Method for achieving relative encoding of a signal

Abstract

Disclosed is a method for encoding a source message via a symbol frame, the source message containing a first number (l) of initial variables (x0, x1,…,xl-1), each initial variable being discrete and taking values among a finite set (F), the method comprising the steps of: - determining a second number (k) of relative variables (y0, y1,…, yk-1) expressed by a change of variable using the initial variables (x0, x1,…,xl-1), - encoding the relative variables (y0, y1,…, yk-1) using a predefined coding matrix (G), said encoding resulting in a third number (n) of coded relative variables (z0, z1,…, zn-1), the third number (n) being greater than the second number (k), - determining a fourth number (m) of coded absolute variables (c0, c1,…, cm-1) expressed by the change of variable using the coded relative variables (z0, z1,…, zn-1), and in which the symbol frame contains said coded absolute variables (c0, c1,…, cm-1).

Description

Description Title: Relative signal encoding method technical field

[0001] This disclosure falls within the domain of communication systems coupled with error correction mechanisms, and more specifically concerns an encoding process enabling the introduction of a relative representation of information in the transmission of a source frame in communication systems. 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, Cyclic Code Shift Keying (CCSK) 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:

[0008] In particular, each Pi / j coefficient 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.

[0009] The relative representation of information (for example, obtained by considering probabilities of relative shifts between CCSK symbols in reception, from a CCSK-CP-OFDM type modulation in transmission, as described previously, or by considering probabilities of angle or phase differences in reception in the case of QPSK modulation—such a relative representation not being limited to CCSK modulation) offers several advantages, particularly useful in information reception. Specifically, it allows, during reception processing, for enriching symbol estimation and exploiting information redundancy by leveraging relationships between the received relative information. For example, the received P matrix reflects symmetry and / or chaining relationships between the coefficients.Typically, Pi / j (probabilities of relative shifts of symbol i with respect to symbol j) and Pj / i (probabilities of relative shifts of symbol j with respect to symbol i) are related; Pi / . a Pa / 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.

[0010] Furthermore, to mitigate errors and transmission defects (e.g., those related to noise) of the message (regardless of its relative or absolute representation), error correction mechanisms are known to be used, 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 multiple times (thus creating redundancy). information redundancy), in order to increase the probability of detecting inconsistencies in the message and obtaining the correct symbols at reception.

[0011] In order to combine the advantages of both relative information representation and error correction in message transmission, there is a need to adapt error correction mechanisms to the relative nature of information representation and its processing upon reception. In particular, the transmission phase—and especially the encoding—of the information to be transmitted requires taking this specific characteristic into account. Summary

[0012] This disclosure is intended to address such a problem.

[0013] A method is proposed for encoding a source message to be transmitted over a transmission channel via a symbol frame, the source message comprising a first number of initial variables, each initial variable being discrete and taking values ​​from a finite set, the method comprising the following steps: determining a second number of variables called relative variables, the relative variables being expressed by a change of variable using the initial variables, encoding the relative variables using a predefined coding matrix, said encoding resulting in a third number of relative variables called coded variables, the third number being greater than the second number, determining a fourth number of variables called coded absolute variables, the coded absolute variables being expressed by the change of variable using the coded relative variables, and in which the symbol frame to be transmitted comprises said coded absolute variables.

[0014] Therefore, the proposed encoding method allows for the introduction of relative relationships between the elements of the source message, namely the initial variables or initial symbols. Such encoding is particularly advantageous for frame reception processing (Le., at the output of the transmission channel) that relies on and / or leverages a relative representation of information. Such processing in relative space can, for example, correspond to demodulation and / or decoding processes based on relative information. This encoding thus allows for the exploitation of the advantages (in particular, improved reproduction of the received signal) offered by the relative representation of information by adapting the signal accordingly at the encoding stage.

[0015] Furthermore, the proposed encoding process allows for the introduction of redundancy of such relative information by encoding, enabling the introduction of a transmission error correction mechanism within the source frame to be transmitted.

[0016] In particular, the process offers an encoding that allows for the expression of relative relationships within the source information, while also enabling transmission in a transmission channel (and more generally via a communication system) in a generic way within a source frame. Regardless of the modulation process used, and in which there is no structure (particularly a relative one) between the symbols received at the output of the transmission channel, the proposed method can be easily integrated as an encoding component into any existing information transmission structure.

