Method for achieving relative decoding of an OFDM frame

Abstract

The invention relates to a method for decoding a coded frame at the output of a transmission channel, said coded frame comprising coded symbols including encoding on data relating to relative offsets between initial variables, the method comprising the following steps: - obtaining, from the coded frame, a tensor of relative distributions (P) comprising a plurality of relative distributions (Pi / i') representing probabilities of relative deviations between two given coded symbols (i, i'), - obtaining coding relationships (S) linking the coded symbols and translating relative relationships between the coded symbols, and supplementing them based on at least one symmetry and / or transitivity relationship between the relative distributions, - based on the coding relationships thus supplemented, expressing relative relationships between the relative distributions, - determining an estimate of decoded symbols via a probabilistic decoding processing operation using the coding relationships (S).

Description

Description Title: Relative decoding method for an OFDM frame technical field

[0001] This disclosure falls within the domain of communication systems coupled with error correction mechanisms, and more specifically concerns a decoding process working on a relative representation of information. Previous technique

[0002] In order to transmit the elements (or symbols) of a message or information through a communication system, modulation (in transmission) and demodulation (in reception) processes are implemented to adapt the message to the transmission channel of the communication system.

[0003] For various reasons, some communication systems (and therefore the associated modulation and demodulation processes) rely on a relative (or differential, as opposed to an absolute) representation of information for its transmission and / or processing. Typically, some receiving processes in communication systems involve processing received information not by considering estimated absolute values ​​for each received symbol, but relative differences or shifts between symbols.

[0004] An example of relative information representation can be simply illustrated by considering a frame of 5 symbols [x0,x1,x2,x3,x4], each symbol encoding k bits of information and therefore able to take 2 k possible values. A relative representation of such a frame could, for example, be [x0 / 1,x1 / 2,x2 / 3,x 3 / 4 ] = [0—x1,x1—x2,x2—x3,x4—3],

[0005] In another example illustrating a possible context for using a relative representation of information, the modulation known as CCSK (Cycling Code Shift Keying) allows two bits (or more, depending on the sequence size) of information to be modulated orthogonally to represent a sequence through rotations of that sequence. Thus, considering a sequence of four complex symbols [a; b; c; d], the binary word '00' could correspond to the transmission of the sequence [a; b; c; d]; the binary word '01' could correspond to the transmission of the sequence [d; a; b; c]; the binary word '10' could correspond to the transmission of the sequence [c; d; a; b], and so on. Such modulation allows information to be encoded relative to a reference sequence, so that the symbols are independent of each other. In particular, a transmission error affecting one CCSK symbol does not affect subsequent symbols.

[0006] The CCSK modulation implemented allows the sequence to be represented as a time-frequency frame, called a CCSK-CP-OFDM frame, in which each of the N K-sized CCSK symbols to be transmitted is transmitted on one of the N time steps and on K frequency subcarriers. Upon reception, such a CCSK-CP-OFDM frame can then be processed by considering a relative representation of the information, for example, through equalization processes. of the transmission channel, to obtain a representation of the frame in the form of a matrix (or tensor) P of probability distributions of relative shifts between symbols of the frame: [Math. 1]

[0007] In particular, each coefficient Pi / j of such a matrix contains a vector of size K (the size of a CCSK symbol) representing the relative shift probabilities between symbols i and j. For example, for a frame containing N=5 CCSK symbols of size K=4 (each encoding 2 bits of information), if P3 / 5 = [ 0.2 ; 0.3 ; 0.1 ; 0.4 ], this means that the probability of a zero shift of symbol 3 with respect to symbol 5 is 0.2, the probability of a shift of one of symbol 3 with respect to symbol 5 is 0.3, the probability of a shift of two of symbol 3 with respect to symbol 5 is 0.1 and the probability of a shift of three of symbol 3 with respect to symbol 5 is 0.4. Thus, the matrix P determined upon reception of a frame allows us to estimate that the most probable offset of the symbol 3 relative to the symbol 5 is Argmax(Ps / 5) = 3.

[0008] The relative representation of information (for example, obtained by considering relative shift probabilities between CCSK symbols in reception, from a CCSK-CP-OFDM type modulation in transmission, as described previously) then offers several advantages, particularly exploitable in information reception. In particular, it allows, during reception processing, for enriching symbol estimation and exploiting information redundancy by leveraging the relationships between the received relative information. For example, the received matrix P reflects symmetry and / or chaining (also called transitivity) relationships between the coefficients. Typically, P / j (relative shift probabilities of symbol i with respect to symbol j) and Pj / i (relative shift probabilities of symbol j with respect to symbol i) are related; P / aPa / j and Pi / j are also related. More generally, the relative representation of information allows a transmitted frame (e.g., in CCSK symbols or with any other modulation) to be represented, upon reception, by multiple estimates of the transmission channel (i.e., each transmission reflects a possible estimate of the relationships between the symbols). Combining these relative estimates during frame reception processing then improves the estimation of each symbol's value. Frame reception processing thus relies on processes working with a relative representation of the symbols.

[0009] Furthermore, in order to mitigate errors and transmission defects (e.g., those related to noise) of the message (regardless of its relative or absolute representation), it is known to use error correction mechanisms, notably error-correcting codes (ECCs), which rely on the redundancy of the transmitted information. Most error-correcting codes are linear codes, a simple example of which is the repetition code. which consists of sending each symbol of the message to be transmitted several times (thus creating redundancy of information), in order to increase the probability of detecting inconsistencies in the message and obtaining the correct symbols at reception.

[0010] In order to combine the advantages of both relative information representation and error correction in message transmission, it is necessary to adapt error correction mechanisms to the relative nature of the information representation chosen for processing upon reception. In particular, decoding the received information requires taking this specificity into account. Furthermore, there is also a need to leverage both the redundancy obtained by the error correction mechanism and by the relative information representation (typically, considering the matrix above illustrating a relative representation of the information frame, there is information redundancy when considering, on the one hand, the relative offset of a symbol x with respect to a symbol y, and on the other hand, the relative offset of the symbol y with respect to the symbol x).Finally, there is also a need to improve the efficiency and performance of the cumulative demodulation and decoding processes, whose often iterative nature multiplies the complexity and processing time at the output of the transmission channel. Summary

[0011] This disclosure is intended to address such a problem.

[0012] A method is proposed for decoding a coded frame output from a transmission channel, said coded frame being associated with a source message comprising a plurality of initial variables and transmitted over said transmission channel, said coded frame comprising data relating to a plurality of coded symbols, said coded symbols including an encoding on data relating to relative shifts between the initial variables, the method comprising the following steps: from the coded frame, obtain a tensor called relative distributions, said relative distributions tensor comprising a plurality of probability distributions called relative distributions, each relative distribution representing probabilities of relative differences between two given coded symbols, obtain coding relations linking the coded symbols, said coding relations depending on the encoding and translating relative relations between the coded symbols,Starting from at least one symmetry relation and / or a transitivity relation between the relative distributions of the relative distribution tensor, complete the coding relations with additional relations; from the coding relations, express relative relations between the relative distributions. determine, via a probabilistic decoding process using coding relations, an estimate of decoded symbols forming the decoded frame.

