 above, which corresponds to a modification of the system in Figure 5 where π is an additional interleaver (700) placed after the parity check encoder and before the rate matcher such that the appropriate bits are punctured. Figure 12 The sorting (702) of the bits after this new interleaver (700) is depicted above. Then, the RM that punctures the last coded bits (as in the 5G NR LDPC coding scheme) discards the bits to be punctured (800) (shown here as the rightmost part).

[0111] Note that the same result can be achieved without adding an interleaver by simply switching the RM (108) and the demultiplexer (110) as depicted in Figure 13 above. In this case, the RM only discards the k′ / (2*m) last symbols.

[0112] Alternatively, the labeled bitstream and the puncturing positions may have different forms, as long as k′ / (2*m) bits of each original labeled bitstream are punctured. This alternative option may result from a (first) interleaver π′(1000) placed after the multiplexer and before the parity encoder, as Figure 14 shown. In this case, a (second) interleaver π(700) sorts the bits such that the Figure 12 sorting obtained at the output is Figure 15 An example of a different sorting (1002) after π′ is shown. This sorting represents the systematic bits provided to the parity encoder and the parity bits output by the parity encoder, as well as alternative puncturing positions (1100) corresponding to the bits to be punctured. Note also that any parity bit may be punctured (not necessarily at the end).

[0113] In summary, under the constraint that x / m bits of each original labeled bitstream are punctured, the proposed technique can achieve a rate R = ((m - 1)k′) / (mk′ - x), where x is the number of punctured bits. The rate of the code used is ((m - 1)k′) / mk′. Note that the latter rate can be obtained by generating more parity bits using parity encoding and directly puncturing some of them (i.e., within block P in the figure).

[0114] Note that the original labeled bitstream defined above for the puncturing of systematic shaping bits should be established after the puncturing of systematic non - shaping bits (i.e., when saying "if the bitstream is the bitstream obtained without any puncturing, then it is original", the puncturing of systematic shaping bits is not considered).

[0115] In summary, regarding the puncturing of both systematic shaping and non - shaping bits, the combination of the proposed techniques can achieve a rate ((m - q)k′ + c′) / ((m - q)k′ + qk′ - d) = ((m - q)k′ + c′) / (mk′ - d), where

[0116] the rate of the code is

[0117] c is the number of systematic non - shaping bits punctured,

[0118] c′ = c + d, where d ≥ 0, and

[0119] x is the number of bits punctured under the constraint that x / m bits of each original labeled bitstream are punctured.

[0120] Figure 16 An example of a system combining the two proposed techniques is shown above. Figure 17Shown above is an example of a possible coded sequence (1604) at the output of parity check coding before puncturing and interleaving. After puncturing, the output coded sequence (1602) is demultiplexed and used to label k' symbols to be transmitted according to a mapping scheme.

[0121] Now proposed is to Figure 16 apply the system to HARQ.

[0122] Consider Figure 16 the scheme where c = 0, m = 4 bits / symbol. After puncturing of the systematic bits, there are 2k' systematic bits and 2k' parity check bits. Suppose we want to design two rounds of HARQ. The target rate for the first round is R0 = 2 / 3. The remaining bits are sent in the second round such that the rate R1 = 2 / 4 is achieved. At the output (1604) of the error correction code, the order of the bits is as Figure 18 depicted in.

[0123] If only 3k' out of 4k' bits should be sent in the first round to achieve the rate R0 = 2 / 3, then x = k' bits should be punctured. The bit streams are punctured as follows: k' / 4 bits of each bit stream B1B2B3B4 are punctured. In this case, the whole system is as Figure 19 depicted above, where π'(1900) is the added interleaver. In the second round, RM selects the rightmost part of the input stream (see Figure 12 ) and punctures the leftmost part.

[0124] List of references

[0125] [BSS2015] G. F. Steiner and P. Schulte, "Bandwidth Efficient and Rate-Matched Low-Density Parity-Check Coded Modulation", IEEE Transactions on Communications, Vol. 63, No. 12, December 2015.

[0126] [DPS2020] Erik Dahlman, Stefan Parkvall and Johan "5G NR, The next generation wireless access technology", 2018.

[0127] [CG2022]Vincent Corlay and Nicolas Gresset, "A Simple Sign-Bit Probabilistic Shaping Scheme", IEEE Communications Letters, Vol. 26, No. 4, April 2022.