[0017] Indeed, by transmitting coded absolute symbols, the proposed encoding method makes the introduction of relative relationships into the information "invisible" to the communication system, since the latter receives a source frame to be transmitted (notably after modulation) containing coded absolute symbols, formatted like any existing coded symbol frame. Thus, any modulation process (differential or otherwise) can be used to modulate the symbol frame to be transmitted, while also allowing, at the receiver, the implementation of processes that specifically exploit relative relationships between elements of the source message.

[0018] The features described in the following paragraphs may optionally be implemented, independently of each other or in combination with each other:

[0019] In one embodiment, the first number of initial variables, denoted I, and the second number of relative variables, denoted k, are related by I - 1 < k.

[0020] Therefore, the proposed encoding method preserves all the elements contained in the source information without any loss of information during relative encoding. Indeed, the number of relative variables expressed allows for the representation of all the information from the initial message, and also introduces information redundancy (as an error correction mechanism) without loss of information, provided that this second number is strictly greater than the first.

[0021] In one embodiment, the change of variable expressing the relative variables and using the initial variables corresponds to: yi = Xi+i - xo where yi is a relative variable, Xi+i is an initial variable, i is a numerical index between 0 and k-1 and xo is a fixed initial variable.

[0022] In one embodiment, the change of variable expressing the relative variables and using the initial variables corresponds to: yi = Xi+i - X where yi is a relative variable, x and x+i are initial variables and i is a numerical index between 0 and k-1.

[0023] In one embodiment, the coded absolute variables are successively determined from: the change of variable expressing the coded absolute variables and using the coded relative variables, and of an initial chaining relationship between a first coded absolute variable and a first initial variable.

[0024] In one embodiment, said initial chaining relation corresponds to xo=co, where xo is the first initial variable and co is the first absolute coded variable.

[0025] In one embodiment, the fourth number of coded absolute variables is strictly greater than the first number of initial variables.

[0026] In one embodiment, the change of variable expressing coded absolute variables and using coded relative variables corresponds to: Zi' = Ci'+1 — Co where Zi is a coded relative variable, cr+i is a coded absolute variable, i' is a numerical index between 0 and n-1 and co is a fixed coded absolute variable.

[0027] In one embodiment, the change of variable expressing coded absolute variables and using coded relative variables corresponds to: Zi' = Ci'+1 — Ci' where Zi is a coded relative variable, cr and c+i are coded absolute variables and i' is a numerical index between 0 and n-1.

[0028] In one embodiment, the coded absolute variables are linked together by coding relations.

[0029] In one embodiment, the coding matrix corresponds to a Hamming code of dimension depending on the second number.

[0030] More generally, the encoding process allows the use of any existing coding matrix.

[0031] According to another aspect, an encoder is proposed comprising at least: a communication unit configured to receive data relating to a source message comprising a first number of initial variables, at least one processing unit comprising at least one processor configured to implement the proposed process.

[0032] According to another aspect, a communication system is proposed that is configured to transmit a source message via a transmission channel, said communication system comprising at least: an encoder as previously proposed, a decoder configured to process a received symbol frame, said frame comprising symbols reflecting relative parity relations linking initial variables contained in the source message.

[0033] In another aspect, a computer program is proposed that includes instructions for implementing all or part of a 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

[0034] Other features, details, and advantages will become apparent upon reading the detailed description below and analyzing the attached drawings, on which: Fig. 1

[0035] [Fig. 1] shows a communication system comprising an encoder according to an embodiment of the present. Fig. 2

[0036] [Fig. 2] shows steps of an encoding process via a relative space according to one embodiment of the present. Fig. 3

[0037] [Fig. 3] shows an encoding scheme via a relative space according to one embodiment of the present. Description of the implementation methods

[0038] Reference is now made to Figure 1. Figure 1 schematically illustrates a communication system 10 (e.g., wired or wireless), 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, in particular, include an encoding entity (itself comprising a signal encoding unit 11 and a transmission channel encoding unit 12), a signal modulation unit 13, the transmission channel 14, a signal demodulation unit 15, and a decoding entity (itself comprising a transmission channel decoding unit 16 and a signal decoding unit 17).

