Methods, devices and programs for adaptive modulation and demodulation of a data frame

Abstract

The invention relates to a method for demodulating a frame comprising N information words [P0.. PN-1], in which a word P i at a position i ϵ [0, N — 1] in the frame is modulated by a symbol C pi from a dictionary of K symbols. The method is characterised in that it comprises steps of: obtaining (300) a priori knowledge about the distribution of symbols at a plurality of positions in the frame; determining (301) a differential representation of the a priori knowledge; determining (303) a differential representation of the received frame; linking (304) the determined differential representations in order to obtain a consolidated estimate of the differences between symbols in the received frame; and demodulating (305) the information words received from the consolidated estimate obtained. The invention also relates to a corresponding modulation method and to devices and programs for implementing the methods.

Description

[0001] DESCRIPTION Title: Methods, devices and programs for adaptive modulation and demodulation of a data frame. Technical field The invention generally belongs to the field of telecommunications and more particularly relates to a modulation technique for improving the demodulation performance of a data frame, in particular in communication systems which rely on a relative representation of the information for the purpose of its transmission and / or its processing. Prior art Communication systems are known which rely on a relative representation of the information for the purpose of its transmission and / or its processing. A common example is the use of differential modulations. Consider for example a frame of 5 symbols [^^0, ^^1, ^^2, ^^3, ^^4], each encoding ^^ bits of information, and thus being able to take 2 ^^ values. A possible differential representation of the frame can be − ^^2, ^^2 − ^^3, ^^4 − ^^3]. In this example, it is therefore the difference between the values ​​that is coded, and a single absolute reference is sufficient to decode the complete frame. Of course, in such a configuration, the subtraction, or any other operation, is done in the finite field considered, here F ^^(i.e. modulo ^^). Such a representation can be used for transmission or signal processing purposes within the communication chain. For example, when variations between consecutive samples are small, transmitting differences between samples can be particularly effective. Such a differential representation of the frame can also be useful in certain receivers, for example when receiving a signal modulated by the cyclic rotation of a root sequence of complex symbols, such as CCSK modulation (for Cyclic Code-Shift Keying in English). CCSK modulation proposes to modulate the data to be transmitted by the cyclic rotation / shift of a sequence of complex symbols called the root sequence. The root sequence is such that its shifted versions are orthogonal to each other, that is to say, it offers a good autocorrelation function.Thus, each binary word to be transmitted is associated with a particular cyclic shift of the same root sequence. For example, by choosing a root sequence composed of the 4 complex symbols [a; b; c; d], CCSK modulation allows 2 bits of information to be modulated orthogonally via the rotations of this sequence. 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], etc. CCSK sequences can advantageously be transmitted in a CP-OFDM frame (for Cylic Prefix Orthogonal Frequency Division Multiplex in English), for example in a time-frequency frame in which each of the N time steps contains a complete CCSK sequence of size K distributed over all the subcarriers in frequency as shown in Figure 2.Knowledge by the receiver of the absolute offset of a particular sequence of the frame allows the demodulation of the entire frame. For example, when the offset of the first sequence is known, for example when a particular sequence is present at the beginning of the frame by convention, the receiver can demodulate the frame by estimating the offsets of the other sequences with respect to the known sequence. It is therefore necessary to have a good knowledge of the differences between the sequences of the same frame to correctly demodulate the data. However, it happens that disturbances do not affect the symbols transmitted in the same frame in the same way, which can cause problems during its demodulation. There is therefore a need for a method that can improve demodulation performance, particularly when a communication relies on a relative representation of the information.Summary of the invention To this end, a method is proposed for demodulating a received data frame, the frame comprising N information words [^^0 ..^^^^−1] in which a word ^^^^ at a location^^ ∈ [0, ^^ − 1] in the frame is modulated by a symbol ^^^^^^ from a dictionary of ^^ symbols, the method being such that it comprises the following steps: - Obtaining a priori knowledge about the distribution of the symbols at a plurality of locations in the frame, - Determining a differential representation of said a priori knowledge, representative of a probability that a difference between two symbols has a particular value, - Determining a differential representation of the received frame, representative of a probability that a difference between two symbols of the frame has a particular value, - Relating the determined differential representations to obtain a consolidated estimate of the differences between symbols of the received frame, - Demodulating the received information words from the consolidated estimate obtained.Suppose a sequence of discrete random variables ^^ = [^^1 ^^2 …. ∈ Ϝ ^ ^ ^ ^ . The definition of an apriori means the choice and / or knowledge of the distribution laws of these variables ^^^^ = [^^^^1 ^^^^2 … . A priori knowledge of the distributions of these random variables constitutes very useful knowledge for estimating the value of said variables, particularly when they have been tainted with error by a disturbing phenomenon, such as noise, likely to uncontrollably modify the distributions of transmitted symbols. It is thus proposed to represent a priori knowledge on the distribution of symbols in the frame in a differential form. Such a priori knowledge is for example obtained by convention or by a prior message exchange. This differential representation of the a priori knowledge is combined by product with a differential representation determined from the symbols actually received, so that the probabilities of differences between symbols are better estimated. The method thus makes it possible to improve the performance of the demodulation.Knowledge of the a priori distributions of the transmitted symbols improves the estimation of the received symbols, especially when the transmission channel is affected by disturbances (noise, attenuation, etc.) which uncontrollably modify the distributions of the transmitted symbols. Thus, in the context of a demodulation algorithm exploiting a differential representation of the data frame, i.e. a representation in which we are interested in the differences between symbols and not in the symbols themselves, the method exploits the knowledge of an a priori on the distribution of the symbols at the generation of the frame to improve the demodulation performances.The step of determining a differential representation of said a priori knowledge thus exploits the a priori knowledge of the distribution laws of each symbol according to its location in the frame, in order to determine the probability that a difference between two symbols at particular locations has a particular value. These are a priori differences, which do not depend on the transmission channel. The step of determining a differential representation of the received frame is carried out from the symbols actually received by estimating, for a plurality of pairs of symbols in the frame, probabilities that a difference between two symbols in the received frame has a particular value. Of course, when there is no certainty as to the value of the demodulated symbols, each received symbol can be seen in a conventional manner as a discrete random variable ^^. i governed by a distribution law ^^ ^^i. The probability that the difference between two symbols has a particular value then takes this uncertainty into account and can be expressed by a differential random variable. In other words, for each symbol C Pi at a position i in the frame, and for each symbol Ck of the dictionary (C1, C2, ... , CK), we determine a probability vector P(CPi = Ck), in which P(CPi = Ck) is the probability that the symbol at position i is the symbol C k . Such a distribution is for example determined in a classical way by cross-correlation operations of the symbol at position i with the different symbols of the dictionary. Each symbol ^^ ^^^^ of the frame is thus represented by a random variable X i , so that the difference between two symbols ^^ ^^^^ and ^^ ^^^^of the frame is, in the sense of the present invention, a differential random variable Y^^,^^ = ^^^^ −^^^^ ∈ F^^ whose distribution, called relative distribution, is noted ^^^^⁄ ^^ . Let us consider for example a frame of symbols as a sequence of discrete random variables ^^ = [^^1 ^^2 … ^^^^−1] ∈ Ϝ ^ ^ ^ ^ of distribution law D ^^ =[D … D ]. It ^^1 ^^^^−1 is possible the matrix containing the set of differential variables Y ∈ Ϝ ^^×^^^^ such that Y^^,^^ = ^^^^ − ^^^^ ∈ F^^ and the matrix of corresponding distributions DY such that DY^^,^^ = D^^^^ ⊛ D^^^^ where ⊛ is the cross-correlation operator. In view of the similarity of the notions of sum and difference in the context of modular arithmetic in a finite field, we can also define the matrix containing the set of random variables Y ∈ such that Y^^,^^ = ^^^^ + ^^^^ ∈ F^^and the matrix of corresponding distributions DY such that DY^^,^^ = D^^^^ where ∗ is this times the convolution operator. In this document we note “Relative distribution D ^^⁄ ^^ » the distribution of the random variable resulting from the difference (or sum) of the two random variables ^^ ^^ and ^^ ^^ . Such a differential representation of the received frame is to be distinguished from a frame differentially modulated at transmission according to a conventional differential modulation technique in which the information is modulated by a transition between two consecutively transmitted symbols. In a particular embodiment, the demodulation method is such that each of the ^^ symbols of the dictionary is associated with a distinct index value of a finite group ^^ of size ^^, and such that: - Obtaining a priori knowledge comprises obtaining, for each symbol ^^ ^^^^of the frame, of a vector of K probability ^^^^ ^^ said prior distribution, in which an element of rank ^^ is a probability that the symbol ^^ ^^^^ be the index symbol ^^ of the dictionary, - The determination of a differential representation of said a priori knowledge includes, for each pair (^^^^^^; ^^^^^^) of a priori distributions, the determination of a vector of K probabilities ^^^^ ^^ / ^^ , called relative prior distribution, in which an element of rank ^^ is a probability, determined by relating the distributions ^^^^ ^^ and ^^^^ ^^ , that the difference between the indexes associated with the symbols ^^ ^^^^ and ^^ ^^^^ is equal to ^^, - The determination of a differential representation of the received frame includes, for each pair of symbols (^^ ^^^^ ; ^^ ^^^^ ) of the received frame, the determination of a vector of K probabilities ^^^^ ^^ / ^^, called relative distribution, determined by relating the symbols ^^ ^^^^ and ^^ ^^^^ , in which an element of rank ^^ is a probability that the difference between the indices associated with the symbols ^^ ^^^^ and ^^ ^^^^ is equal to ^^, and - The relation of the determined differential representations includes a term-by-term product of the distributions ^^^^ ^^ / ^^ with the distributions ^^^^ ^^ / ^^. Such an arrangement makes it possible to determine a first matrix comprising so-called relative probability distributions obtained from pairs of symbols of the frame, that is to say a matrix determined from the received symbols, comprising for each pair of symbols of the frame, a probability that the difference between these symbols has a certain value, as well as a second matrix comprising so-called a priori relative distributions, determined from a priori knowledge on the distribution of the symbols, comprising for each pair of symbols of the frame, a probability that the difference between these symbols has a certain value. The product of these matrices makes it possible to obtain a consolidated matrix in which each element is a consolidated probability that a difference between the symbols ^^ ^^^^ and ^^ ^^^^take a certain value. Of course, it may be necessary to normalize the distributions obtained by product, given their probabilistic nature. We specify here that a group is a set equipped with an associative internal composition law admitting a neutral element. Such a group is said to be "finite" when it is made up of a finite number of elements. By associating a distinct index value with each element of the dictionary, it is possible to express differences between the symbols by differences between the indices associated with these symbols. To do this, the K symbols of the dictionary are associated with K distinct symbols of a finite group ^^ of order K whose composition law is addition (and therefore with the value 0 as the neutral element).Such an arrangement makes it possible to perform operations on the indexes, in particular the sums and differences modulo the cardinality K of the symbol dictionary when assuming an indexing in the form {0, 1, …, K-1}, so that any difference (or sum) modulo K between elements of the set is also a value belonging to the set. According to a particular embodiment, an information word is modulated by a sequence of K complex values ​​obtained by a particular cyclic shift of a root sequence. The information words are thus modulated by CCSK type sequences which are particularly suitable for obtaining a differential representation of the frame. The index associated with a symbol is for example the value of the shift of the sequence transmitted in the symbol with respect to the root sequence.The use of such modulation lends itself particularly well to a differential representation of the frame, the offsets being able to be expressed absolutely, with respect to the root sequence, or relatively between pairs of sequences which compose the frame. According to a particular embodiment, the received frame is a time-frequency frame in which each of the N time steps contains a complete symbol of size K distributed over a set of K subcarriers in frequency. The CCSK sequences are thus integrated within a CP-OFDM frame to obtain, in its simplest form, a time-frequency frame in which each of the N time steps contains a complete CCSK sequence of size K distributed over all the subcarriers in frequency, so that the method determines a representation of the OFDM frame in the form of a matrix of the probability distributions of the relative offsets between symbols of the frame.This matrix is ​​combined with a matrix comprising probability distributions of the relative a priori offsets between the symbols of the frame, determined on the basis of knowledge obtained beforehand on the distribution of the offsets for each word of the frame. Such an arrangement makes it possible to exploit the different CCSK symbols contained in the CP-OFDM frame as multiple estimations of the transmission channel, thus allowing a better estimation of the latter and / or transmission schemes without pilots. The CCSK-CP-OFDM modulation is thus particularly suitable for the transmission of small packets for the IoT, with high energy efficiency. According to a particular embodiment, the method is such that a priori knowledge is received beforehand in a message. This indication is for example obtained in a configuration message transmitted by the transmitter or by a control device of the communication system.Such an arrangement allows a priori knowledge about symbol distributions to be dynamically adapted, for example, depending on the communication context. Correspondingly to the demodulation method, a method is also proposed for modulating a data frame to be transmitted, the frame comprising N information words [^^0 .. ^^^^−1] in which a word ^^^^ at a location ^^ ∈ [0, ^^ − 1] in the frame is modulated by a symbol ^^. ^^^^ of a dictionary of ^^ symbols, the process being such that at least one information word is modulated by a symbol from a subset ^^ ^^ from the symbol dictionary, the subset ^^ ^^ being selected according to the location ^^ of the word in the frame and / or a target reliability level for the transmission of said word. Thus, it is proposed to modulate at least one information word ^^ ^^ of the frame by a symbol ^^ ^^^^ from a particular subset ^^^^ of the symbol dictionary. The subset of symbol used to modulate a word ^^ ^^is selected according to the location of the word in the frame and / or according to a desired level of reliability for the transmission of the word. For example, when high reliability is desired for transmitting the symbol, the method makes it possible to select a subset comprising few symbols. In this way, the amount of information that can be transmitted for a word at a particular location in the frame is reduced while increasing the reliability of the transmission of this word. Indeed, by reducing the number of its possible values, a symbol then carries less information but offers greater a priori knowledge to the receiver and therefore increased transmission reliability. The terms "location" or "position" in the frame correspond to the position of a word relative to the others. These terms do not relate to a position in a bit stream, so the position or location of a word in the frame does not depend on the size