Method and device for transmitting binary data

Abstract

A method for transmitting binary data using an M-ASK constellation divided into M / 2 sets of two symbols is disclosed, where each set of index i has a probability p i First, m-1 bits are obtained from a binary information source, where m=log2M. Then, a binary information source corresponding to the m-1 bits is selected from a plurality of binary information sources, and each binary information source with index i is associated with p i The probability of outputting a zero bit is associated with a probability of 0, which is equal to m-1 bits. The symbols of the M-ASK constellation are obtained, which are associated with a binary word formed by the m-1 bits and one bit obtained from the selected information source. The symbols are finally transmitted to the receiver via the communication channel.

Description

[Technical Field]

[0001] At least one embodiment of the present invention generally relates to a method for transmitting binary data using an M-ASK constellation (ASK is the English acronym for "Amplitude Shift Keying") and at least one embodiment of the present invention also relates to a corresponding transmitter. [Background technology]

[0002] In a communication system, a transmitter is connected to a receiver via a communication channel (e.g., optical fiber). The transmitter usually includes an encoder configured to encode input data, e.g., a bit stream, into symbols belonging to a finite set called a constellation. One-dimensional ASK (an acronym for Amplitude Shift Keying) and two-dimensional QAM (an acronym for Quadrature Amplitude Modulation) are examples of such constellations. Here, a one-dimensional or two-dimensional constellation means that the symbols are R or R, respectively. 2 This means that R takes the value of R. R is the set of real numbers.

[0003] These symbols are then transmitted over a communication channel to a receiver, which includes a decoder configured to decode the received symbols into output data.

[0004] Communication systems that transmit uniformly distributed symbols typically suffer from shaping losses. Therefore, it is known that in order to approach the channel capacity, the transmitter needs to process the input data to change the probability distribution of the transmitted symbols. More precisely, the input data is processed so that the transmitted symbols have a non-uniform probability distribution that matches the communication channel. This process, called stochastic shaping, can result in energy savings, also known as shaping gain. It is known that in Gaussian channels, the Maxwell-Boltzmann distribution results in suboptimal performance. However, processing the input data to match the Maxwell-Boltzmann distribution is complex to implement. Summary of the Invention [Problem to be solved by the invention]

[0005] It is therefore desirable to have a method for transmitting binary data that is high performance yet easy to implement, and that is adapted to non-Gaussian channels. [Means for solving the problem]

[0006] At least one of the embodiments of the present invention generally comprises a method in a transmitter for transmitting binary data using an M-ASK constellation divided into M / 2 sets of two symbols, each set of index i having a probability p i and the probability of transmitting the second symbol of the set, 1-p i and each symbol of the M-ASK constellation is associated with a binary word defined using natural labeling. a) obtaining m-1 bits from a binary information source, where m=log2M; b) selecting a binary information source corresponding to m-1 bits from a plurality of binary information sources, where each binary information source with index i is p i and c) obtaining one bit from the selected source; and d) obtaining symbols of an M-ASK constellation associated with a binary word formed by m-1 bits obtained from the binary information source and 1 bit obtained from the selected information source; e) transmitting the resulting symbols to a receiver via a communication channel; The present invention relates to a method, including:

[0007] This transmission method is easier to implement than transmission methods that try to fit the Maxwell-Boltzmann distribution. More precisely, it allows us to perform the shaping operation using a small number of binary sources.

[0008] In one embodiment, the given labeling is a natural labeling, and each set with index i includes the i-th symbol and the i+M / 2-th symbol of the M-ASK constellation, where i∈[1;M / 2].

[0009] In one embodiment, the given labeling is a Gray labeling, and each set of index i includes the i-th symbol and M / 2+1-i symbols of the M-ASK constellation, where:

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[0010] In one embodiment, the m-1 bits obtained from the binary information source are the less significant bits of the binary word, and the 1 bit obtained from the selected information source is the most significant bit of the binary word.

[0011] In one embodiment, the binary information source is an equiprobable binary information source.

[0012] In one embodiment, selecting a binary information source corresponding to m-1 bits from the plurality of binary information sources comprises: determining the decimal value of a binary sequence formed by the m-1 bits; selecting a binary source whose index is equal to said decimal value incremented by one; Includes:

[0013] In one embodiment, the plurality of binary information sources comprises: m-1 Contains binary information sources.