[0013] Therefore, the proposed method enables the decoding of a received symbol frame by leveraging a relative representation of the source information. This representation is predicted and encoded during transmission at the encoding stage and is represented at reception by considering the relative relationships between the received encoded symbols. Specifically, such a relative representation underlies the received symbols, which are absolute and formatted for transmission via the communication system. The proposed decoding method relies on processes specifically adapted to relative space to implement optimized frame decoding, enabling an enriched reconstruction of the source information.

[0014] In particular, the method proposes to manipulate not variables representing the values ​​of the symbols, but relative distributions reflecting probability vectors of observed deviations between the symbols (such a deviation could, for example, correspond to a difference between numerical values ​​associated with the received symbols, such as a cyclic shift of a sequence relative to a reference sequence, or a deviation between received CCSK symbols, or even to a difference in angle or phase in the case of QPSK (Quadrature Phase Shift Keying) modulation or to a difference in amplitude or phase in the case of QAM (quadrature amplitude modulation) modulation).This type of data allows for probabilistic decoding, which can be enriched by the information redundancies observed in the distributions, not only due to the encoding, but also due to the relationships imposed by the encoding and / or deducible from the relative distribution tensor (e.g., symmetry or transitivity relationships linking relative distributions in the tensor). The relative representation of information thus multiplies the information on which decoding can be based (e.g., a distribution of possible deviations of a symbol i from a symbol j is linked to a distribution of possible deviations of symbol j from symbol i).

[0015] The coding relationships thus contain so-called direct relationships, arising directly from the encoding phase, which link the received symbols. Such coding relationships can also be extended to include additional relationships, arising from symmetry and / or transitivity relationships resulting from the relative distributions in the matrix. These coding relationships then allow for the introduction of additional information redundancy (beyond the redundancy inherent in the encoding mechanism itself) in the decoding process, enriching the relationships that can be defined between the distributions (and therefore between the relative differences between the received symbols).

[0016] The features described in the following paragraphs may optionally be implemented, independently of each other or in combination with each other:

[0017] In one embodiment, the relative relationships expressed between the relative distributions include considering, from the received coded symbols, random variables representing differences (or relative shifts) between received symbols, such random variables following the associated relative distributions.

[0018] In one embodiment, the coding relations are further determined by associating the negation of a random variable with an inversion completed by a circular rotation of one positive step of the respective distribution.

[0019] In one embodiment, the relationships are further determined by associating the sum of two random variables with a convolution of their respective distributions.

[0020] In one embodiment, the probabilistic decoding process includes: from the coding relations, determining corrected relative distributions, and in which the decoded symbols are estimated from the corrected relative distributions.

[0021] In one embodiment, the decoded symbols are determined by estimating a relative shift between two decoded symbols by considering the maximum probability value in the associated relative distribution and estimating the values ​​of the decoded symbols from said estimate of the relative shift. The estimation of the values ​​of the decoded symbols may, in particular, be made from at least one pilot symbol of a fixed, known, or predetermined value.

[0022] In one embodiment, the probabilistic decoding process relies on a belief propagation algorithm, called Belief Propagation or BP, in which edges, variable nodes and parity nodes of a factor graph associated with said Belief Propagation algorithm translate the coding relations, the edges of said graph being associated with random variables representing relative shifts between the coded symbols received and according to the relative distributions.

[0023] In one embodiment, a propagation of a message in the factor graph corresponds to an update of at least one relative distribution associated with the edges involved in said propagation.

[0024] In one embodiment, the factor graph further includes negation nodes defining a negation relation of a random variable corresponding to an incoming edge on said negation node.

[0025] In one embodiment, the probabilistic decoding process is iterative and includes the following iterative steps, until a predefined stopping criterion is satisfied: calculate the messages from the variable nodes to the parity nodes, calculate the messages to the variable nodes, based on the messages received by the parity nodes.

[0026] In one embodiment, a set of outgoing messages from each variable node is determined by the product of all messages from the parity nodes.

[0027] In one embodiment, the corrected relative distributions are determined by the product of the relative distributions and the set of outgoing messages from the variable nodes of the factorization graph.

[0028] In one embodiment, the probabilistic decoding process relies on at least one element from among a symmetry relation and a transitivity relation linking the relative distributions present in the relative distributions tensor.

[0029] In one embodiment, the encoding relations include direct relations and symmetry and / or transitivity relations—also referred to as chaining—(arising respectively from a symmetry and / or a transitivity) linking the relative distributions present in the tensor of relative distributions, and the probabilistic decoding process includes at least one of the following: an iterative decoding process using the direct relations and the symmetric and / or transitivity relations alternately at each iteration, an iterative decoding process using the direct relations and the symmetric and / or transitivity relations cumulatively at each iteration, at least a first iterative decoding process using the direct relations and a second iterative decoding process using at least some of the symmetric and / or transitivity relations, the processes being parallelized and / or combined.

[0030] In one embodiment, the probabilistic decoding process is integrated with a demodulation process of the coded frame.

[0031] Therefore, it is proposed to optimize the receiving frame processing by combining the demodulation and decoding processes. Such joint processing saves time and storage space, and optimizes both processes, as one iteratively enriches the data processed by the other.

[0032] In one embodiment, the probabilistic decoding process and the demodulation process are iterative, and in which each iteration of the demodulation process includes several iterations of the probabilistic decoding process.

[0033] In one embodiment, at each iteration of a demodulation process, the probabilistic decoding process alternates between the use of one or more coding relations from the encoding and the use of symmetry and / or transitivity relations.

[0034] According to another aspect, a decoder is proposed comprising at least one processing unit including at least one processor configured to implement the proposed decoding process.

[0035] In another aspect, a joint decoding and demodulation unit is proposed, comprising at least one processing unit including at least one processor configured to implement the proposed decoding method. In particular, the processor can be configured to implement the proposed decoding process in conjunction with a demodulation process, as described previously.