[0039] The encoding entity (also referred to as the encoder) is configured to transform the source information, for example, an analog or digital signal, into coded data. Specifically, in the context of this description, the encoder is configured to generate, from source information, coded data containing a relative representation of the information. To this end, the encoding may include a processing circuit comprising at least one processor, a memory unit, and communication means enabling the implementation of such a relative encoding process as described later in Figures 2 and 3.

[0040] The modulation unit 13 (also referred to as the modulator) is configured to adapt the source information (in particular, coded information) to the transmission channel 14, for example by adapting the information spectrum to the frequency range suitable for transmission. The modulation put The operation implemented by 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 modulation unit 13 can, for example, be illustrated as follows:

[0041] [Math.

[0042] Such a framework, 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 G (i 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.

[0043] The modulation unit can be any existing modulator, for example a CCSK-CP-OFDM type modulation unit configured to adapt the symbols output from the encoding unit to the transmission channel into a T frame s , called CCSK-CP-OFDM as illustrated in [Math. 2], More generally, an OFDM modulation can be used for example.

[0044] Once encoded and modulated, the encoded and modulated source information, represented by a symbol frame, can be transmitted via transmission channel 14. Transmission channel 14 then allows the information to pass from the transmitting side 11, 12, 13 to a receiving side 15, 16, 17. Such a transmission channel can, for example, be 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 15, 16, 17 differs from the T frame s transmitted. A problem on the receiver side 15, 16, 17 is then the demodulation and decoding of the T frame rreceived with a view to reproducing the source information as faithfully as possible. In particular, certain demodulators 15 and / or decoders 16, 17 configured to implement processes relying specifically on a relative representation of the received information are considered here.

[0045] The demodulation unit 15 (also referred to as the demodulator) is configured to perform the inverse operation of the modulator, namely to extract the received symbols from the frequency subcarriers of the received frame T r .

[0046] In a particular example, such a demodulation unit 15 may be linked to, or include, a receiving processing unit, for example a transmission channel equalization unit, enabling the acquisition of a representation of the received frame T r in the form of a matrix (or tensor) P of probability distributions of relative shifts between symbols of the received frame T r, as represented in [Math.1], such an equalization unit and its process for obtaining the matrix P is illustrated, for example, in the document [DFTLink]. In other examples, all Reception processing that allows obtaining a differential representation of the received frame, in the form of data relating to differences between symbols of the received frame in particular, can be used.

[0047] In such an embodiment, the demodulation unit 15 then allows the processing of data relating to the received frame T r , corresponding for example to the matrix P, so as to obtain a demodulated frame (containing coded demodulated symbols). For this, the demodulation unit 15 used, at least in part, can be that described in the document [GLAD],

[0048] The decoding entity (also referred to as the decoder) 16, 17 can then be configured to receive and decode the demodulated frame output from the demodulation unit 15. In particular, such a decoding entity is configured to implement a decoding of the demodulated symbols specifically adapted to the relative representation of the symbols, due to the relative encoding proposed via the method 200.

[0049] For example, in the embodiment including an equalization unit resulting in the matrix P, such a decoding entity can correspond to a so-called soft decoder, using a probabilistic decoding algorithm based on belief propagation. Thus, the decision to reconstruct symbols from the received frame relies on a probabilistic decision.

[0050] In another example, regardless of the demodulation method used, the decoding entity can also take advantage of a frame received at the output of the transmission channel encoded using relative encoding. For example, the decoding entity could be a so-called hard decoder, using a parity matrix H for decoding and calculating syndromes, that is, vectors obtained by multiplying data relating to the received coded elements (e.g., the symbols encoded in the received frame T). r (possibly after processing by the equalization unit) by the parity matrix H. Such an example of decoding taking advantage of the relative representation introduced during the encoding phase will be described later.

[0051] In another example, the receiving side, namely the demodulation entities 15 and decoding entities 16, 17, together with the equalization unit, can correspond to a joint demodulation-decoding entity, so that entities 15, 16, 17 can be grouped into a single entity, as an alternative to the schematic representation in Figure 1.