of the information word.It is thus possible to finely adapt the frame yield, by making the transmission of certain symbols more robust, to make the different symbols more reliable in an adaptive manner according to their levels of importance, or to integrate information with a strong a priori throughout the frame by reinforcing the a priori on certain symbols. According to a particular embodiment, the modulation method is such that each of the K symbols of the symbol dictionary is associated with a distinct index value of a finite group H of order K, and such as a subset ^^. ^^of symbols selected for a particular location consists of the symbols which are associated with index values ​​which belong to a subset of said finite group H. It is recalled here that a group, in the mathematical sense of the term, is a set equipped with a unique internal composition law which is associative, having a neutral element. A finite group is a group whose number of elements is finite. A subgroup G of a finite group H is a subset of H including the neutral element of H, and such that the compound of two elements of G according to the law of H always belongs to G and the inverse (according to the composition law of H) of any element of G itself belongs to G. By associating a distinct index value with each element of the dictionary, it is possible to express differences between the symbols by differences between the indexes associated with these symbols.To do this, the K symbols of the dictionary are associated with K distinct symbols of a finite group of order K whose composition law is addition (and therefore with the value 0 as neutral element). Such an arrangement makes it possible to carry out operations on the indexes, in particular the sums and differences modulo the cardinality K of the dictionary of symbols when we assume an indexing in the form {0, 1, …, K-1}, so that any difference (or sum) modulo K between elements of the set is also a value belonging to the set. According to a particular embodiment, the modulation method is such that the finite group^^ is the group ^^ℤ / ^^^^ℤ with ^^ > 0. The group law on ℤ / ^^ℤ is defined by (^^ ^^^^^^ ^^) + (^^ ^^^^^^ ^^) = (^^ + ^^) ^^^^^^ ^^, so that ℤ / ^^ℤ is a commutative group admitting a neutral element, zero. For example, for a dictionary of K=4 symbols, the index set is {0, 1, 2, 3}.The group ^^ℤ / ^^^^ℤ is thus constituted by the multiples of ^^. With K=4 symbols and m = 2, the set of indices is {0, 2, 4, 6}. The sum and difference operations in such a group are performed modulo ^^^^ . In a particular embodiment, the modulation method is such that a subset of symbols selected for a particular location is constituted by the symbols which are associated with index values ​​belonging to a subgroup of said finite group, the subgroup comprising only values ​​which are multiples of a value M such that K is an integer multiple of M greater than 1. In this way, it is possible to define subsets of symbols whose cardinality depends on the value of M. By varying M, the frame rate, i.e. the number of useful bits that a symbol can carry, is varied. Thus, a value of M=K has zero rate but offers good transmission reliability.Conversely, when M=1 the efficiency is maximum, but the reliability of the transmission is reduced. In other words, for fixed ^^, the larger ^^ the lower the transmission efficiency. By reducing the number of possible values, a symbol then carries less information ^^ (in this case log2 per symbol) but offers stronger a priori knowledge to the receiver and therefore a. of increased transmission. The value of ^^ thus provides information on the possible symbols at a particular location and thus makes it possible to restrict the probability distribution to a certain symbol, and consequently to determine the probability distributions of symbols for a given location. According to a particular embodiment, the modulation method is such that it further comprises a step of transmitting to a recipient, a message comprising information representative of at least one symbol probability distribution at a particular location in the frame. The recipient is for example a communication control entity or the terminal for which the modulated frame is intended. Such an arrangement allows the recipient to obtain a priori knowledge of the value of the symbols transmitted. According to another aspect, the invention relates to a device for demodulating a data frame,the frame comprising N information words [^^0 .. ^^^^−1] in which a word ^^^^ at a location ^^ ∈ [0, ^^ − 1] in the frame is modulated by a symbol ^^^^^^ from a dictionary of ^^ symbols, the device comprising a processor (502) coupled to a memory (501) in which are recorded program instructions (503) configured to implement the following steps: - Obtaining a priori knowledge on the distribution of the symbols at a plurality of locations in the frame, - Determining a differential representation of said a priori knowledge, representative of a probability that a difference between two symbols has a particular value, - Determining a differential representation of the received frame, representative of a probability that a difference between two symbols of the frame has a particular value,- Relating the determined differential representations to obtain a consolidated estimate of the differences between symbols of the received frame, - Demodulating the received information words from the obtained consolidated estimate. Correspondingly to the demodulation device, the invention also relates to a device for modulating a data frame to be transmitted, the frame comprising N information words [^^0 .. ^^^^−1] in which a word ^^^^ at a location ^^ ∈ [0, ^^ − 1] in the frame is modulated by a symbol ^^, ^^^^ of a dictionary of ^^ symbols, the device comprising a processor (602) coupled to a memory (601) in which are stored program instructions (603) configured to implement the following steps, -For each word ^^^^ of the frame, ^^ ∈ [0, ^^ − 1]:- Selection of a particular subset of symbols from among the K symbols of the dictionary according to the location ^^ of the word ^^ ^^in the frame and / or according to a target reliability level for the transmission of the word ^^ ^^ , - Modulation of the word ^^ ^^by a symbol from the selected subset, - Transmission of the modulated frame. The invention also relates to a terminal comprising a demodulation device and / or a modulation device as described above, as well as a communication system comprising such devices and / or terminals. In a particular embodiment, the different steps of the modulation and demodulation methods are determined by computer program instructions. Consequently, the invention also relates to a computer program comprising instructions adapted to the implementation of the steps of a modulation and / or demodulation method as described above, when the program is executed by a processor. This program can use any programming language, and be in the form of source code, object code, or intermediate code between source code and object code, such as in a partially compiled form,or in any other desirable form. The invention also relates to a computer-readable information medium on which is recorded a computer program comprising instructions for executing the steps of a modulation method and / or a demodulation method as described above. The information medium may be any entity or device capable of storing the program. For example, the medium may comprise a storage means, such as a ROM, for example a CD ROM or a microelectronic circuit ROM, a flash memory, or a magnetic recording means, such as a hard disk. Furthermore, the information medium may be a transmissible medium such as an electrical or optical signal, which may be conveyed via an electrical or optical cable, by radio or by other means. The program according to the invention may in particular be downloaded from a network such as the Internet. Alternatively,the information carrier may be an integrated circuit in which the program is incorporated, the circuit being adapted to execute or to be used in the execution of the methods in question. The various embodiments or characteristics mentioned above may be added independently or in combination with each other, to the steps of the modulation and demodulation methods. The devices, terminals, systems, programs and information carriers have advantages similar to those conferred by the methods to which they correspond. Brief description of the figures Other characteristics and advantages will appear on reading a preferred embodiment described with reference to the appended drawings among which: - Figure 1 represents a communication system adapted to implement the modulation and demodulation methods according to a particular embodiment,- Figure 2 illustrates a time-frequency frame in which each of the N time steps contains a CCSK symbol of size K distributed over all the frequency subcarriers, - Figure 3 is a flowchart representing the main steps of a demodulation