[0036] In another aspect, a computer program is proposed that includes instructions for implementing all or part of a decoding process as defined herein when executed by a processor. In another aspect, a non-transient, computer-readable recording medium is proposed on which such a program is recorded. Brief description of the drawings

[0037] Other features, details, and advantages will become apparent upon reading the detailed description below and analyzing the attached drawings, on which: Fig. 1

[0038] [Fig. 1] shows a communication system comprising a decoder according to an embodiment of the present. Fig. 2

[0039] [Fig. 2] shows steps of a process for receiving a frame encoded via a relative space according to an embodiment of the present. Fig. 3

[0040] [Fig. 3] shows steps of a process for decoding a frame encoded via a relative space according to an embodiment of the present. Fig. 4

[0041] [Fig. 4] illustrates a joint decoding and demodulation process according to one embodiment. Fig. 5

[0042] [Fig. 5] illustrates a probabilistic decoding treatment via a factorization graph according to one embodiment. Fig. 6

[0043] [Fig. 6] illustrates a probabilistic decoding treatment via a factorization graph according to one embodiment. Fig. 7

[0044] [Fig. 7] illustrates a probabilistic decoding treatment via a factorization graph according to one embodiment. Fig. 8

[0045] [Fig. 8] illustrates a probabilistic decoding treatment via a factorization graph according to one embodiment. Fig. 9

[0046] [Fig. 9] illustrates a probabilistic decoding treatment via a factorization graph according to one embodiment. Fig. 10

[0047] [Fig. 10] illustrates a probabilistic decoding treatment via a factorization graph according to one embodiment. Fig. 11

[0048] [Fig. 11] illustrates a probabilistic decoding treatment via a factorization graph according to one embodiment. Description of the implementation methods

[0049] Reference is now made to Figure 1. Figure 1 schematically illustrates a communication system 10 (e.g., wired or wireless) considered in this disclosure, configured to transmit a source information sequence, also referred to as the source message (e.g., an audio signal), from a source entity (e.g., an audio transmitter) to a destination entity (e.g., an audio receiver) via a transmission channel 14. Such a communication system 10 may include, in particular, an encoding entity, or encoder 12 (comprising a signal encoding unit 121 and a transmission channel encoding unit 122), a signal modulation unit, or modulator 13, the transmission channel 14, an equalization unit 150, a signal demodulation unit, or demodulator 15, and a decoding entity, or decoder 16 (comprising a transmission channel decoding unit 161 and a signal decoding unit). 162).

[0050] The encoder 12 is configured to transform the source message, for example an analog or digital signal, into so-called coded data. In particular, within the context of this description, the encoder 12 is configured to generate, from source information, coded symbols containing a relative representation of the information (e.g., by encoding differences or gaps between elements constituting the source information), while also generating absolute symbols that can be modulated in any way and transmitted via the transmission channel 14. In other words, the encoder 12 is configured to create coding relationships (or coding schemes) that will be usable at the receiver after relationships between received symbols have been considered.

[0051] The modulator 13 is configured to adapt the source information (in particular, encoded information) to the transmission channel 14, for example by adapting the information spectrum to the frequency range suitable for transmission. The modulation implemented by the modulation unit 13 can, for example, consist of transforming the encoded source information into a time-frequency frame composed of CCSK symbols distributed over a plurality of time steps, each CCSK symbol being distributed over a plurality of frequency subcarriers. Such an example of a frame obtained at the output of the modulator 13 can, for example, be illustrated as follows: [Math.

[0052] Such a source frame, denoted T sThe frame comprises N columns representing N time steps and K rows representing K frequency subcarriers. Each CCSK symbol in the frame, denoted c (where i is between 0 and N-1), corresponds to a symbol to be transmitted, obtained from the encoding entity using the relative encoding method 200. Each symbol Ci has a size K (e.g., is composed of K bits of information). The set of symbols CO,...CN-I thus constitutes a representation of the source information, containing, in particular, information redundancy due to the encoding.

[0053] Modulator 13 can correspond to any existing modulator, for example an OFDM or CCSK-CP-OFDM modulator, configured to adapt the symbols output from the encoding unit to the transmission channel in a T frame s , called CCSK-CP-OFDM as illustrated in [Math. 2], In particular, such modulation may be differential or not.

[0054] Once encoded (by encoder 12 in relative space) and modulated, the encoded and modulated source information is represented by a source frame of symbols T s The information, as illustrated in [Math. 2], can be transmitted via transmission channel 14. Transmission channel 14 then allows information to pass from the transmitting side 11, 12, 13 to a receiving side 150, 15, 16. Such a transmission channel 14 can, for example, correspond to a radio channel, a wired channel, or an optical channel. During such a transmission, transmission channel 14 is particularly likely to affect the T frame. s transmitted, for example by noise, so that the symbol frame T r received on the receiver side 150, 15, 16 differs from the T frame s transmitted. A problem on the receiver side (150, 15, 16) is then the processing – including demodulation and decoding – of the T frame rreceived, with a view to reproducing the source information as faithfully as possible. In particular, within the framework of this disclosure, receiving entities 150, 15, 16 are considered here—and specifically demodulators 15 and decoders 16 configured to implement processes based specifically on a relative representation of the received information (i.e., considering data relating to differences between the symbols of the received frame T). r .

[0055] The equalization unit 150 of the transmission channel is configured to implement symbol processing of the received frame T r , so as to determine a matrix (or tensor) P of probability distributions of relative shifts between symbols of the source frame T s, as illustrated in [Math. 1], Such an equalization unit and its equalization process are described in particular in the document [DFTLink] and in the description of figure 2.

[0056] The demodulation unit, or demodulator, 15 is configured to perform an operation inverse to that of the modulator 13, namely to extract the received symbols from the frequency subcarriers of the received frame T r .

[0057] In particular, in the context of this disclosure, such a demodulator 15 is connected to the output of the equalization unit 150 of the transmission channel, so that the demodulator 15 is configured to process a matrix (or tensor) P of probability distributions of relative shifts between symbols of the source frame T s , as represented in [Math.1],

[0058] From such a matrix P, the demodulator 15 is configured to determine a demodulated frame (containing coded demodulated symbols). The demodulator 15 and its demodulation process are described in particular in document [GLAD] and in the description of Figures 2 and 3.

[0059] The decoder 16 proposed in this disclosure is configured to receive and decode the frame demodulated at least partially by the demodulator 15. In particular, the decoder 16 is configured to implement a decoding of the demodulated symbols specifically adapted to the relative representation of the symbols, due to the relative encoding by the encoder 12 and the demodulation in relative space by the demodulator 15. For this purpose, the decoder 16 includes a processing circuit including at least one processor, a memory unit and communication means, enabling the implementation of a decoding process 300 of an encoded frame as described in Figure 3.

[0060] In a particular embodiment of the communication system 10, alternative to the representation in Figure 1, the structures of the demodulator 15 and the decoder 16 can be merged into a joint demodulation-decoding unit, with the respective demodulation and decoding processes being implemented jointly and feeding into each other. Such an embodiment is illustrated in Figure 4 – where the decoder 16 is integrated into the demodulator 15 – and will be described in more detail in Figures 2 and 3.

[0061] Reference is now made to Figure 2. Figure 2 illustrates steps in a 200 process for receiving a so-called received frame T r , comprising coded symbols output from a transmission channel 14 of a communication system as illustrated in Figure 1. In particular, such a method 200 can be implemented by a receiving side 150, 15, 16 of the communication system 10.