[0052] Reference is now made to Figure 2. Figure 2 illustrates steps of a relative encoding process 200, which can be implemented by an encoder 11, 12 of a communication system 10 as shown in Figure 1. In particular, the relative encoding process 200 described is specifically adapted to a communication system using, on the receiving side 15, 16, 17, a relative demodulation process, for example by implementing an equalization process as described in [DFTLink], followed by a demodulation process as described in [GLAD] and a decoding taking into account the relative nature of the received demodulated symbols in order to restore the source information [possibly to be supported with decoding aspects of the other request].

[0053] At step S200, the encoder receives a source message to be transmitted via the communication system 100. Such a source message can, for example, consist of a sequence of I initial variables xo, xi, ..., xi-i. Each initial variable Xi (i being a numeric index between 0 and 1-1) is discrete and can take values ​​from a set of values ​​in a finite field FK of size K. For example, when the initial variables xo, xi, ..., xi-i correspond to bits, i.e., binary values ​​(i, 0s, and 1s), FK=2 is a binary field. Thus, xo, xi, ..., xi e FK 1 .

[0054] At an S210 step, the encoder defines k new variables called relative variables, yo, yi,... , yk-i, the relative variables yo, yi,... , yk-i being expressed by a change of variable using the initial variables xo, xi,... ,xi-i.

[0055] The number k of relative variables can in particular be related to the number I of initial variables xo, xi,...,xi-i by I - 1 < k, so that all the initial variables xo, xi, ... ,xi-i are represented and contained in the relative variables yo, yi,..., yk-i.

[0056] The variable change implemented in step S210 could, for example, be:

[0057] [Math. 3] yi = x+i - xo,

[0058] where i is a numerical index between 0 and k-1 and xo is the first initial variable.

[0059] More generally, the change of variable can be defined in relation to the same fixed initial variable (denoted for example Xf), different from the variable xo.

[0060] The change of variable implemented in step S210 can, in another example (which will be considered as an illustrative example in the remainder of the description of process 200), be:

[0061] [Math. 4] yi = x+i - x,

[0062] where i is a numerical index between 0 and k-1.

[0063] Therefore, the variable change implemented in step S210 introduces a relative representation (Le., in a relative space) of the elements constituting the source message. The information processed at this stage is thus no longer absolute information (i.e., values ​​of the initial variables xo, xi, ..., xi-i directly translating the content, e.g., the words, of the source message) but relative information, here typically the offset between two elements constituting the source message.

[0064] At step S220, the relative variables yo, yi, ..., yk-i are encoded using a predefined coding matrix (or code-generating matrix) G. In other words, step S220 allows the definition of new coded elements containing both the source information (e.g., information related to the source message, reflected by the relative variables yo, yi, ..., yk-i) and redundancy (e.g., relationships between the source message elements). Furthermore, the number n of coded elements (Le., the size of the coded message or word) can be defined, where n is greater than k. Thus, the encoding efficiency implemented at step S220 can be defined as k / n.

[0065] To achieve this, step S220 defines an encoding relation for the relative variables yo, yi, ... , yk-i which can be expressed as follows:

[0066] [Math. 5] z = yx G

[0067] where G corresponds to the coding matrix, y corresponds to a matrix y = [yo, yi,... , yn] containing the relative variables yo, yi, ..., yk-i, and z corresponds to the coded elements obtained, called coded relative variables, denoted zo, zi,... , z n -i.

[0068] The coding matrix G, expressed in the same finite field FK as the initial variables, can for example correspond to a Hamming code C(n,k), where k corresponds to the number of relative variables yo, yi,..., yk-i, and n corresponds to the number of coded relative variables zo, zi,..., z n -i.

[0069] The number of coded relative variables zo, zi,..., z n -i is greater than the number of relative variables yo, yi,... , yk-i.

[0070] For example, considering a number I = 5 of initial variables xo, xi,... ,X4 and a yield code of k / n = 4 / 8, we define k=4 relative variables y = [yo, yi, yo, yo] resulting in n=8 coded relative variables, z = [zo, zi,..., z?].