method according to a particular embodiment, - Figure 4 is a flowchart representing the main steps of a modulation method according to a particular embodiment, - Figure 5 is a diagram representing the architecture of a device suitable for implementing the demodulation method in a particular embodiment, and - Figure 6 is a diagram representing the architecture of a device suitable for implementing the modulation method according to a particular embodiment. In the following description, embodiments are described on the basis of non-limiting examples making it possible to explain the concepts on which the invention is based. In particular,Although the examples and terminology employed may refer to certain well-known technologies or standards, these references are not limiting and other technologies may be adapted to implement the concepts of the invention. For example, the CCSK modulation technique referred to may be replaced by other modulation techniques, such as QPSK (Quadrature Phase Shift Keying), or QAM (Quadrature Amplitude Modulation), without it being necessary to modify the invention. Figure 1 represents an environment adapted to implement the modulation and demodulation methods according to a particular embodiment. The environment comprises a communication system 100,comprising a transmitting device 101 and a receiving device 102. The transmitting device 101 is for example a communication terminal, a user equipment (UE), a base station, a connected object, etc. The receiving device 101, for example a user equipment, a terminal, a connected object or any other device suitable for receiving data. The devices 101 and 102 comprise radio frequency communication means, for example a transceiver suitable for allowing the devices 101 and 102 to communicate by exchanging time-frequency data frames, for example CP-OFDM frames. In a particular embodiment, such frames comprise a plurality of information words, for example binary words of size ^^ bits, a binary word being modulated by a CCSK symbol,that is, by a particular sequence of complex values ​​obtained by cyclic shifting of a root sequence of size 2, ^^ which has a good autocorrelation function. Such a sequence is, for example, a Zadoff-Chu sequence. Thus, the communication system 100 implements a CCSK-CP-OFDM modulation. The CCSK-CP-OFDM approach combines the CP-OFDM technique with CCSK modulation with the aim of achieving small packet communications for the IoT, with high energy efficiency. It may however be noted that other modulation techniques can be envisaged without modifying the invention. For example, a BPSK, QPSK or QAM modulation can be used. Figure 2 represents an example of a CCSK-CP-OFDM frame in which each of the N time steps contains a complete CCSK sequence of size K = 2 pdistributed over the set of K subcarriers in frequency, so that each symbol corresponds to a word of maximum size p bits. The set of K CCSK symbols constitutes a dictionary of symbols of cardinality K. Each symbol of the dictionary is associated with a distinct index so that the K symbols of the dictionary are respectively associated with K index values. In the case of CCSK modulation, each CCSK sequence of the dictionary is thus associated with a unique digital value, for example a value representing the offset of the sequence with respect to the root sequence. According to a particular embodiment, the K index values ​​with which the symbols of the dictionary are associated constitute a finite group H of size K, so that each symbol of the dictionary is associated with a distinct value belonging to the finite group H.Index operations, in particular sums and differences, are thus performed in a finite group of size K, i.e. modulo the cardinality K of the symbol dictionary when assuming indexing in the form {0, 1, …, K-1}, so that any difference (or sum) modulo K between elements of the set is also a value belonging to the set. In a particular realization, the index values ​​of the finite group ^^ are defined by the group ^^ℤ / ^^^^ℤ, considering modular arithmetic on the remainders of division by ^^^^ and ^^ a strictly positive integer, ℤ being the set of relative integers. For example, with m=2 and K=4, we obtain a set of indices [0, 2, 4, 6] such that any difference (or sum) modulo ^^^^ between elements of the set is also a value belonging to the set.So, in this example, we actually observe that 0 – 2 = -2 [8] = 6, 0 - 4 = -4 [8] = 4, 2 – 4 = -2 [8] = 6, etc…In a particular realization, an information word Pi has a location ^^ ∈ [0, ^^ − 1]. of the frame is modulated by a symbol from a subset of symbols usable for coding a word at location ^^, the subset being selected according to the position ^^ of the word to be coded and / or a target reliability level for the transmission of the information word. Such a subset consists of the symbols associated with indices whose values ​​belong to a particular subset of the finite group H. Thus, according to a particular embodiment, each information word of the frame is associated with a particular symbol dictionary according to its position in the frame and / or a desired reliability level for transmitting a word at a particular position.More generally, some words in the same frame may be encoded by a symbol from a dictionary of K values, while other words may be encoded by symbols from a first subset of the dictionary, and still other words may be encoded by symbols from a second subset of the dictionary. The first and second subsets may have distinct cardinalities depending on a desired reliability level for the transmission of the information words respectively associated with these subsets. Indeed, the lower the number of symbols that can be used to encode a word at a particular location in the frame, the more reliable the transmission. In other words, by reducing the number of possible values ​​for a symbol, the symbol carries less information but offers stronger a priori knowledge to the receiver and therefore increased transmission reliability.Of course, the symbol dictionary used by a transmitter is known to the receiver to enable demodulation. Furthermore, according to a general principle of the invention, the receiver is aware of the probability distributions of symbols in a received frame. This knowledge is for example obtained by convention (reference to a standard) or by a configuration message. Such an arrangement makes it possible to improve the demodulation performance by a receiver device adapted to exploit differences between symbols of the frame and not only the absolute values ​​of these symbols nor the differences between the symbols and a reference symbol. For example, in the case of CCSK type modulation, demodulation can be carried out from the differences between the symbols of the frame.In such a case, a priori knowledge of the symbol distributions at each location in a frame allows a priori knowledge of the relative distributions to be established, i.e., a priori knowledge of the distributions of the probabilities of differences between pairs of symbols in the frame. This performance improvement is achieved by a demodulator adapted to relate a differential representation of the a priori knowledge about the a priori symbol probability distributions to a differential representation of the received frame, so that the differences between symbols are better estimated. In the case of differential modulations, i.e., when a value associated with a symbol can be expressed by a difference with a value associated with another symbol, performance is improved.Correspondingly, a modulator is provided suitable for modulating information words of a data frame from a symbol dictionary, the modulator being such that at least one information word is modulated by a symbol whose value is selected from a subset of the symbol dictionary, the subset being selected according to the position of the word in the frame and / or a target reliability level for the transmission of said word or according to a probability distribution of symbols associated with the location of the word. The operation of difference between symbols referred to in this document may vary according to the modulation technique used without it being necessary to modify the invention. Such a difference corresponds for example to the value of a cyclic shift of the sequence considered with respect to another sequence in the case of CCSK type modulation, to phase or angle shifts in the case of QPSK modulation, etc.The difference between symbols may also correspond to a difference between index values ​​associated with the symbols in a symbol dictionary, following an indexing system equal to the set {0,1,…,K-1} up to an isomorphism, and their respective probabilities. The difference is thus estimated in a finite group of size K, i.e. modulo the cardinality of the symbol dictionary when assuming an indexing in the form {0,1,…,K-1}. In a particular embodiment, a priori knowledge about the distribution of the symbols at a particular location ^^ ∈ [0, ^^ − 1] in the frame consists of a vector of size K comprising a number of elements equal to the cardinality K of the symbol dictionary, in which an element of index ^^ comprises a probability that the value associated with the symbol at location ^^ of the frame is the symbol in the dictionary that is associated with the value ^^.In this document, such a vector is referred to as a "prior distribution." For example, when all symbols in the dictionary are likely to be used to modulate a word at a particular location in the frame, the prior distribution associated with that location is a uniform distribution. As another example, when only symbols associated with even index values ​​in the dictionary are likely to be used at a particular location in the frame, the distribution includes zero probabilities at odd indices. This prior knowledge about the distribution of symbols in the frame is used to determine "relative prior distributions." A relative prior distribution ^^^^. ^^ / ^^is determined for a pair of locations ^^, ^^ ∈ [0, ^^ − 1], from the prior distributions respectively associated with these two locations. Such a relative prior distribution includes, for each pair of locations ^^, ^^ ∈ [0, ^^ − 1] of the frame, a probability that the difference between the symbols at locations ^^, ^^ of the frame has a certain value. For example, a relative prior distribution ^^^^ ^^ / ^^ is a vector of K elements corresponding to the K elements of the symbol dictionary, in which an element ^^^^ ^^ / ^^ [^^] is a probability that the difference between the symbol values ​​at locations ^^ and ^^ in the frame has the value ^^. This gives a relative prior distribution for each pair of locations (^^, ^^) in the frame, allowing us to construct a matrix in which an element with coordinates (i, j) is a relative prior distribution ^^^^ ^^ / ^^. In a particular embodiment, this matrix of a priori distributions is combined with a second matrix comprising relative distributions, representative of the differences between symbols or values ​​associated with the symbols actually received in the frame. These relative distributions are determined for all pairs of symbols (^^^^^^, ^^^^^) of the frame, ^^, ^^ ∈ [0, ^^ − 1], by cross-correlation or convolution operations. More precisely, a difference between a symbol ^^ ^^^^ and a symbol ^^ ^^^^ is determined by relating these symbols by cross-correlation or convolution. For example, this difference can be the value of an offset between two CCSK sequences. Thus, for each pair of symbols (^^^^^^, ^^^^^^), we determine a vector ^^^^ / ^^ whose size is equal to the cardinality K of the symbol dictionary, and whose each element ^^ ^^ / ^^[^^] includes a probability that the difference between the symbols ^^ ^^^^ and ^^ ^^^^ has the value ^^. These relative distributions allow us to obtain a matrix of relative distributions in which an element of coordinates (i, j) is a relative distribution ^^ ^^ / ^^. These two matrices are combined by product, so that the probabilities of differences between the values ​​associated with the symbols actually received are weighted by the probabilities determined from the a priori knowledge about the values ​​of these symbols. Of course, it may be necessary to normalize the distributions obtained by product, given their probabilistic nature. The matrix resulting from this combination thus includes distributions called "consolidated relative distributions", which are better estimated because they take into account the a priori knowledge about the symbol distributions. Considering for example a frame containing 5 CCSK symbols of size 4 (each encoding 2 bits of information) and a relative distribution: ^^3 / 5 = [0.2, 0.1, 0.3, 0.4], representative of the probabilities of the shifts between symbols of index 3 and 5, we deduce that the most probable relative shift of symbol 3 with respect to symbol 5 is Argmax 3.In other words, the values ​​of these two symbols are related by ^^3 = ^^5 +3 ^^^^^^ 4. If, for example, the a priori knowledge concerning the distributions ^^3 and ^^5 follows a subset of the even indices such that ^^3 = [0.5, 0.0, 0.5, 0.0] and ^^5 = [0.5, 0.0, 0.5, 0.0], we can determine the following relative a priori distribution, obtained after cross-correlation and normalization: ^^^^3 / 5 = [0.5, 0.0, 0.5, 0.0]. The product of the a priori distribution ^^^^. 3 / 5 and distribution ^^ 3 / 5gives us the following consolidated distribution, after normalization: ^^3 / 5 = [0.4, 0.0, 0.6, 0.0]. We note that this consolidation allows us to obtain Argmax (^^3 / 5) = 2, different from the initial estimate. The initial estimate is thus improved thanks to a priori knowledge. In the case of CCSK type modulation, the information words are modulated by cyclic shifts of a particular sequence called the root sequence, for example by cyclic shifts of a Zadoff-chu sequence (these sequences have good autocorrelation properties and are particularly suitable for this use). It is thus possible to express the difference between two symbols by the shift between these symbols. Similarly, the difference between two BPSK symbols can be expressed by a difference between the respective angles associated with these symbols.More generally, the differences can be expressed between index values ​​associated with the symbols in the symbol dictionary, as described previously. For this, according to a particular embodiment, the K symbols of the dictionary are associated with K distinct index values ​​from a finite group of order K. Such a set of indices provides modular arithmetic suitable for expressing differences between all the symbols of the dictionary. This improved estimation of the relationships between the symbols of a received frame can advantageously be used during the demodulation of the frame. For example, when the frame comprises at least one symbol whose value is known at a known position, such as a pilot symbol, it is proposed to use the consolidated relative distributions to demodulate the other information words.To do this, it is possible to use a single row of the consolidated relative distribution matrix, which includes information allowing us to know the shift probabilities between all the symbols in the frame. However, it is possible to combine data from different rows of this matrix to further improve the estimation. Indeed, by transitivity, a relative distribution ^^. ^^ / ^^ can be expressed by relating relative distributions ^^ ^^ / ^^ and ^^ ^^ / ^^. Such a linking can be done by cross-correlation or convolution. By selecting from the matrix combinations of distributions associated with the highest probabilities, the estimation of the symbols with respect to the pilot symbol can be improved. According to another example, when no symbol is known absolutely, the determined consolidated relative distributions allow the implementation of a shifted demodulation. The shifted demodulation consists of demodulating the frame by taking as reference an arbitrary symbol value and of carrying out an integrity check on the information words thus obtained. If the integrity check does not allow the frame to be validated, a new demodulation is carried out by taking as reference another symbol value and a new integrity check is carried out. These steps are repeated until the frame is validated by the integrity check.Figure 3 illustrates the main steps of a demodulation method according to a particular embodiment. The method is for example implemented by the device 102 of Figure 2. During a first step 300, the method comprises a step of obtaining information relating to the symbol distributions in one or more frames. As seen, this knowledge may be contained in a message received by the device 102, for example in a communication configuration message. This knowledge may take the form of probability distributions associated with one or more locations in the frame, or consist of a transmitted value from which it is possible to determine such distributions. This knowledge may also be determined by convention, for example by reference to a communication standard.The method comprises a step 301 during which the device 102 determines relative a priori distributions from the knowledge obtained in step 300. These relative a priori distributions are obtained as described previously, by a cross-correlation operation or a convolution applied to a priori distributions determined from the a priori knowledge obtained and, according to a particular embodiment, are arranged in a matrix in which an element (i, j) comprises a relative a priori distribution representative of the probabilities of differences between the values ​​associated with symbols at locations i and j of a data frame. In a particular embodiment, steps 300 and 301 merge so that the relative a priori distributions are directly obtained in a configuration message or by reference to a standard.In step 302, the device 102 determines a probability distribution for each symbol of the received frame. For example, the