[0062] At an S200 stage, a frame is received T r is obtained at the output of transmission channel 14. Such a received frame T r results from the transmission, via channel 14, of a source frame T s of the CCSK-CP-OFDM frame type, for example, as represented in [Math. 2] and formed by symbols, or coded absolute variables co, ci, ..., c m -i (considering a number N=m of time steps). Such received absolute variables have notably been coded in transmission, so as to reflect relative relationships between source variables xo, xi, ..., xi-i forming the source information, when, in reception, the received symbols, denoted bo, bi, ..., b m -i, are processed to consider differences between symbols. Such a source frame T s is affected during its transmission via channel 14 by disturbances (e.g., noise), so that the received frame T rand the corresponding m symbols, denoted received symbols bo, bi, ..., b m -i differ from the transmitted symbols co, ci, ..., Cm-1. In other words, the values ​​of the coded symbols co, ci, ..., c m -i of the source frame T s issued can be understood as random variable draws (representing the source information, e.g., of letters of a word, the values ​​derived from the symbols representing given letters forming a word). On reception, the values ​​of the received symbols bo, bi, ..., b m -i can then be understood as the draws in transmission (unknown in reception) to which is added a draw (e.g., random) of the noise or of the transmission channel.

[0063] At an S210 step, the received frame T r and in particular the symbols contained bo, bi, ..., b m -i are processed by the equalization unit 150. For this, the received frame T ris interpreted by the equalization unit 150 as a sequence of values ​​of discrete random variables Xo, Xi, ..., X m -i, each random variable Xi (i being a numerical index between 0 and m-1) taking values ​​in a finite field FK of dimension K. For example, when the finite field FK corresponds to the binary field, K=2 and the bo, bi, ..., b m -i are sequences of values ​​from 0 or 1.

[0064] As described previously, the transmitted symbols co, ci, ..., c m -i just like the received symbols bo, bi, ..., b m -i then correspond to two sequences of draws from the sequence of discrete random variables Xo, Xi, ..., X m -i. Such a sequence of random variables Xi can then be understood as a word forming the source information.

[0065] In particular, each discrete random variable Xi follows a distribution law, denoted Dxi, representing the probability distribution of possible values ​​of the i-th transmitted symbol. The equalization unit 150 is then able to determine, for each discrete random variable Xi (Le, for each symbol i forming the source message), the associated distribution law Dxi. For example, such a distribution law Dxi can be determined by assuming a Gaussian transmission channel 14.

[0066] From such distributions Dxi, step S210 may also include determining a relative probability of shift between two symbols i and j, by a convolution (or cross correlation) operation between their respective distributions Dxi and Dxj.

[0067] More precisely, considering a sequence of random variables X = [X o X ... X m -i] e F™ of distribution law: It is possible to express a matrix (or tensor) containing the set of so-called differential random variables, namely Yt = X t — Xj e F ;< The corresponding distribution, denoted D Y , is obtained by:

[0068] where * corresponds to the cross convolution operator. Equivalently, in the context of modular arithmetic in a finite field FK, it would also be possible to consider random sum variables, namely Yi = Xt + Xj e F ;< The corresponding distribution, denoted D Y ..., is obtained by: Dy. . = Dy. « Bç .

[0069] where * this time corresponds to the convolution operator. In the remainder of this disclosure, differential random variables (Xi-Xj) are considered and the associated distributions are more simply denoted Pi / j.

[0070] Thus for each pair (i,j) e [0; m - l]2 In step S210, a probability distribution Pi / j of possible relative shifts of symbol i with respect to symbol j is determined. This results, at the end of step S210, in a tensor P of probability distributions of relative shifts between symbols of the source frame T. s , calculated from the received symbol values ​​bo, bi, ..., b m - 1:

[0071] As described previously, each coefficient Pi / j of such a matrix P contains a vector of size K (the size of a CCSK symbol, or more generally, the size of the finite field in which each symbol can take given values) with values ​​in the finite field FK, representing the relative shift probabilities between symbols i and j. In other words, each coefficient Pi / j contains a probability value for each possible value of a CCSK symbol. For example, for a source frame T scontaining N=5 CCSK symbols of size K= 4 (each encoding 2 bits of information), if P3 / 5 = [ 0.2 ; 0.3 ; 0.1 ; 0.4 ], this means that the probability of a zero shift of the symbol 3 with respect to the symbol 5 is 0.2, the probability of a shift of one of the symbol 3 with respect to the symbol 5 is 0.3, the probability of a shift of two of the symbol 3 with respect to the symbol 5 is 0.1 and the probability of a shift of three of the symbol 3 with respect to the symbol 5 is 0.4. Thus, the matrix P determined upon reception of a frame allows us to estimate that the most probable offset of the symbol 3 with respect to the symbol 5 is Argmax(Ps / 5) = 3. Such a representation can be calculated for any symbol frame without modifying the invention, regardless of the type of modulation (CCSK, QPSK, or QAM, etc.), and more broadly for any sequence of discrete random variables.For example, in the case of QPSK modulation, the difference operator can be adapted to estimate phase or angle shifts.

[0072] Demodulation and decoding steps are then implemented. In one embodiment, these steps are implemented successively (S220, S230). In another embodiment, these steps are implemented jointly via a single step (S231). The demodulation (S220) and decoding (S230) steps will be described separately hereafter; the joint implementation of these steps in a single step (S231) will be detailed later.

[0073] At step S220, the process of demodulating the data relating to the received frame T ris applied by a processing implemented on the tensor P obtained in step S210. In particular, such a demodulation step S220 includes a recombination of the relative Pi / j distributions, for example via the process described in the document [GLAD]. In particular, such a process relies on a probabilistic graphical iterative algorithm operating in two main steps: partial relative distributions are obtained using cross correlation and convolution operations on the relative Pi / j distributions, a recombination of the partial relative distributions by product.

[0074] Such an S220 demodulation step from the relative Pi / j distributions is for example shown schematically in figure 4. The greyed element 16 on figure 4 corresponds to the joint implementation of the decoding process in the demodulation process, which will be described later.

[0075] Referring to Figure 4, the demodulation considered is an iterative process, taking as input, on the one hand, the matrix P of relative distributions Pi / j and, on the other hand, values ​​of variables internal to the demodulation process, which can, for example, be initialized by default in a predefined way (e.g., with a uniform distribution) independently of the received frame T r The demodulation process considered then allows us to determine, at each iteration, relative up-to-date distributions contributing to the formation of an up-to-date matrix, denoted P, and internal up-to-date states (which are destined for the next iteration for further updates of the relative distributions).