[0014] In one embodiment,

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[0015] In one embodiment,

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[0016] In one embodiment, each binary information source of index i in the plurality of binary information sources is

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[0017] In one embodiment, the method comprises: encoding r×(M-1)*k bits obtained from an equiprobable binary information source using an error-correcting code into (m-1)*n bits, where n and k are integers; Obtained from an equiprobable binary source

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[0018] In one embodiment, the method comprises selecting a probability p from the table. i and transmitting to the receiver at least one index entry indicative of the obtained probability.

[0019] In one embodiment, the method comprises: selecting a probability p from a predetermined communication channel distribution; i and transmitting the estimated probability to the receiver.

[0020] In one embodiment, the method comprises receiving from the receiver a probability p i and receiving the

[0021] At least one embodiment of the present invention generally discloses a transmitter configured to transmit binary data using an M-ASK constellation divided into M / 2 sets of two symbols, each set with index i having a probability p of transmitting the first symbol of the set. i and the probability of transmitting the second symbol of the set, 1-p i and each symbol of the M-ASK constellation is associated with a binary word defined using natural labeling. a) obtaining m-1 bits from a binary information source, where m=log2M; b) selecting a binary information source corresponding to m-1 bits from a plurality of binary information sources, where each binary information source with index i is p i and c) obtaining one bit from the selected source; and d) obtaining symbols of an M-ASK constellation associated with a binary word formed by m-1 bits obtained from the binary information source and 1 bit obtained from the selected information source; e) transmitting the resulting symbols to a receiver via a communication channel; The method includes at least one processor configured to:

[0022] The various embodiments disclosed with respect to the method also apply to the transmitter.

[0023] A computer program product is disclosed, comprising program code instructions that can be loaded into a programmable device, the program code instructions causing the programmable device to perform a method according to any one of the preceding embodiments when the program code instructions are executed by the programmable device.

[0024] Disclosed is a storage medium storing a computer program including program code instructions that, when read from the storage medium and executed by a programmable device, cause a method according to any one of the preceding embodiments to be performed.

[0025] The characteristics of the invention will emerge more clearly from a reading of the following description of at least one example of embodiment, the said description being made with reference to the accompanying drawings, in which: [Brief explanation of the drawings]

[0026] [Figure 1] 1 is a diagram illustrating a schematic diagram of a communication system according to a particular embodiment; [Figure 2] FIG. 1 illustrates symbols of an 8-ASK constellation. [Figure 3A] 1 illustrates the principle of division of an M-ASK constellation into M / 2 sets of two symbols according to a particular embodiment; [Figure 3B] 1 illustrates the principle of an alternative division of an M-ASK constellation into M / 2 sets of two symbols according to a particular embodiment; [Figure 4A] FIG. 2 is a block diagram of a shaping encoder according to a particular embodiment. [Figure 4B] FIG. 10 is a block diagram of a shaping encoder according to another particular embodiment. [Figure 4C] FIG. 10 is a block diagram of a shaping encoder according to another particular embodiment. [Figure 5] 1 is a flowchart of a transmission method according to a particular embodiment; [Figure 6] FIG. 10 is a block diagram of a shaping encoder according to another particular embodiment. [Figure 7] FIG. 10 is a block diagram of a shaping encoder according to another particular embodiment. [Figure 8] 4 is a flowchart of a decoding method according to a particular embodiment; [Figure 9]2 is a diagram illustrating an example of a hardware architecture of a shaping encoder according to a particular embodiment; [Figure 10] 2 is a diagram illustrating an example of a hardware architecture of a decoding device according to a particular embodiment; DETAILED DESCRIPTION OF THE INVENTION

[0027] 1 shows a schematic diagram of a communication system 1 in which the present embodiment can be implemented. The communication system 1 comprises a transmitter 10 and a receiver 14 coupled to each other via a communication channel 12. The transmitter 10 is supplied with input data by at least one equiprobable binary source S0 and outputs symbols selected from a given alphabet X of symbols. The input data may be, for example, bits of an audio / video bitstream. In one exemplary embodiment, the alphabet X is an M-ASK constellation, where M=2 m where m is an integer. The symbols of the M-ASK constellation are defined as follows:

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[0028] As a result, each symbol in this constellation can be represented by a sequence of m=log2M bits. Figure 2 shows the symbols of an 8-ASK constellation, where the first symbol is -7 and the last symbol is 7. In the following, various embodiments are described with reference to ASK modulation. However, it will be understood that embodiments of the present invention are not limited to ASK modulation. By way of example, embodiments of the present invention may use QAM modulation.