device determines a vector ^^. ^^ of size ^^ including each element ^^ ^^ [^^] is a probability that the symbol ^^ ^^^^ is the of index ^^ in the dictionary. In the case of CCSK modulation, an element ^^ ^^ [^^] contains for example the probability value of the shift between the sequence ^^ ^^^^ and a reference sequence of value ^^. For this, the device 102 compares each sequence ^^ ^^^^with the root sequence, for example from a cross-correlation (or convolution) operation to determine for each symbol the probability of an offset value with respect to the root sequence. During a step 303, for a plurality of pairs of symbols (^^^^^^^, ^^^^^^) of the received frame, the device 102 estimates a relative distribution representative of a difference between symbols ^^^^^^ and ^^^^^^ of the received frame, with ^^, ^^ ∈ [0, ^^ − 1]. As indicated, when the K symbols of the dictionary are associated with K distinct index values ​​belonging to a finite group of order K, the difference is estimated in the finite group K, that is to say modulo the cardinality of the dictionary of symbols when an indexing in the form {0, 1, …, K-1} is assumed, or modulo ^^^^ when the symbols are indexed by values ​​belonging to the finite group ^^ℤ / ^^^^ℤ, with ^^ a strictly positive integer.In a particular embodiment, this processing results in a representation of the frame in the form of a matrix of the probability distributions of the relative offsets between CCSK symbols of the frame (or relative distributions in the sense of the invention): ]. In this matrix, each index ^^ ^^⁄ ^^ thus contains a vector of size ^^ in which each element of the vector ^^ ^^⁄ ^^ [^^] contains the probability that the value of the difference between the symbols ^^ ^^^^ and ^^ ^^^^of the frame is of value ^^. Of course, it is conceivable to determine only a subset of these relative distributions a posteriori without modifying the invention. During a step 304, the relative distributions a priori determined in step 301 are combined with the corresponding relative distributions determined in step 303 to obtain consolidated relative distributions. In a particular embodiment, the device 102 performs for this purpose a product of the matrices in which the relative distributions a priori and the relative distributions a posteriori are respectively arranged. The method finally comprises a demodulation step 305 during which at least part of the consolidated relative distributions are used to estimate the value of a symbol from another taken as reference.As indicated above, the demodulation can be carried out from the consolidated probabilities of differences between a symbol whose value and location in the frame are known, for example a pilot symbol, and the other symbols of the frame. According to another example, the device 102 carries out a shifted demodulation from the consolidated relative distributions. Although the method is described here with reference to discrete laws, the present proposal can be generalized to continuous laws, for example by approximating the continuous law by a discretized law, or by modeling the distributions by their parameters (for example the mean ^^ and the variance ^^ as parameters of a normal law). It is then appropriate to express the relationship between the parameters of the relative distributions. Figure 4 illustrates the main steps of a modulation method according to a particular embodiment.The modulation method is for example implemented by the device 101 of figure 2. The method comprises a first step 400 of obtaining a data frame to be transmitted comprising N information words [^^0, .. , ^^^^−1]. The information words are for example binary words of maximum size ^^ bits. During a step 401, the device 101 determines a symbol dictionary to be used to modulate the binary words of the frame. Such a symbol dictionary comprises at least ^^ = 2^^ symbols which are respectively associated with ^^ distinct index values.The K index values ​​constitute a finite group of order ^^, equipped with a neutral element and an addition law, so that the sum or difference operations between the index values ​​are performed within the framework of modular arithmetic, i.e. modulo the cardinality ^^ of the symbol dictionary when assuming an indexing in the form {0, 1, …, K-1}, so that any difference (or sum) modulo ^^ between elements of the set is also a value belonging to the set. In a particular realization, the index values ​​are defined by the group ^^ℤ / ^^^^ℤ, considering modular arithmetic on the remainders of division by ^^^^, and ^^ a strictly positive integer, ℤ being the set of relative integers. According to a particular embodiment, the method comprises a step 402 during which the device 101 associates a particular subset ^^. ^^of symbols to a particular information word ^^^^ at a location ^^ in the frame, ^^ ∈ [0.. ^^]. Such a subset of symbols is composed of the symbols of the dictionary which are associated with index values ​​forming a particular subset of the finite group ^^. For example, such a subset is composed exclusively of the symbols of the dictionary which are associated with even values, or exclusively of the symbols of the dictionary which are associated with odd values. In a particular embodiment, such a subset is composed exclusively of the symbols of the dictionary which are associated with values ​​which are multiples of a strictly positive value ^^ and divisor of ^^, the value ^^ being determined according to the position of the information word in the frame and / or according to a target reliability level for the transmission of the information word. Thus, for fixed ^^, the larger ^^, the lower the transmission efficiency.By reducing the possible number, a symbol then carries less information (in this case log. 2 bits per symbol) but provides greater a priori knowledge to the receiver and therefore increased transmission reliability. Of course, one can consider associating several distinct subsets with distinct information words of the frame, so that it is possible to finely adapt the reliability and efficiency of the transmission. Consider for example a CCSK-CP-OFDM frame of size ^^ = 5 symbols of size ^^ = 8, and a dictionary of symbols indexed by distinct values ​​of the finite group ℤ / ^^ℤ. The frame can be constructed as follows: - A symbol ^^ ^^0 , for example a pilot symbol, selected from a subset of the symbol dictionary consisting of symbols associated with index values ​​that are multiples of a value ^^ = 8. This symbol has a useful throughput of^^ = 0 bit / symbol, - A symbol ^^^^1 selected from a subset of the symbol dictionary consisting of symbols associated with index values ​​multiple of a value ^^ =^^ - A symbol ^^ ^^2 selected from a subset of the symbol dictionary consisting of symbols associated with index values ​​that are multiples of a value ^^ = 2. This symbol has a useful throughput - Two symbols ^^ ^^3 and ^^ ^^4 , non-critical, whose values ​​are selected from a subset of the symbol dictionary consisting of symbols associated with index values ​​that are multiples of a value ^^ = 1. This symbol has a useful throughput of The characteristics of the subsets of symbols associated with the different symbols of the frame make it possible to determine a priori distributions of these symbols. In a particular embodiment, the device 101 determines a particular subset of symbols available for modulating an information word at a particular position of the frame by applying a communication standard also known to the receiver 102. In a particular embodiment, the device 101 determines a particular subset of symbols available for modulating an information word at a particular position of the frame according to the content of a configuration message transmitted by the receiver 102, a communication control entity, or a radio access point such as a base station or a WiFi® router.In a particular embodiment, the device 101 determines a particular subset of available symbols for modulating an information word at a particular position of the frame according to data characteristic of the transmission channel, for example communicated by the receiver 102. In a particular embodiment, the method comprises a step 403 of transmitting a message to the device 101 or a communication control entity, the message comprising at least one distribution of symbols associated with one or more information words and / or particular positions of the frame. It is understood that the symbol distributions can thus be communicated to the receiver 101 at any time, for example prior to the transmission of a plurality of frames. Of course, such a message can comprise a priori distributions relating to a plurality of frames, to a particular type of frame, or even to a communication session.The method comprises a step 404 during which the information words are modulated from the symbol dictionary, and / or subsets of symbols determined to code a particular word. For this, for each word to be coded at a particular