[0076] At a step 151 of a considered iteration, the relative distribution matrix P is crossed with the internal states obtained at the end of the previous iteration (or the predefined initial states if it is the first iteration).

[0077] At step 152 of the iteration under consideration, the structure of the matrix P is used to combine related symbol distributions i, j. In other words, the matrix P is used to determine relationships between symbols i, j. For example, the P0 / i and P1 / 2 distributions of the matrix P can be related to improve the estimation of the P0 / 2 distribution. In another example, the Pi / j distributions can be used to improve the estimation of the Pj / i distributions.

[0078] At steps 153 and 154 of the iteration under consideration, updated distributions progressively forming the updated matrix, and updated internal states are determined. In particular, at step 153, certain internal variables can be masked to avoid self-influence loops over the iterations of the demodulation process (e.g., to calculate an updated distribution of P2 / 3 at the next iteration, the current value (intrinsic information) of P2 / 3 can be masked).

[0079] The S220 demodulation process can, for example, be stopped when all the Pi / j distributions have been updated, and / or according to any other stopping criterion (e.g., accuracy of the obtained distributions, number of iterations, number of information combinations performed, etc.). This results in a matrix of updated distributions P, containing relative distributions updated with respect to the Pi / j distributions output from the equalization unit 150. In particular, the matrix P has a shape similar to the P matrix output of the equalization unit 150 (e.g., from the algorithm described in the [DFTLink] document).

[0080] To simplify the description of the sequence, and in particular because the demodulation and decoding processes can be considered jointly, reference will henceforth be made generally to the Pi / j distributions and the tensor P for the description of the decoding process. It is understood that in the context of decoding, the relative Pi / j distributions considered can correspond to those from the matrix P (at the output of the equalization unit 150, e.g., if decoding is joint with demodulation) or to those from the day matrix P (particularly if the described demodulation is performed separately and upstream of decoding).

[0081] Thus, at step S230, a process of decoding the received symbol frame T r is implemented by processing data relating to said received symbol frame T r, namely the elements of the relative distribution matrix (P or ), as described previously. Such a decoding process is iterative and takes as input at least a part of a relative distribution tensor Pi / j (P or P). The decoding process then allows the determination of data relative to decoded relative symbols. More precisely, the decoding process allows the determination of corrected relative distributions, denoted P^,, at least for some symbols i,j (e.g., those that can be corrected because they are relevant to the encoding scheme at transmission, Le., have been encoded). Such corrected distributions can then be used in recombination or substitution of the matrix P, for example in a final demodulation step, so as to obtain a corrected final matrix.

[0082] In particular, as an alternative to the successive steps S220 and S230, a joint implementation S231 of the demodulation and decoding processes can be implemented. For this, each iteration or group of iterations of the decoding process can be inserted into an iteration of the demodulation process, as illustrated in Figure 4. For example, at each of the demodulation iterations (Le., an update of the Pi / j distributions), several decoding iterations (e.g., several round-trip propagations in a propagation graph enabling decoding, as described below) can take place.

[0083] Whether through S220 demodulation followed by S230 decoding, or through a joint S231 decoding-demodulation process, a corrected matrix ^ results, containing corrected relative distributions P^j that effectively represent probability estimates of relative shifts between two symbols i and j. Such corrected relative distributions P^ are then relative data from which values ​​of the received symbols at an S240 step can be estimated.

[0084] At step S240, the elements obtained at the output of decoder 16 (or at the output of decoder 16 connected to demodulator 15) can be processed and / or used, particularly to estimate the absolute symbols, denoted xj, obtained at the end of the transmission. In other words, the resulting corrected matrix P can then be used to determine decoded absolute symbols. For this purpose, step S240 can, for example, rely on one or more pilot symbols, whose values ​​are accepted or known. For example, if the received value corresponding to the symbol 0 (denoted O) is accepted, the corrected relative distributions P^ o The outputs of decoder 16 contain, by definition, all possible relative shifts of all symbols with respect to 0. It is then possible to find estimated absolute values ​​of the symbols 0 to m-1, for example, using the following relationship: [Math. + Argmax(Pi / o)

[0085] where i is an index between 0 and m-1 (Le., number of symbols in the received frame T) r ), x L is the estimated value of the received symbol i, = x^ is the known accepted value of the symbol 0, Pi / o is the distribution of relative deviations of the symbol i with respect to the symbol 0 obtained at the end of the decoding.

[0086] By performing such an estimation for each symbol j and using the corresponding corrected relative distributions The S240 step then allows us to estimate all the values ​​of the symbols received in the T frame r at reception.

[0087] The two alternative embodiments of the decoding process (downstream of the demodulation process or jointly with it) are generally designated in Figure 3 by a detailed decoding process 300 below.

[0088] Reference is now made to Figure 3. Figure 3 illustrates in detail the steps of a process for decoding a received frame T r , implemented, at least partially, by a decoder 16 of a communication system 10 as illustrated in Figure 1. In particular, the proposed decoding method relies on processing using a relative representation of the coded information, exploiting initial coding relationships, denoted S, between symbols contained in the received frame T r .

[0089] At an S300 step, from the received coded frame T r , a tensor of relative distributions P or P is obtained, the tensor of relative distributions P or comprising a plurality of relative distributions Pi / j, each relative distribution Pi / j representing probabilities of relative deviations between two relative symbols coded i, j. Such a tensor P or P can be obtained in particular via step S210 and / or step S220 described previously.

[0090] At an S310 step, the coding relations S linking received coded symbols co, ci, ..., c m - 1, and related to the source message are obtained or received. Such S-coding relations can, for example, be received by the decoder 16 via a dedicated protocol exchange aimed at configuring the decoder 16 or via a predefined standard. Such a step of receiving S-coding relations can also occur upstream of the S300 step.

[0091] The coding relations S are known at the decoding stage and result from a coding scheme planned during the encoding phase of the source information (and in particular the initial variables xo, xi, ..., xi-i constituting the source information). Such a coding scheme then allows the definition of relative relations between the received coded variables co, ci, ..., c m -i. In particular, such relative relations reflect a relative representation of the source information, especially when such coded variables result from the encoding of relative variables with respect to the initial variables xo, xi,... ,xi-i.

[0092] For example, the coded symbols co, ci, ..., c m-i can first result from a change of variable from the initial variables xo, xi,... ,xi-i (for example, y = x+ix) so as to create relative variables, denoted yo, yi, ... , yk-i, carrying a relative relationship of the source information, and then to encode such relative variables yo, yi,... , yk-i (e.g., using a Hamming code), so as to obtain coded variables, denoted zo, zi,... , z n -i, carrying a relative representation of the information. Such relative variables coded zo, zi,... , z n -i can then be transformed back into coded absolute variables, denoted co, ci, ..., c m -i, using the same change of variable with the coded relative variables (for example, zi = cn-i-Ci), so as to obtain absolute variables ci to transmit, while applying a coding scheme on relative variables zi, Le., on variables (CH-I-CÎ),

[0093] Such a coding scheme can then result in a set of coding relations S, linking the coded variables co, ci, ..., c m -i transmitted in the source frame T s Such S-coding relations can, for example, be written as follows:

[0094] Such S-coding relations represent relative constraints expressed between transmitted coded absolute values. These can then be verified at the receiver.