[0029] Referring to Figure 1, let X be a function of the probability distribution p(x i )=p(X i =x i ), x i Let p(y|x i) is the channel distribution. For example, for a Gaussian channel, i Regarding p(y|x i )~N(x i ,σ 2 ) Let Y be the random variable of the communication channel output. For a Gaussian channel, Y is defined as Y = X + W, where W is Gaussian noise, e.g., W ~ N(0, σ 2 )

[0030] For a Gaussian channel, the signal-to-noise ratio (SNR) is defined as:

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[0031] Given any communication channel, p * Let (x) be the distribution of input X that maximizes the mutual information (MI) for a given constellation.

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[0032]

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[0033] The goal of stochastic shaping is to process the inputs so that their probability distributions maximize or nearly maximize the mutual information I(X;Y). In other words, if the distribution of the inputs is such that

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[0034] In M-ASK constellations, p(x) is often chosen as the MB distribution (an English acronym for Maxwell-Boltzmann distribution). Indeed, in this case, the performance obtained is * (x) (i.e., for small ε,

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[0035] According to a first particular embodiment defined to limit the complexity for the M-ASK case, the set of possible distributions is restricted to those that can be expressed as follows: All

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[0036] Therefore, according to the present principle, the M-ASK constellation is divided into M / 2 sets, each set of index i having

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[0037] Thus, a shaping encoder according to one embodiment selects one of the M / 2 sets with equal probability (i.e., α). i is chosen randomly, and therefore with probability p i Set i transmit the first symbol of i The second symbol is transmitted with the set . An error correcting code may be used to select the set. i For each, probability p i is known by both the transmitter and the receiver.

[0038] According to a second particular embodiment defined to limit the complexity for the M-ASK case, the set of possible distributions is restricted to those that can be expressed as follows: All

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[0039] Therefore, according to the present principle, the M-ASK constellation is divided into M / 2 sets, each set of index i having

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[0040] Thus, a shaping encoder according to one embodiment selects one of the M / 2 sets with equal probability (i.e., α). i is chosen randomly, and therefore with probability p i Set i transmit the first symbol of i The second symbol is transmitted with the set . An error correcting code may be used to select the set. i For each, probability p i is known by both the transmitter and the receiver.

[0041] In the first embodiment, the probability value p i is calculated offline for a given channel distribution. For example, for a Gaussian distribution of noise in the channel, the probability value p i is calculated offline once and therefore does not change thereafter.

[0042] In the second embodiment, the probability value p i is calculated offline for a given range of parameters of the communication channel and stored in a table shared between the transmitter 10 and the receiver 14. For example, if the channel distribution is Gaussian, the parameter can be the SNR of this communication channel. Thus, in the table, p iOne predetermined set of values ​​is associated with each predetermined range of SNR values, so that the transmitter 10 selects p from the table in response to the current SNR value. i A predetermined set of values ​​is selected and the receiver 14 is notified accordingly.

[0043] In a third embodiment, the channel distribution is estimated by the receiver 14 after receiving the pilot symbols. Then, the receiver 14 calculates p i The receiver 14 optimizes the values ​​of p and feeds them back to the transmitter 10 by using a signaling channel. Alternatively, the receiver 14 estimates the channel distribution and transmits the estimated channel distribution to the transmitter 10. The transmitter 10 then i values ​​and feeds these back to the receiver 14. i The optimization step for the set of values ​​can be a linear search, i.e., the set of possible p i Define a subset of values ​​and calculate the mutual information associated with the estimated channel distribution. i The value is the one that maximizes the mutual information. i The set of values ​​is obtained by solving an optimization problem such as equation (1), where the following constraints, p i+M / 2 =1-p i Ga p i applied to the value.

[0044] For an M-ASK constellation where each symbol in the constellation is represented by a binary sequence with natural labeling with the less significant bit on the left, as shown in Figure 3A, the shaping encoder 100 can be implemented as shown in Figures 4A and 4B, where the most significant bit b m are the shaping bits. The natural labeling of the 8-ASK constellation is given by Table 1 below. [Table 3]

[0045] For an M-ASK constellation where each symbol in the constellation is represented by a binary sequence using Gray labeling with the less significant bit on the left, as shown in Figure 3B, the shaping encoder 100 can be implemented as shown in Figure 4C. The Gray labeling for the 8-ASK constellation is provided by Table 2A below. [Table 4]

[0046] In this case, the shaping bit is b m-1 and so the shaping bit is not the most significant bit.