[0071] The S220 encoding step can then use a code-generating matrix, corresponding to a Hamming C(8,4) code, as follows: 1 0 0 0 1 1 1 0'

[0072] [Math. 6]: 0 1 0 0 1 1 0 1 0 0 1 0 1 0 1 1 0 0 0 1 0 1 1 1.

[0073] In another embodiment, any other type of existing code-generating matrix can also be used.

[0074] In such an example, the encoding relation defined in [Math. 5] is expressed as follows:

[0075] [Math. 7]: [zo, zi,..., z?] = [yo, yi, yo, yo]

[0076] Such a relationship [Math. 7] can then be translated into a system of equations linking the relative and relative variables coded as follows:

[0077] [Math.

[0078] Step S220 then allows us to obtain, from k = 4 relative variables containing the source information (in a relative representation), coded relative variables containing both: the relative representation of the source information (Le., the first four coded relative variables zo, zi, Z2, Z3 contain the source information, resulting in an identity relationship between the relative variables and coded relative variables), and the introduction of a redundancy of source information due to the coding (Le., the last four coded relative variables z4, zs, ze, z?, resulting in relationships between the relative variables).

[0079] The number n = 8 of coded relative variables therefore allows us to quantify the coding and thus the amount of redundancy introduced in step S220.

[0080] At step S230, a second variable change linked to the first variable change is implemented on the relative variables coded zo, zi,... , z n -i, so as to determine m so-called absolute variables coded co, ci, ..., c m -i. Such a second change of variable corresponds in particular to the same change of variable used in step S210 to obtain the relative variables yo, yi,... , yk-i.

[0081] For example, considering the change of variable used corresponding to [Math. 4] in step S210, we can define the m (where m = n+1 due to the change of variable) absolute variables coded co, ci,... , c m -i in the following way:

[0082] [Math. 9]: Zi = c+i - Ci,

[0083] where i is a numerical index between 0 and n-1.

[0084] Applying relation [Math. 9] to the previous example with the expression [Math. 8] of the coded relative variables zo, zi,... , z n -i, we obtain a new system of equations following at step S230, defining new coded absolute variables co, ci,... , c m -i to transmit: (ci - c o) = z0 = 7o = (xi - x0)

[0086] In particular, the number m of coded absolute variables co, ci, ..., c m -i then follows directly from the number n of coded relative variables zo, zi,... , z n -i and the change of variable used, here m = n+1 (as illustrated in Figure 3 with the n+1 variables co, ci,..., c n ).

[0087] At the end of step S230, process 200 then allows the introduction of m coded absolute variables co, ci, ..., c m-i formatted for transmission via communication system 100. In particular, such coded absolute variables allow both: visualizing the source information in a relative form (Le., the initial variables xo, xi,... ,xi-i of the source message appear as relative relations), and to introduce information redundancy due to coding (Le., the m=8 absolute coded variables allow 4 new variables to appear, where the source message only contains 4 initial variables).

[0088] The S230 step then allows the expression of absolute symbols coded co, ci,... , c m -i for transmission via the communication system.

[0089] At step S240, the values ​​of such m absolute variables coded co, ci,... , c m -i are determined for the purpose of their transmission. For this, the absolute variables coded co, ci,..., c m-i are successively, step by step, determined from: the change of variable expressing the absolute variables coded co, ci, ..., c m -i and using the coded relative variables zo, zi,... , z n -i, and an (initial) chaining relation between a first absolute variable coded co and a first initial variable xo. Such a chaining relation can also link other variables, depending on the change-of-variable relation used in step S210.

[0090] For example, with reference to the example illustrated previously, the absolute variables coded co, ci,... , Cm-i are determined with the following rule:

[0091] [Math.

[0092] Thus, at step S240, the m absolute variables coded co, ci,... , c m -i to be transmitted can all be determined absolutely.

[0093] In particular, by definition of the coded absolute variables co, ci, ..., c m -i, parity relations (or coding relations) S exist between these and can constrain the subsequent decoding process. In the example considered, such parity relations can be expressed as follows, in relative and absolute terms respectively: ((c5- c4) = (Cl - c0) + (c2- C4) + (c3- c2)

[0094] [Math. 12]: S = (c6- c5) = (Ci - C0) + (c2- Ci) + (c4- c3) (c7- c6) = (Ci - c0) + (c3- C2) + (c4- c3) V(c8- c7) = (c2- C4) + (c3- c2) + (c4- c3)

[0095] [Math.