position in the frame, the device can consult a table in which a position ^^ in the frame is associated with an identifier of a subset ^^. ^^ of symbols, the subset ^^ ^^ to be used for the modulation of a word ^^ ^^ being determined according to a target reliability level for the transmission of a symbol. The device modulates the information word by a symbol selected from the subset ^^ ^^associated with the position ^^ of the information word in the frame. The method finally comprises a step 405 of transmitting the modulated frame to the device 102. In a particular embodiment, the frame is transmitted by OFDM modulation, according to which each of the N time steps contains a complete CCSK coding sequence of size K for an information word, distributed over all the subcarriers in frequency. Figure 5 represents a simplified architecture of a device 500 adapted to implement the demodulation method according to a particular embodiment. The device 500 comprises a data processing module comprising a storage space 501, for example a memory (MEM), a processing unit 502, equipped for example with a microprocessor (PROC), and controlled by a computer program (PGR) 503 whose instructions are configured to implement the demodulation method as described previously in relation to Figure 3.At initialization, the code instructions of the computer program 503 are for example loaded into the memory 501 before being executed by the processor of the processing unit 502. The microprocessor of the processing unit 502 implements, according to the instructions of the computer program 503, the steps of the demodulation method described above with reference to FIG. 3. For this, in addition to the memory 501 and the processor 502, the device comprises communication means 504, for example an OFDM transducer adapted to receive a signal on a plurality of orthogonal carriers. The communication means 504 are for example configured by computer program instructions to allow the reception of at least one time-frequency frame in which each of the N time steps contains a complete symbol of size K, for example a CCSK sequence, distributed over all the subcarriers in frequency, and to demodulate the N OFDM symbols received.The device 500 also comprises a module 505 for determining one or more a priori distributions of the symbol probabilities in the received frame. The module 505 is for example implemented by program instructions configured to associate a vector of size K with at least one information word of the frame received by the communication module 504, in which each index element ^^ comprises a probability that the value of the symbol at the position with which the vector is associated is the symbol of index ^^ in a symbol dictionary of size K. The program instructions are further configured to construct such a priori distributions by reference to a standard, by receiving a message from a control entity or from the transmitter of the frame, the message comprising at least one indication making it possible to identify a particular distribution of symbols for one or more particular locations.The device 500 comprises a module 506 for determining a set of relative prior distributions from the prior distributions determined by the module 505, the module 506 being implemented by program instructions configured to determine a vector of K elements corresponding to the K elements of the symbol dictionary, in which an element of index ^^ is a probability that the difference between the symbol values ​​at locations ^^ and ^^ of the frame has the value ^^. The program instructions are further configured, according to a particular embodiment, to construct a matrix from the determined relative prior distributions, in which an element at coordinates (i, j) comprises a relative prior distribution of the differences between the symbol values ​​at locations i and j of the frame received by the communication module.The device 500 also comprises a module 507 for determining a set ^^ of probability distributions, for example a matrix, called relative distributions, each element ^^. ^^ / ^^ of the matrix being a vector of K probabilities representative of at least one difference between index values ​​associated with symbols ^^ ^^^^ and ^^ ^^^^ of a plurality of pairs of symbols (^^ ^^^^ ; ^^ ^^^^) formed from the symbols composing a frame received by the communication means 504, with ^^ ∈ [0; ^^ − 1] and ^^ ∈ [0; ^^ − 1], a difference being calculated according to modular arithmetic. The module 507 is for example implemented by computer program instructions configured to calculate a difference between index values ​​associated with two symbols of the frame by a cross-correlation and / or convolution operation and to store the result of the difference between the elements of a pair (^^^^^^^ ; ^^^^^^) of sequences at the coordinates (^^; ^^) in the matrix. The device comprises a consolidation module 508 adapted to combine the relative distributions a priori determined by the module 506 with the relative distributions determined by the module 507.The module is for example implemented by program instructions configured to perform a product of the matrices constructed by the modules 506 and 507 and thus obtain a matrix comprising consolidated relative distributions. The device 500 finally comprises a demodulation module 509 adapted to demodulate the symbols transmitted in the received frame from the relative distributions consolidated by the module 508. For example, the module 509 is implemented by program instructions adapted to carry out an offset demodulation of the data frame based on the consolidated relative offsets between sequences of the frame, for example from the offsets updated in one or more particular rows of the consolidated matrix. According to another example, the instructions are configured to demodulate the symbols of the frame from the differences between these symbols and a reference symbol whose location and value are known.In a particular embodiment, the device 500 is integrated into a communication terminal, a connected object, a vehicle, a gateway, an access point or even a base station. Figure 6 represents a simplified architecture of a device 600 adapted to implement the modulation method according to a particular embodiment. The device 600 comprises a data processing module comprising a storage space 601, for example a memory (MEM), a processing unit 602, equipped for example with a microprocessor (PROC), and controlled by a computer program (PGR) 603 whose instructions are configured to implement the modulation method as described previously in relation to Figure 4. At initialization, the code instructions of the computer program 603 are for example loaded into the memory 601 before being executed by the processor of the processing unit 602.The microprocessor of the processing unit 602 implements, according to the instructions of the computer program 603, the steps of the modulation method described above with reference to FIG. 4. For this, in addition to the memory 601 and the processor 602, the device 600 comprises a module 604 for obtaining a frame comprising N information words, for example N binary words of maximum size ^^ bits. For example, the module 602 can be implemented by instructions adapted to form a frame by segmenting an application data stream and adding a value to it for checking its integrity. The device also comprises a module 605 for selecting at least one subset of symbols from a symbol dictionary to modulate at least one information word at a particular position.For this, the module 605 is for example implemented by program instructions adapted to select a subset of symbols according to the location in the frame of a word to be modulated and / or a desired reliability level for the transmission of said information word. The device 600 comprises a module 606 for modulating the information words from the subset of symbols determined by the module 605 for each information word. The device comprises communication means 607, for example an OFDM transducer adapted to transmit a signal on a plurality of orthogonal carriers.The communication means 607 correspond for example to a 3G, 4G, 5G or WiFi® network interface configured by computer program instructions to allow the transmission of at least one time-frequency frame in which each of the N time steps contains a complete symbol of size K, for example a CCSK sequence, distributed over all the frequency subcarriers. According to a particular embodiment, the communication means are configured by instructions to transmit to a receiving device at least one item of information characteristic of the probability distribution of the symbols at one or more locations of one or more frames. In a particular embodiment, the device 600 is integrated into a communication terminal, a connected object, a vehicle, a gateway, an access point or even a base station.According to a particular embodiment, the modulation and demodulation devices are included in the same device.