[0047] In one variant, a different gray labeling is used, as shown in Table 2B, where the last two rows are inverted compared to Table 2A. In this latter case, the shaping encoder 100 can be implemented as shown in FIG. 4A, with the most significant bit b m is the formatting bit. [Table 5]

[0048] The shaping encoder 100 is part of the transmitter 10. The shaping encoder 100 includes a switch 102 and a symbol mapper 104 that can use natural labeling or gray labeling, and is configured to implement a shaping method as shown in the flowchart of FIG. 5. Optionally, the shaping encoder 100 further includes an ECC (Error Correction Code) module 106, also called a channel coding module. The ECC module 106 typically receives k*(m-1) bits as input and outputs n*(m-1) bits, where k and n are predetermined integer values, e.g., k=500 and n=1000. The larger n*(m-1) (for a given ratio k / n), the better the performance. However, the latency increases with n*(m-1).

[0049] 4A and 4C, a shaping encoder 100 receives binary information sources S0 to S2 m-1 Bits are supplied by S max Let S+1 be the number of distinct binary sources (i.e., including S0). max =2 m-1 The source S0 outputs multiple bits with equal probability p(0) = p(1) = 1 / 2. i∈[1;2 m-1 ], each source Si has probability p i outputs a 0 bit, so with probability (1-p i ) to output a 1 bit.

[0050] 4B, the shaping encoder 100 is fed by a single binary source S0 that outputs multiple bits with equal probability p(0)=p(1)=1 / 2. In this case, the sources S1-S2 m-1 From this single source S0, for example, by using a binary DM (an English acronym for distribution matcher), that is, by m-1 Binary DMs are disclosed, for example, in Boehnke et al., "Polar coded distribution matching," Electron. Lett., vol. 55, no. 9, pp. 537-539, 2019. However, embodiments of the present invention use information sources S1 to S2. m-1 It will be understood that the present invention is not limited to this particular method of obtaining .

[0051] If the shaping encoder 100 of FIG. 4B does not include an ECC module for each given source S i , then D mi takes as input the

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[0052] In the example in which the shaping encoder 100 of FIG. 4B includes an ECC module 106 that encodes k*(m-1) bits into n*(m-1) bits and repeats this operation r times, each DMi has as input the

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[0053] Returning to Figure 5, in step S300, (m-1) bits are obtained from source S0. In one embodiment (natural labeling), these (m-1) bits are divided into (b1, b2, ..., b m-1 ) which forms the LSB of the symbol. The M-ASK constellation is

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[0054] In another embodiment (gray labeling in Table 2B), these (m-1) bits are (b1, b2,..., b m-1 ) which forms the LSB of the symbol. The M-ASK constellation is

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[0055] In another embodiment (gray labeling of Table 2A), these (m-1) bits are the bits (b1, b2,..., b m-2 ,b m )

[0056] In step S302, 2 m-1 Among the binary information sources, one information source Si is selected by the switch 102, corresponding to the (m-1) bits obtained from S0. In fact, for each possible binary sequence of (m-1) bits, m-1 A set of individuals (hence, 2 m-1 In the case of natural labeling or gray labeling in Table 2B, the index i of the selected set / source is a binary sequence (b1, b2, ..., b m-1 ) decimal value D(b1,b2,...,b m-1 ) is increased by 1, i.e., 1+D(b1,b2,...,b m-1 ) Each symbol in the constellation is represented by a binary sequence with natural labeling with the more significant bit on the left, and has the value

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[0057] In step S304, a bit called a shaping bit is obtained from this selected information source. In the case of natural labeling and the gray labeling of Table 2B, the obtained bit is the MSB b m In the case of gray labeling in Figure 2A, the resulting 1 bit is b m-1 Therefore, the (m-1) bits obtained in S300 control the switch to select one source from which the MSB is output, for example, in the case of natural labeling and gray labeling in Table 2B.