[0096] At an S250 step, a T frame scoded symbols can therefore be determined at the output of the encoder to be modulated and then transmitted via the transmission channel 14 of the communication system 100. Such coded symbols correspond in particular to the coded absolute variables co, ci,... , Cm-i.

[0097] It should be noted that such absolute variables coded co, ci, ..., c m -i can be interpreted in a conventional way by any communication system, and in particular can be processed by any modulator 13, for the purpose of transmitting a source frame T s Such absolute variables coded co, ci,..., c m -i nevertheless contain information that can be interpreted in a relative way by everyone downstream process (demodulation and / or decoding) based on a relative representation of the information.

[0098] The 200 process, as described in Figure 2, is schematically summarized in Figure 3. Figure 3 illustrates the specific nature of the proposed processing, which works on both absolute and relative spaces (Le., spaces for representing values, variables, and symbols), both to introduce relative relationships between the variables of the source message and to enable generic, absolute transmission by any communication system (in particular, any modulation unit and any transmission channel). Such an encoding process can therefore be introduced into any communication system, regardless of the modulation and demodulation used, and allow for appropriate decoding based on a relative representation of the information.

[0099] For example, a decoding method taking advantage of the proposed relative encoding can use a parity matrix H, expressed in the same finite field FK as G, and compute syndromes, that is, vectors obtained by multiplying the received coded elements (Le., the encoded symbols in the received frame T) by the received coded elements (Le., the encoded symbols in the received frame T). r ) by the parity matrix H. Such a matrix H can be defined by:

[0100] [Math. 14]: GH T =0,

[0101] where G corresponds to the coding matrix used in the encoding process at step S220.

[0102] For example, taking the example of the coding matrix G = C(8,4) illustrated in [Math. 6], the parity matrix H considered in decoding, considered in the finite field FK=4, can be:

[0103] [Math.

[0104] The syndrome denoted s can then be defined as:

[0105] [Math. 16]: s = bH T

[0106] where b is a received coded element (different from the coded absolute values ​​because it is potentially affected during transmission) and H is the parity matrix of the code.

[0107] Here, due to the chosen encoding, the received coded elements are not directly vectors of received symbols translating the source information, but relative virtual symbols calculated at the receiver (for example, via the algorithm described in the [DFTLink] document or any other process allowing the calculation of relative relationships between received symbols) based on the symbols actually received. Thus, if the received symbols are denoted p t , the relative symbols can be calculated as differences between received symbols and noted p^j = p t - pj.

[0108] Similarly, the error e LThe error actually experienced by the physical symbol i of the source frame is not the same as the error perceived by the decoding mechanism, which works on relative symbols and therefore on errors that are themselves relative. i / 7 = e L - e7.

[0109] Considering z = [zo, zi,..., z n -i] the vector of coded relative values ​​obtained previously in step S220, p z the corresponding relative symbol vector calculated at reception, and e z The vector of relative errors experienced by the system shows that:

[0110] [Math. 17]: s = p z H T = (z + e z )H T = (yG + e z ) H T = yGH T + e z H T = e z H T

[0111] Thus, we see that the value of the syndrome s depends only on the error vector e, which is relative in this case. Furthermore, (for error vectors containing a number of errors in the error-correcting capacity of the code under consideration), there is a unique error vector associated with each syndrome s, such that calculating the syndrome allows us to unambiguously deduce the error vector that affected the communication. The resulting error correction then enables the following decoding:

[0112] [Math. 18]: z = p z - e) = p z - f(s) = p z - z tt T )

[0113] where z is the estimate of the relative coded element transmitted (from which it is possible to deduce the corresponding "absolute" symbols, denoted x) and f(s) is the bijective function uniquely associating a syndrome with the corresponding error vector, f(s) being able to be seen as a table (where, for all possible error vectors, the corresponding syndromes are calculated). List of reference signs