Claims

1. A method for transmitting K” symbols in a data transmitter, where K” is a positive integer, the method comprising the steps of: - Obtaining input bit sequences representing a first data stream and a second data stream, The first data stream includes at least k’×(m - q) shaping bits representing at least m - q input marker bit streams, where k’ is a positive integer greater than or equal to k”, m is the number of bit streams to be output by a demultiplexer, and q is a positive integer, The second data stream includes c' non-integer bits, where c' is a positive integer less than or equal to (q - 1)K ′ and the c' non-integer bits include at most q - 1 quantization and / or sign bits - Puncturing at least a portion of the non - shaping bits of the second data stream, thereby obtaining at most q - 1 incomplete bit streams, and - Obtaining the K” symbols based at least on the at most q - 1 incomplete bit streams and on the m - q input marker bit streams of the first data stream.

2. The method according to claim 1, the method further comprising the following steps: The input bit sequence is sorted by placing c non - shaping bits out of the c’ non - shaping bits at system puncturing positions, where c is a positive integer less than or equal to c’, and where puncturing at least a portion of the non - shaping bits of the second data stream includes puncturing at least the c non - shaping bits at the system puncturing positions.

3. The method according to claim 1, the method further comprising the steps of: The positions of at least c non - shaping bits out of the c’ non - shaping bits in the input bit sequence are designated as system puncturing positions, and where puncturing at least a portion of the non - shaping bits of the second data stream includes puncturing at least the c non - shaping bits at the system puncturing positions.

4. The method according to claim 2 or 3, the method further comprising the steps of: - Using a systematic error - correcting coding scheme and receiving bits associated with the input bit sequence as input to obtain an output of an encoder, the output of the encoder including qk’ - d parity bits, where d = c’ - c, and d is a positive integer or zero, - Completing the at most q - 1 incomplete bit streams with (qk’ - d)-k’ of the qk’ - d parity bits, thereby obtaining at most q - 1 completed bit streams, and wherein obtaining the K” symbols is based on: The m - q input marker bit streams of the first data stream, The at most q - 1 completed bit streams, and The parity bits output by the encoder and not used to complete the at most q - 1 incomplete bit streams.

5. The method according to claim 4, wherein The step of obtaining the K” symbols based on m original marker bit streams includes the steps of: - Sorting an output bit sequence including the m original marker bit streams by placing x bits at additional puncturing positions, where x is a positive integer, the x bits including x / m bits of each of the m original marker bit streams, - Puncturing the x bits placed at the additional puncturing positions to obtain m punctured marker bit streams, and - Marking corresponding input symbols using one bit of each of the respective punctured marker bit streams to obtain the K” symbols.

6. The method according to any one of claims 2 to 5, wherein, c ′ = k'.

7. The method according to any one of claims 2 to 5, wherein c = c ′ .

8. The method according to claim 7, wherein, The additional puncturing positions correspond to the end of the output bit sequence after sorting the output bit sequence.

9. The method according to any one of claims 1 to 4, wherein, The step of obtaining the K” symbols includes the steps of: - Mark the corresponding input symbols using one bit of each of the original marker bitstreams, thereby obtaining the k” symbols and additional symbols, and - Discard the additional symbols using a rate matcher.

10. The method according to any one of claims 1 to 9, the method further comprising the steps of: After transmitting the k” symbols, transmit separately the symbols marked with c punctured non-shaping bits and x punctured bits.

11. A data transmitter configured to transmit k” symbols, where k” is a positive integer, at least by: - Obtain input bit sequences representing a first data stream and a second data stream, The first data stream includes k’×(m - q) shaping bits, The first data stream represents at least m input marker bitstreams, The second data stream includes c′ non-shaping bits associated with the shaping bits, where m is the number of bitstreams to be output by a demultiplexer, where q is the number of non-shaping bits of the second data stream associated with at least a portion of the shaping bits of the first data stream, The non-shaping bits include q’ quantization bits and symbol bits, where c' is a positive integer less than or equal to k ′ ​ - Puncture at least a portion of the non-shaping bits of the second data stream, thereby obtaining at most q - 1 incomplete bitstreams, and - Obtain the k” symbols based at least on the at most q - 1 incomplete bitstreams and on the m - q input marker bitstreams of the first data stream.

12. A computer program comprising instructions that, when executed by a computer, cause the computer to perform the method according to any one of claims 1 to 10.

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