[0058] Therefore, in step S306, the symbol mapper 104 generates a symbol to be transmitted corresponding to the binary word formed by the (m-1) bits (b1, b2, ..., b3) obtained in S300 as the LSB and the selected one bit obtained in S304 as the MSB in the case of the natural labeling and the gray labeling of Table 2B. Therefore, in the case of the gray labeling of Table 2A, the symbol mapper 104 generates a symbol to be transmitted corresponding to the binary word formed by the (m-1) bits (b1, b2, ..., b3) obtained in S300 as the MSB. m-2 ,b m ), and the selected one bit b obtained in S304 m-1 Therefore, the binary word is formed by (b1, b2, ..., b m-1 ,b m ), with the LSB on the left.

[0059] In step S308, the resulting symbols are transmitted to receiver 14 via communication channel 12. Steps S300 to S308 can be repeated for the next set of (m-1) bits.

[0060] 4A or 4C includes an ECC module 106 that outputs n sets of (m-1) bits, each set of (m-1) bits is used independently to select one information source S i and thus one shaping bit in step S302. In other words, steps S300 to S308 are repeated for each set of (m-1) bits output by the ECC module 106.

[0061] Below we provide an example for M=8 and m=3, in which case the various sets are defined in the table below. [Table 6]

[0062] From the two bits "10" obtained from S0 in S300, the set of index 2 is selected, so the switch 102 is positioned to select the source S2 in S302. If the bit obtained from S2 in S304 is "1", the resulting binary word is "101", so it is mapped to symbol 3 of the constellation in S306. Symbol 3 is therefore output by the symbol mapper 104 and transmitted in S308.

[0063] In another example, where the two bits obtained from S0 in S300 are "11", the set with index 4 is selected in S302. The switch is positioned at source S4. If the bit obtained from S4 in S304 is "1", the symbol mapper outputs symbol 7 (corresponding to the binary word "111") in S306. If the bit obtained from S4 in S304 is "0", the symbol mapper outputs symbol "-1" (corresponding to the binary word "110") in S306.

[0064] Below we provide another example for M=8 and m=3, in which case the various sets are defined in the table below. [Table 7]

[0065] From the two bits "10" obtained from S0 in S300, the set of index 2 is selected, and thus switch 102 is positioned to select source S2 in S302. If the bit obtained from S2 in S304 is "1", the resulting binary word is "110", and thus is mapped to symbol -3 of the constellation in S306 (see Table 2 for Gray labeling). Symbol -3 is therefore output by symbol mapper 104 and transmitted in S308.

[0066] In another example, where the two bits obtained from S0 in S300 are "01", the set with index 4 is selected in S302. The switch is positioned at source S4. If the bit obtained from S4 in S304 is "1", the symbol mapper outputs symbol 1 (corresponding to the binary word "011") in S306. If the bit obtained from S4 in S304 is "0", the symbol mapper outputs symbol "7" (corresponding to the binary word "001") in S306.

[0067] For some channels, such as Gaussian channels, p * (x) is symmetric. As a result,

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[0068] Referring to Figure 3A, p3 = 1 - p2 and p4 = 1 - p1. Taking this symmetry into account, the shaping encoder 100 of Figure 4A can be further simplified as shown in Figure 6. The number of binary sources is divided by 2, and bit reversal is used when some sources are selected. In this case, S max =2 m-2 is.

[0069] b1,b2,...,b m-1 Let be the m-1 bits obtained from the binary information source S0 in S300.

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[0070] Below we provide an example for M=8 and m=3, in which case the various sets are represented in the table below: In this case, only three binary sources (S0, S1 and S2) are needed instead of five. [Table 8]

[0071] From the two bits "10" obtained from S0 in S300, the set of index 2 is selected, so the switch 102 is positioned to select the source S2 in S302. If the bit obtained from S2 in S304 is "1", the resulting binary word is "101", so it is mapped to symbol 3 of the constellation in S306. Symbol 3 is therefore output by the symbol mapper 104 and transmitted in S308.

[0072] In another example, where the two bits obtained from S0 in S300 are "11", the set with index 4 is then selected. Therefore, the switch 102 is positioned to select the information source S1 in S302. If the one bit obtained from S1 in S304 is equal to "1", it is inverted (i.e., changed to 0) by the inversion module 108. Finally, the symbol mapper outputs the symbol "-1" (corresponding to the binary word "110"). If the one bit obtained from S1 in S304 is equal to "0", it is inverted (i.e., changed to 1) by the inversion module 108. Finally, the symbol mapper outputs the symbol "7" (corresponding to the binary word "111"). Therefore, bit inversion is only applied when the sets with indexes 3 and 4 are selected.