[0095] Indeed, in transmission, the source frame T s contains coded symbols co, ci,... , c m -i having specific given values ​​(carrying the source information to be transmitted). Upon reception, the received frame T r corresponds to a measure of received symbols bo, bi,... , b m -i. Due to uncertainty about the accuracy of the received symbols bo, bi,..., b m-i, the received symbols are modeled as random variables Xi whose precise distribution, called corrected distribution P, we seek to calculate in order to deduce the estimated values ​​of the received symbols (denoted b^.b^ ....b^ , as detailed in S240. Such a definition of the random variables Xi is detailed in particular previously in step S210.

[0096] At step S320, the coding relations S are expressed on the random variables Xi considered at reception. More precisely, at step S320, the coding relations S are expressed on a relative representation of the received symbols, namely the random variables (Xi - Xj) representing relative shifts between received symbols considered at reception. The coding relations S can then be defined at reception as follows:

[0097] where the notation X, for a given random variable X of distribution D, corresponds to the negation of the random variable X, defined as the random variable associated with a distribution D obtained by an inversion completed by a circular rotation of one positive step of the distribution D (Le., the distribution D, eg, [0.2 ; 0.3 ; 0.1 ; 0.4] is traversed from the end eg, [0.4 ; 0.1 ; 0.3 ; 0.2], then shifted by one positive step Le., that the last coefficient of the distribution becomes the first, the first becoming the second etc., eg, [0.2 ; 0.4 ; 0.1 ; 0.3]).

[0098] Therefore, step S320 allows us to express the coding relations S in reception on the relative variables (Xi - Xj). Equivalently, step S320 also allows us to express these coding relations S on the Pi / j distributions of such variables (Xi - Xj).

[0099] Indeed, by defining the distribution of a sum of two random variables as corresponding to the convolution of their respective distributions as described previously (step S210), it is then possible to translate the coding relations S on the relative distributions Pi / j as follows:

[0100] where * corresponds to the convolution operator, Pi / j correspond to the relative distributions of the tensor P or obtained in step S300, 5[0] corresponds to a zero Dirac indicating that the relative shift from the sum of the relative symbols is certain and of zero value (Le., the resulting distribution is zero everywhere except for the shift value 0, Le., a zero shift).

[0101] Thus, at the end of step S320, the coding relations S were expressed on the relative variables (Xi - Xj) and the associated distributions Pi / j.

[0102] At an S330 stage, the coding relations S between the different random variables (Xi - Xj) reflecting the relative differences between symbols i and j, and therefore the associated relative distributions Pi / j, can be represented in the form of a factor graph, also called a factorization graph or propagation graph.

[0103] Such a factor graph allows in particular to represent the coding relations S of [Math. 7], expressed between relative probability distributions, and is for example represented in figure 5.

[0104] Referring to Figure 5, the edges of the graph represent the random variables (Xi - Xj) and the nodes describe constraints between these random variables (Xi - Xj). In particular: A variable node imposes an equality constraint, namely that all random variables connected to it must have the same value. A parity node imposes a zero-sum constraint on the variables connected to it. A negation node imposes a negation on the random variable connected to it (Le., a negation node links symmetric variables (X f - Xj) and (Xj - X t ).

[0105] For example, the edge and node connections highlighted in Figure 5 describe the relationship

[0106] It should be noted that such a representation in the form of a factor graph is strictly equivalent to the system of equations represented in [Math. 7] reflecting the coding relations S expressed on the relative distributions.

[0107] Such a graph representation of factors then makes it possible to describe the relationships between Pi / j distributions of the values ​​of the random variables (Xi - Xj) and to determine corrected relative distributions P^j by solving the graph, as detailed later in step S350.

[0108] At an S340 stage, the representation of such a factor graph can be adapted, completed and / or enriched, before its resolution, by exploiting a symmetry and / or a transitivity arising from the relative distributions Pi / j present in the relative distribution tensor P or P.

[0109] Indeed, by definition of the distribution matrix P or P, so-called symmetry relations or so-called chaining relations between different relative distributions Pi / j can be observed and exploited within the framework of the factor graph.

[0110] Step S340 then allows the coding relations S expressed (Le., either as a system of equations as in [Math. 7] or as a factor graph as in Figure 5) to be supplemented or enriched by additional relations derived from the matrix P or P. In particular, such a step S340 can be implemented concurrently or successively with step S320, so that the factor graph representation considered in step S330 takes such additional relations into account.

[0111] Step S340 then results in completed (or enriched) coding relations S. Such completed coding relations S contain, on the one hand, the (so-called direct) coding relations expressing the coding scheme and derived directly from the encoding (e.g., those of [Math. 5], [Math. 6], [Math. 7] equivalently). These can further be supplemented with additional “indirect” relations of symmetry and / or chaining, deduced from the matrix P or P and allowing to express other relations between the Pi / j.

[0112] Examples of such additional relationships, of symmetry or of chaining, are detailed below.

[0113] In a first example, the relative distributions Pi / j and Pj / i of the matrix P are linked by the symmetric relation Pi / j = Pj / i, Le., that the relative distribution Pi / j corresponds approximately to reading the relative distribution Pj / i starting with its last coefficient.

[0114] Thus, the factor graph as illustrated in Figure 5 can be modified by replacing the negation nodes and the corresponding edges with their respective symmetric distributions, already available in the matrix P or P, as illustrated in Figure 6. Such an adapted factor graph is then equivalent to the coding relations S completed as follows:

[0115] In a second example, also exploiting the symmetric relationship Pi / j = Pj / i, it is possible to consider the combination of two symmetric factor graphs using negation nodes, as illustrated in figure 7.

[0116] In a third example, also exploiting the symmetric relationship Pi / j = Pj / i, it is possible to consider the partial combination of symmetric relative distributions, as illustrated in figure 8.

[0117] In a fourth example, also exploiting the symmetrical relationship Pi / j = Pj / i, it is possible to determine two equivalent factor graphs, by exploiting the coding relations S completed as follows:

[0118] This results in two equivalent graphs, as illustrated in figure 9, based on the symmetry of relative distributions of the matrix P.

[0119] In a fifth example, chaining relations (or Chasles relations) exist between relative distributions of type P a / j, Pi / a and Pi / j by transitivity. Thus, it is possible to do introducing new relative distributions through chaining relations, thus creating new coding relations. For example, the first coding relation of [Math. 8] can be rewritten as:

[0120] The second coding relation from [Math. 8] can be rewritten as: [Math.