Claims

CLAIMS 1. Method for demodulating a received data frame, the frame comprising N words d ’information [^^0 .. ^^^^−1] dans lequel un mot ^^^^ à un emplacement ^^ ∈ [0, ^^ − 1] dans the frame is modulated symbol ^^ ^^^^ of a dictionary of ^^ symbols, the method being such that it comprises the following steps: - Obtaining (300) a priori knowledge on the distribution of the symbols for a plurality of locations of the received frame, - Determining (301) a differential representation of said a priori knowledge, representative of a probability, for a plurality of pairs of locations ( ^^, ^^), avec ^^, ^^ ∈ [0, ^^ − 1], qu’une différence entre deux symboles à ceslocations in a frame have a particular value, - Determining (303) a differential representation of the received frame, representative of a probability that a difference between two symbols received from the frame has a particular value, - Relating (304) the determined differential representations to obtain a consolidated estimate of the differences between symbols of the received frame, - Demodulating (305) the received information words from the obtained consolidated estimate.

2. Method according to claim 1 wherein each of the ^^ symbols of the dictionary is associated with a distinct index value of a finite group ^^ of size ^^, and wherein: - Obtaining a priori knowledge comprises obtaining, for each symbol ^^ ^^^^ of the frame, of a vector of ^^ probability ^^^^ ^^ said prior distribution, in which an element of rank ^^ is a probability that the symbol ^^ ^^^^be the index symbol ^^ of the dictionary, - The determination of a differential representation of said a priori knowledge c omprend, pour chaque couple (^^^^^^; ^^^^^^) de distributions à priori, la détermination of a vector of K probabilities ^^^^ ^^ / ^^ , called relative prior distribution, in which an element of rank ^^ is a probability, determined by relating the distributions ^^^^ ^^ and ^^^^ ^^ , that the difference between the indexes associated with the symbols ^^ ^^^^ and ^^ ^^^^ be equal to ^^, - The determination of a differential representation of the received frame includes, for each pair of symbols (^^ ^^^^ ; ^^ ^^^^ ) of the received frame, the determination of a vector of ^^ probabilities ^^^^ ^^ / ^^ , called relative distribution, determined by relating the symbols ^^ ^^^^ and ^^ ^^^^ , in which an element of rank ^^ is a probability that the difference between the indices associated with the symbols ^^ ^^^^ and ^^ ^^^^is equal to ^^, and - The connection of the determined differential representations includes a term-by-term product of the distributions ^^^^ ^^ / ^^ with the distributions ^^^^ ^^ / ^^ .

3. Method according to any one of the preceding claims in which an information word is modulated by a sequence of ^^ complex values ​​obtained by a particular cyclic shift of a root sequence of size ^^.

4. Method according to any one of the preceding claims in which the received frame is a time-frequency frame in which each of the ^^ time steps contains a complete symbol of size ^^ distributed over a set of ^^ frequency subcarriers.

5. Method according to any one of the preceding claims in which the a priori knowledge is received beforehand in a message.

6. Method of modulating a data frame to be transmitted, the frame comprising ^^ m ots d’information [^^0 .. ^^^^−1] dans lequel un mot ^^^^ à un emplacement ^^ ∈ [0, ^^ − 1] in the frame is modulated by a symbol ^^ ^^^^of a dictionary of ^^ symbols, the process being such that at least one word of information ^^ ^^ is modulated by a symbol from a subset ^^ ^^ from the symbol dictionary, the subset ^^ ^^ being selected according to the location ^^ of the word in the frame and / or a target reliability level for the transmission of said word.

7. The method of claim 6 wherein each of the ^^ symbols of the dictionary is associated with a distinct index value of a finite group ^^ of size ^^, and wherein a subset of symbols ^^ ^^ selected for a particular location ^^ consists of the symbols which are associated with index values ​​which belong to a subset of said finite group ^^.

8. Method according to claim 7 in which the finite group ^^ is the group ^^ℤ / ^^^^ℤ, ^^ being strictly positive.

9. Method according to any one of claims 6 to 8 in which a subset of symbols selected for a particular location is made up of the symbols which are associated with index values ​​which belong to a subgroup of said finite group ^^, the subgroup comprising only values ​​which are multiples of ^^ such that ^^ is an integer multiple of ^^ greater than 1.

10. Method according to any one of claims 6 to 9 such that it further comprises a step of transmitting to a recipient, a message comprising information representative of at least one symbol probability distribution at a particular location of the frame.

11. Device for demodulating a data frame, the frame comprising ^^ words of ’information [^^0 .. ^^^^−1] dans lequel un mot ^^^^ à un emplacement ^^ ∈ [0, ^^ − 1] dansthe frame is modulated by a symbol ^^ ^^^^ of a dictionary of ^^ symbols, the device comprising a processor (502) coupled to a memory (501) in which are recorded program instructions (503) configured to implement the following steps: - Obtaining a priori knowledge on the distribution of the symbols at a plurality of locations of the frame, - Determining a differential representation of said a priori knowledge, representative of a probability, for a plurality of pairs of locations (^^, ^ ^), avec ^^, ^^ ∈ [0, ^^ − 1], qu’une différence entre deux symboles à ces emplacements in a frame has a particular value, - Determination of a differential representation of the received frame, representative of a probability that a difference between two symbols received from the frame has a particular value, - Linking the determined differential representations to obtain a consolidated estimate of the differences between symbols of the received frame, - Demodulation of the information words received from the consolidated estimate obtained.

12. Device for modulating a data frame to be transmitted, the frame comprising ^^ m ots d’information [^^0 .. ^^^^−1] dans lequel un mot ^^^^ à un emplacement ^^ ∈ [0, ^^ − 1] in the frame is modulated by a symbol ^^ ^^^^ of a dictionary of ^^ symbols, the device comprising a processor (602) coupled to a memory (601) in which are recorded program instructions (603) configured to implement the following steps, - Pour chaque mot ^^^^ de la trame, ^^ ∈ [0, ^^ − 1] : - Selection of a particular subset of symbols from the ^^ symbols in the dictionary according to the location ^^ of the word ^^ ^^ in the frame and / or according to a target reliability level for the transmission of the word ^^ ^^ , - Modulation of the word ^^ ^^by a symbol from the selected subset, - Transmission of the modulated frame.

13. Communication terminal comprising a demodulation device according to claim 11 and / or a modulation device according to claim 12.

14. Computer program comprising instructions adapted to the implementation of the steps of a demodulation method according to any one of claims 1 to 5, and / or a modulation method according to any one of claims 6 to 10, when the program is executed by a processor.

15. Information medium readable by a computer on which is recorded a computer program comprising instructions for the execution of the steps of a demodulation method according to any one of claims 1 to 5, and / or a modulation method according to any one of claims 6 to 10.

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