[0073] In one variant (not shown in FIG. 6), the shaping coder 100 is fed by a single binary source S0 that outputs multiple bits with equal probability p(0)=p(1)=1 / 2. In this case, the sources S1-S2 m-2 From this single source S0, we use a binary DM (an acronym for distribution matcher) to generate a set of sources S1 to S2, as shown in Figure 4B. m-2Therefore, if the shaping encoder does not have an ECC module for each given source Si, then DMi takes as input the ECC modules generated by the source S0.

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[0074] In the example where the shaping encoder comprises an ECC module that encodes k*(m-1) bits into n*(m-1) bits and repeats this operation r times, each DMi takes as input the

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[0075] Referring to Figure 3B (Gray labeling of Table 2A), p1 = p3 and p2 = p4. Taking this symmetry into account, the shaping encoder 100 of Figure 4C can be further simplified by dividing the number of binary sources by 2. In this case, the selected binary sources are those with indices D(b1, b2, ..., b m-2 ,b m )+1 mod(M / 2+1).

[0076] In the case of the gray labeling of Table 2B, the shaping encoder 100 of FIG. 4A can be further simplified by dividing the number of binary sources by 2. In this case, the selected binary sources are the binary sources with indices D(b1, b2, ..., b m-1 )+1 mod(M / 2+1).

[0077] To further reduce complexity, the number of distinct binary information sources can be reduced by forcing adjacent symbols to have the same probability. For example, in the case of 8-ASK, p2 is set equal to p1. i The symbols associated with select bits from the same binary source. max Even if is small (e.g., equal to 2),

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[0078] Generally, only a single binary information source S0 is available. In one example, the binary information source S0 is equiprobable. Therefore, as shown in FIG. 4B, additional binary information sources are derived from the single binary information source S0. FIG. 7 shows a shaping encoder 100 according to a particular embodiment in which two additional binary information sources are derived from the single binary information source S0. In this embodiment, S max = 2 and bits must be processed packet by packet (e.g., due to latency or system constraints). i ) is the parameter p i First, let us represent the binary entropy with the information source S0 as follows:

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[0079] Switch to first DM

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[0080] Once the M-ASK symbols are obtained using any of the shaping coders described above with respect to Figures 4A-7, the transmitter 10 transmits them across several dimensions, such as polarization, time, frequency, and space. For example, the transmitter 10 can group two ASK symbols in a complex symbol, one real part and the other imaginary part. In this case, the M-ASK modulation is also referred to as QAM modulation.

[0081] In various embodiments, the shaping encoder 100 may optionally include an ECC module 106 that is used to encode the less significant bits. In one example, the ECC module is configured to encode these bits using multi-level polar coding. The principles of multi-level coding are disclosed below.

[0082] The mutual information between the input X and output Y of a communication channel can be expressed using the chain rule as follows:

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[0083] The 1-bit level is I(B i ;Y|B1,...,B i-1 ) when transmitting information over this ith level using a binary code, the coding rate is I(B i ;Y|B1,...,B i-1 ) In practice, a backoff is applied that depends on the code used. The communication channel can also be characterized by the log-likelihood ratio (LLR).

[0084] B1=b1,...,B i-1 =b i-1 Given

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[0085] Since the bits at the first level remain equally probable, p(B i =1|B1=b1,...,B i-1 =b i-1 )=p(B i =0|B1=b1,...,B i-1 =b i-1 )=0.5 and the mutual information is calculated as follows:

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[0086] Regarding the last bit level used for formatting,

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[0087] For the range of SNRs considered, the shaped bits b m does not need to be coded using a channel code. m |B1,...,B m-1) is equal to the entropy of the corresponding level, i.e., the communication channel is "clean". m is not encoded with a channel code in the above disclosed embodiment. As a result, the value of k in FIG.

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[0088] Then multilevel polar coding simply means that each bit level has a rate I(Y;B i |B1,...,B i-1 ) The block length refers to the size of the polar code used.

[0089] At the receiver side, the polar codes are decoded using list decoding, as disclosed in Tal et al., "List decoding of polar codes," IEEE Transactions on Information Theory, vol. 61, no. 5, pages 2213-2226, (2013). The list decoder performs MAP decoding. As a result, the decoder takes the LLRs as input (see equation (2)), which requires knowledge of the input distribution to be calculated. In other words, the receiver uses p i You need to know the value of .

[0090] FIG. 8 shows a flowchart of a decoding method according to a particular embodiment.