[0121] The third coding relation of [Math. 8] can be rewritten as: [Math.

[0122] The fourth coding relation of [Math. 8] can be rewritten as:

[0123] Such new coding relations [Math. 10], [Math. 11], [Math. 12], [Math. 13] then allow us to complete the S relations from the coding scheme and result in enriched coding relations, and thus obtain the equivalent factor graph, as illustrated in figure 10, each of the rewritten (enriched) coding relations with new relative distributions being illustrated by a type of line (respectively in irregular (alternating) dotted lines, in long dotted lines, in thick lines and in short dotted lines).

[0124] In the same way as for symmetry relations, it is possible to consider other examples of enrichment of the factor graph, for example by considering the symmetries of the new distributions involved in the new coding relations determined by transitivity.

[0125] The representation in one or more factor graphs as illustrated in the previous steps S330 and S340 then allows the factor graph to be used in the context of a decoding algorithm, at a step S350, via a belief passing algorithm, also called a message passing algorithm, or Belief Propagation (non-binary), more simply referred to in the following as the BP algorithm.

[0126] More generally, the BP algorithm implemented on the factor graph(s) as represented in Figures 5 to 10 corresponds to a probabilistic decoding process, allowing information to be propagated iteratively throughout the factor graph as defined above. In particular, the information propagated throughout the graph (between the different nodes) corresponds to relative probability distributions, associated with differences in random variables (Xi - Xj) representing relative shifts between symbols i, j of a frame.

[0127] The decoding algorithm corresponding to the probabilistic decoding process implemented in step S350 includes the following steps.

[0128] First, the initial relative distributions (i.e., before any decoding step) are provided as incoming messages to the graph (at the levels of the graph's half-edges, i.e., the edges connected to a single node). The messages associated with the other edges of the graph are initialized with uniform distributions or any other prior knowledge about the distributions.

[0129] Then, negations are applied to branches where such negation nodes are present, thus completing the set of messages to be provided to the variable nodes.

[0130] The probabilistic decoding process then comprises the following iterative steps I and II, until a predefined stopping criterion is met: I) Messages from variable nodes to parity nodes are calculated, II) Based on the messages received by the parity nodes, the messages destined for the variable nodes are calculated.

[0131] The predefined stopping criterion can correspond to a desired number of decoding iterations reached or an expected decoding result, for example, depending on the intended use or the expected level of accuracy.

[0132] Then, the outgoing messages from each variable node are calculated as the product of all messages from the parity nodes. On branches where necessary, the negation operator can be applied.

[0133] Finally, the corrected relative distributions at the output of the graph are calculated as the respective products of the initial relative distributions and the set of outgoing messages from the respective variable nodes (taking into account the negation nodes on the branches where they are present).

[0134] Thus, at the end of step S350, the iterative probabilistic decoding process by the BP algorithm makes it possible to determine corrected relative distributions, by iteratively traversing all the information represented on the factor graph(s) used, and by iteratively correcting the relative distributions with the information contained in the graph(s).

[0135] In particular, such an iterative implementation of the probabilistic decoding process can be optimized according to two variants of the realization, considered alternatively or cumulatively.

[0136] In a first embodiment, the probabilistic decoding process S350 can be implemented in conjunction with the demodulation process as described in step S220 of Figure 2. Indeed, the direct use of relative probabilities in the proposed decoding process, similar to the demodulation process considered in document [GLAD], allows to consider the direct application of the proposed decoding to the relative distributions from the matrix of distributions P, for example as obtained at the output of the equalization unit 150 as presented in the document [DFTLink],

[0137] In this embodiment, the demodulator 16 can be integrated into the structure of the demodulator 15, as illustrated in Figure 4, and at each iteration of a demodulation step, several decoding iterations are executed, thus allowing the respective performances of the decoding and demodulation processes to be mutually and iteratively improved. This results in the use of a joint demodulation-decoding process.

[0138] In a second embodiment variant, when at step S340 the factor graph is enriched or completed by symmetric relations (e.g., figures 6, 7, 8, 9) and / or chaining (e.g., figure 10), the probabilistic decoding processing (carried out separately or jointly with demodulation) can be adapted and / or optimized.

[0139] For example, with reference to Figure 9 illustrating two equivalent factor graphs, one derived from the direct relationships between relative probabilities (Le., obtained by directly transposing the direct coding relationships S from the encoding scheme) and the other exploiting the additional symmetry relationships between the relative distributions contained in the matrix P, it is possible to envision a probabilistic decoding process that includes at least one of the following: an iterative decoding process using direct and symmetric relationships alternately at each iteration. In other words, a single factor graph is instantiated and used alternately with direct and symmetric relationships. Alternatively, an iterative decoding process using direct and symmetric relationships cumulatively at each iteration.In other words, the two factor graphs are instantiated and the decoding processes are parallelized.

[0140] Such implementation alternatives can also be considered between the direct relationships and the chaining relationships illustrated in Figure 10.

[0141] In particular, as mentioned previously, such a decoding process can be combined with the demodulation process. In the case of decoding based on direct and symmetry (or chaining) relations, at each iteration of the demodulation algorithm, the decoding algorithm can notably alternate between the use of direct relations and symmetry and / or chaining relations.

[0142] In another example of the second variant of the implementation, with reference to Figure 7 illustrating two factor graphs combined into one using negation nodes, it is then possible to disseminate and combine knowledge of the relative distributions and their symmetry relations during the iterations of the decoding process, thus multiplying the correction of the relative distributions by taking optimized advantage of the relations between the relative distributions.

[0143] The example in Figure 8, which allows only partial recombination of direct relations and symmetry relations, reduces the complexity of the decoding process.

[0144] In another example of the second implementation variant, with reference to Figure 10 illustrating a suitable factor graph with chaining relationships, the probabilistic decoding process is optimized by a more in-depth exploration of the matrix of distributions P and the various relationships linking them. The decoding then takes advantage of a redundancy specifically related to the relative nature of the representation, in the form of relative distributions.

[0145] In particular, the multiplied exploitation of the relations linking the relative distributions is made possible at the decoding stage, despite a limited size coding scheme (e.g., the first coding relations S introduced 4 new variables compared to the initial variables, the number of links between distributions that can be exploited at the decoding stage is potentially greater).

[0146] In a third example of the second embodiment, it is possible to leverage symmetry and / or chaining relationships between relative distributions in probabilistic decoding by considering different, smaller factor subgraphs, each covering a portion of the coding relationships under consideration, and then recombining the decoding results obtained from each subgraph. Such a partition of the coding relationships is illustrated in Figure 11. With reference to Figure 11, each of the four subgraphs G1, G2, G3, and G4 can correspond to four factor subgraphs represented using, respectively, direct relationships, symmetry relationships, chaining relationships, and other relevant relationships between the relative distributions (e.g., the symmetries of the relative distributions of the chaining).