[0091] In step S400, the index i of the set, and therefore of the information source selected at the transmitter in step S302, is first obtained. If the set selection is performed block-wise by the transmitter using an error correction code, the index i is obtained by channel decoding (i.e., a block of indices of the set are decoded together).

[0092] In step S402, when the set index i is decoded, one of the two symbols in set i is detected based on the received y. Most channel decoders perform maximum a posteriori (MAP) decoding. The detection of the transmitted symbols in set i can also perform MAP detection. MAP decoding requires knowledge of the input distribution. In other words, the receiver must know p for efficient decoding. i You need to know the value of .

[0093] In some cases, it is sufficient to perform maximum likelihood (ML) detection on set i (because the reliability is high enough that posterior probabilities do not need to be taken into account). As a result, p i Knowledge of can only be used by the channel decoder.

[0094] In step S404, inverse mapping is applied to recover bits from the detected symbols. This step is the inverse of step S306. In step S406, the inverse of step S302 is applied. Thus, switch 102 is positioned to transmit the shaped bits to the appropriate source, i.e., the MSB bits in the case of natural labeling or gray labeling in Table 2B. Optionally, if binary DM is used at the transmitter side, inverse binary DM is applied.

[0095] If bit reversal is applied at the transmitter side, bit reversal is applied at the receiver side by the reversal module 108 in step S406.

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[0096] FIG. 9 illustrates a schematic diagram of an example hardware architecture of a transmitter 10, according to a particular embodiment.

[0097] The transmitter 10 comprises a processor or CPU (acronym for Central Processing Unit) 111, a random access memory RAM 112, a read-only memory ROM 113, a storage unit 114 such as a hard disk or a storage medium reader, for example an SD (acronym for Secure Digital) card reader, and at least one set of communication interfaces COM 115 that allow the transmitter 10 to send and receive data, connected by a communication bus 110.

[0098] The processor 111 is capable of executing instructions loaded into the RAM 112 from the ROM 113, from an external memory (such as an SD card), from a storage medium (such as a HDD), or from a communication network. When the transmitter 10 is powered on, the processor 111 is capable of reading and executing instructions from the RAM 112. These instructions form a computer program that causes the processor 111 to perform the methods described with respect to Figures 4A-7.

[0099] The methods described with respect to Figures 4A-7 may be implemented in the form of software by execution of a set of instructions by a programmable machine, for example a DSP (acronym for Digital Signal Processor), microcontroller or GPU (acronym for Graphics Processing Unit), or in the form of hardware by a machine or dedicated component (chip or chipset), for example an FPGA (acronym for Field Programmable Gate Array) or an ASIC (acronym for Application Specific Integrated Circuit). Generally, the transmitter 10 includes electronic circuitry adapted and configured to perform the methods described with respect to Figures 4A-7.

[0100] FIG. 10 illustrates a schematic diagram of an example hardware architecture for receiver 14, according to a particular embodiment.

[0101] The receiver 14 comprises a processor or CPU (acronym for Central Processing Unit) 201, a random access memory RAM 202, a read-only memory ROM 203, a storage unit 204 such as a hard disk or a storage medium reader, for example an SD (acronym for Secure Digital) card reader, and at least one set of communication interfaces COM 205 that enable the receiver 14 to send and receive data, connected by a communication bus 210.

[0102] The processor 201 is capable of executing instructions loaded into the RAM 202 from the ROM 203, from an external memory (such as an SD card), from a storage medium (such as a HDD), or from a communication network. When the receiver 14 is powered on, the processor 201 is capable of reading and executing instructions from the RAM 202. These instructions form a computer program that causes the processor 201 to perform the method described with respect to FIG.

[0103] The method described with respect to Figure 8 may be implemented in the form of software by execution of a set of instructions by a programmable machine, for example a DSP (acronym for Digital Signal Processor), a microcontroller or a GPU (acronym for Graphics Processing Unit), or in the form of hardware by a machine or dedicated component (chip or chipset), for example an FPGA (acronym for Field Programmable Gate Array) or an ASIC (acronym for Application Specific Integrated Circuit). Generally, the receiver 14 includes electronic circuitry adapted and configured to perform the method described with respect to Figure 8.

Claims

1. A method in a transmitter for transmitting binary data using an M-ASK constellation divided into M / 2 sets of two symbols, each set of index i having a probability p ｉ and the probability of transmitting the second symbol of each set, 1-p ｉ and each symbol of the M-ASK constellation is associated with a binary word defined using a given labeling, and the method comprises: a) Obtaining m-1 bits from a binary source, where m=log ２ Being a masochist, b) selecting a binary information source corresponding to the m-1 bits from a plurality of binary information sources, each binary information source with index i being p ｉ and c) obtaining one bit from the selected binary information source; d) obtaining symbols of the M-ASK constellation associated with the binary word formed by the m-1 bits obtained from the binary information source and the 1 bit obtained from the selected binary information source; e) transmitting the resulting symbols to a receiver over a communication channel; Including, The given labeling is a Gray labeling, and the M / 2 sets are composed of a set of index i including the i-th symbol and the M / 2+i-1th symbol, and a set of index M / 2+i including the M / 2+ith symbol and the M / 2+M / 2+1-ith symbol, where i∈[1;M / 4].

2. 2. The method of claim 1, wherein the m-1 bits obtained from the binary information source are less significant bits of the binary word, and the 1 bit obtained from the selected binary information source is a most significant bit of the binary word.

3. The method of claim 1 or 2, wherein the binary information sources are equiprobable.

4. Selecting a binary information source corresponding to the m-1 bits from the plurality of binary information sources includes: determining a decimal value of a binary sequence formed by said m-1 bits; selecting a binary information source whose index is equal to said decimal value incremented by one; 3. The method of claim 1 or 2, comprising:

5. The plurality of binary information sources are ｍ－１ The method of claim 1 or 2, comprising binary information sources.

6. Each binary information source with index i in the plurality of binary information sources is [Equation 1] obtained from the binary information source by applying binary distribution matching to a sequence of bits, where S ｍａｘ is the number of sources in the multiple binary sources, and H(p ｉ ) is the parameter p ｉ 3. The method of claim 1, wherein r is an integer greater than or equal to 1.

7. The method comprises: channel encoding r*(m-1)*k bits obtained from the binary information source into r*(m-1)*n bits using an error correcting code, where n and k are integers, and r is an integer greater than or equal to 1; obtained from the binary information source [Equation 2] obtaining each binary information source of index i in the plurality of binary information sources from the binary information source by applying binary distribution matching to a sequence of bits, wherein S ｍａｘ is the number of information sources in the plurality of binary information sources, and H(p ｉ ) is the parameter p ｉ Denote the binary entropy with applying a) to e) to each of n sets of (m-1) bits; The method of claim 1 or 2, further comprising:

8. From the table, the probability p ｉ and transmitting to the receiver at least one index entry indicative of the obtained probability.

9. From a given communication channel distribution, the probability p ｉ 7. The method of claim 6, further comprising estimating the probability .times. ...

10. The receiver sends the probability p ｉ The method of claim 6 , further comprising receiving:

11. 1. A transmitter configured to transmit binary data using an M-ASK constellation divided into M / 2 sets of two symbols, each set with index i having a probability p ｉ and the probability of transmitting the second symbol of each set, 1-p ｉ and each symbol of the M-ASK constellation is associated with a binary word defined using a given labeling, and the transmitter a) Obtaining m-1 bits from a binary source, where m=log ２ Being a masochist, b) selecting a binary information source corresponding to the m-1 bits from a plurality of binary information sources, each binary information source with index i being p ｉ and c) obtaining one bit from the selected binary information source; d) obtaining symbols of the M-ASK constellation associated with the binary word formed by the m-1 bits obtained from the binary information source and the 1 bit obtained from the selected binary information source; e) transmitting the resulting symbols to a receiver over a communication channel; at least one processor configured to: The given labeling is Gray labeling, and the M / 2 sets are composed of a set of index i including the i-th symbol and the M / 2+i-1th symbol, and a set of index M / 2+i including the M / 2+ith symbol and the M / 2+M / 2+1-ith symbol, where i∈[1;M / 4].

12. 12. The transmitter of claim 11, wherein the m-1 bits obtained from the binary information source are less significant bits of the binary word and the 1 bit obtained from the selected information source is the most significant bit of the binary word.

13. 3. A computer program comprising program code instructions loadable into a programmable device, said program code instructions causing the programmable device to perform the method of claim 1 or 2 when said program code instructions are executed by said programmable device.

14. 3. A storage medium storing a computer program including program code instructions that, when read from the storage medium and executed by a programmable device, cause the method of claim 1 or 2 to be performed.

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