[0147] Each subgraph then leads to corrected relative distributions called intermediate, denoted respectively P|G1, |G2, P|G3, P|G4. The combination of such intermediate results to obtain the final corrected distributions P can then be carried out using a product of the distributions or a consensus approach (e.g., majority vote on the different subgraphs) for example. List of reference signs

[0148] - 10: communication system - 12: encoder - 121: signal encoding unit - 122: transmission channel encoding unit - 13: modulation unit - 14: transmission channel - 150: equalization unit - 15: demodulation unit - 16: decoder - 161: transmission channel decoding unit - 162: signal decoding unit - 151, 152, 153, 154: demodulation subunits - T s : source frame transmitted as input to the transmission channel - xo, xi,... ,xi-i: initial variables - yo, yi,..., yk-i: relative variables - zo, zi,..., Zn-i: coded relative variables - co, ci,... , Cm-i: coded (absolute) variables transmitted - T r frame received at the output of the transmission channel - bo, bi, ..., bm-i: values ​​of the received coded symbols - C = [Xo, Xi, ..., X m -i] : vector of random variables corresponding to the symbols of the received frame - D = [Xxo, Xxi, ..., Xxm-i]: vector of distributions associated with the random variables Xi - P: matrix (or tensor) of relative distributions - P: matrix (tensor) of the relative distributions at day - Pi / j: relative probability distribution of relative differences between two symbols i and j - S: set of coding rules - (Xj - X): random variable following the Pi / j distribution - (Xj - Xi): negation of the random variable (Xj - Xi) - G1, G2, G3, G4: factor subgraphs - P^ L : set of intermediate corrected relative distributions at the output of the subgraph Gi - P: corrected relative distribution matrix - P^j: corrected relative distribution : estimated values ​​of the symbols received List of documents cited Patent documents For the record, the following patent documents are cited: - [DFTLink]: FR 23 06540 - [GLAD] : FR 23 14765).

Claims

Demands

1. Method for decoding (300) a coded frame (T r ) at the output of a transmission channel (14), said coded frame (T r ) being associated with a source message comprising a plurality of initial variables (xo, xi,... ,xi) and transmitted on said transmission channel (14), said coded frame (T r ) comprising a plurality of coded symbols (co, ci, ..., c m -i), said coded symbols (co, ci, ... , c m -i) including encoding on data relating to relative shifts between the initial variables (xo, xi,...,xi-i), the process (300) comprising the following steps: from the coded frame (T r), (S300) obtain a tensor called relative distributions (P), said relative distributions tensor (P) comprising a plurality of probability distributions called relative distributions (Pi / j), each relative distribution (Pi / j) representing probabilities of relative deviations between two given coded symbols (i, j), (S310) obtain coding relations (S) linking the coded symbols (co, ci,... , c m -i), said coding relations (S) depending on the encoding and translating relative relations between the coded symbols (co, ci,..., c m -i), from at least one symmetry relation and / or a transitivity relation between the relative distributions (Pi / j) of the relative distribution tensor (P), (S340) complete the coding relations (S) with additional relations, from the coding relations (S), (S320) express relative relations between the relative distributions (Pi / j), (S350) determine, via a probabilistic decoding process using the coding relations (S), an estimate of decoded symbols forming the decoded frame.

2. A method (300) according to claim 1, wherein the probabilistic decoding process comprises: from the coding relations (S), determining corrected relative distributions and in which the decoded symbols are estimated from the corrected relative distributions

3. A method (300) according to any one of the preceding claims, wherein the probabilistic decoding process relies on a (S330) belief propagation algorithm, wherein edges, variable nodes, and parity nodes of a factor graph associated with said Belief Propagation algorithm translate the coding relations (S), the edges of said graph being associated with random variables (Xi - Xj) representing relative shifts between the received coded symbols (co, ci, ..., c m -i) and according to the relative distributions (Pi / j).

4. Method (300) according to claim 3, wherein a propagation of a message in the factor graph corresponds to an update of at least one relative distribution (Pi / j) associated with the edges involved in said propagation.

5. Method (300) according to any one of claims 3 and 4, wherein the factor graph further comprises negation nodes defining a negation relation of a random variable corresponding to an incoming edge on said negation node.

6. A method (300) according to any one of claims 3 to 5, wherein the probabilistic decoding process is iterative and comprises the following iterative steps, until a predefined stopping criterion is satisfied: calculate the messages from the variable nodes to the parity nodes, calculate the messages to the variable nodes, based on the messages received by the parity nodes.

7. A method (300) according to any one of claims 3 to 6, wherein a set of outgoing messages from each variable node is determined by the product of all messages from the parity nodes.

8. Method (300) according to any one of claims 3 to 7 combined with claim 2, wherein the corrected relative distributions (f^,) are determined by the product of the relative distributions (Pi / j) and the set of outgoing messages from the variable nodes of the factorization graph.

9. A method (300) according to any one of the preceding claims, wherein the probabilistic decoding process relies on at least one element among the symmetry relations and transitivity relations linking the relative distributions (Pi / j) present in the relative distribution tensor (P).

10. A method (300) according to any one of the preceding claims, the coding relations (S) comprising direct relations and symmetry and / or transitivity relations linking the relative distributions (Pi / j) present in the relative distributions tensor (P), and wherein the probabilistic decoding process comprises at least one of: an iterative decoding process using the direct relations and the symmetric and / or transitivity relations alternately at each iteration, an iterative decoding process using the direct relations and the symmetric and / or transitivity relations cumulatively at each iteration, at least a first iterative decoding process using the direct relations and a second iterative decoding process using at least some of the symmetric and / or transitivity relations, the processes being parallelized and / or combined.

11. A method (300) according to any one of the preceding claims, wherein the probabilistic decoding process is integrated with a demodulation process (S220) of the coded frame (T r ).

12. Method (300) according to claim 11, the probabilistic decoding process and the demodulation process being iterative, and wherein each iteration of the demodulation process includes one or more iterations of the probabilistic decoding process.

13. A method (300) according to the preceding claim, wherein at each iteration of a demodulation process, the probabilistic decoding process alternates between the use of one or more coding relations from the encoding and the use of one or more symmetry and / or transitivity relations.

14. Decoder (16) comprising at least one processing unit comprising at least one processor configured to implement the method according to one of the preceding claims.

15. Joint decoding and demodulation unit (15, 16) comprising at least one processing unit comprising at least one processor configured to implement the method according to any one of claims 11 to 14.

16. Computer program comprising instructions for carrying out the method according to any one of claims 1 to 13 when this program is executed by a processor.

17. Non-transient computer-readable recording medium on which is recorded a program for implementing the method according to any one of claims 1 to 13 when this program is executed by a processor.

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