[0114] - 10: communication system - 11: Signal encoding unit - 12: transmission channel encoding unit - 13: modulation unit - 14: transmission channel - 15: demodulation unit - 16: transmission channel decoding unit - 17: signal decoding unit - 1: (first) number of initial variables - xo, xi,... ,xi-i: initial variables - FK: finished body of size K - k: (second) number of relative variables - yo, yi,..., yk-i: relative variables - y: matrix of relative variables - n: (third) number of coded relative variables - zo, zi,..., Zn-i: coded relative variables - z: matrix of coded relative variables - m: (fourth) number of coded absolute variables - co, ci,... , Cm-i: coded absolute variables - G: Coding matrix. List of cited documents. Patent documents

[0115] For the record, the following patent documents are cited: - [DFTLink]: FR 23 06540 - [GLAD] : FR 23 14765.

Claims

Demands

1. A method for encoding a source message to be transmitted over a transmission channel via a symbol frame, the source message comprising a first number (I) of initial variables (xo, xi, ..., xi-i), each initial variable being discrete and taking values ​​from a finite set (F), the method comprising the following steps: determining a second number (k) of so-called relative variables (yo, yi, yk-i), the relative variables (yo, y1, ..., yk-i) being expressed by a change of variable using the initial variables (xo, xi, ..., xi), encoding the relative variables (yo, yi, ..., yk-i) using a predefined coding matrix (G), said encoding resulting in a third number (n) of so-called coded relative variables (zo, zi, ..., z n -i), the third number (n) being greater than the second number (k), determine a fourth number (m) of so-called absolute coded variables (co, ci, ..., c m-i), the coded absolute variables (co, ci, ..., c m -i) being expressed by the change of variable using the coded relative variables (zo, zi, ... , z n -i), and in which the symbol frame to be transmitted includes said coded absolute variables (co, Cl, ..., Cm-l).

2. A method according to claim 1, wherein the first number (I) of initial variables (xo, xi,... ,xi-i) and the second number (k) of relative variables (yo, yi,..., yk-i) are related by I - 1 < k, where i is the first number and k is the second number.

3. A method according to claim 2, wherein the change of variable expressing the relative variables (yo, yi,..., yk-i) and using the initial variables (xo, xi, ... ,xi-i) corresponds to: yi = Xi+i - xo where yi is a relative variable, Xi+i is an initial variable, i is a numerical index between 0 and k-1 and xo is a fixed initial variable.

4. A method according to claim 2, wherein the change of variable expressing the relative variables (yo, yi,..., yk-i) and using the initial variables (xo, xi, ... ,xi-i) corresponds to: yi = Xi+i - X where yi is a relative variable, x and x+i are initial variables and i is a numerical index between 0 and k-1.

5. A method according to any one of the preceding claims, wherein the coded absolute variables (co, ci,... , Cm-i) are successively determined from: the change of variable expressing the coded absolute variables (co, ci,... , c m -i) and using the coded relative variables (zo, zi,... , z n -i), and of an initial chaining relation between a first coded absolute variable (co) and a first initial variable (xo).

6. Method according to claim 5, wherein said initial chaining relation corresponds to xo=co where xo is the first initial variable and co is the first absolute coded variable.

7. A method according to any one of the preceding claims, wherein the fourth number (m) of coded absolute variables is strictly greater than the first number (I) of initial variables (xo, xi,... ,xi-i).

8. A method according to claim 3, wherein the change of variable expresses the coded absolute variables (co, ci, ..., Cm-i) and uses the coded relative variables (zo, zi, ..., z n -i) corresponds to: Zi' = Ci'+1 — Co where Zi is a coded relative variable, cr+i is a coded absolute variable, i' is a numerical index between 0 and n-1 and co is a fixed coded absolute variable.

9. A method according to claim 4, wherein the change of variable expresses the coded absolute variables (co, ci, ..., Cm-i) and uses the coded relative variables (zo, zi, ..., z n -i) corresponds to: Zi' = Q'+1 — Ci' where Zi is a coded relative variable, cr and c+i are coded absolute variables and i' is a numerical index between 0 and n-1.

10. A method according to any one of the preceding claims, wherein the coded absolute variables (co, ci,... , Cm-i) are linked together by coding relations (S).

11. Encoder (11, 12) comprising at least: a communication unit configured to receive data relating to a source message comprising a first number (I) of initial variables (xo, xi, ..., xi-i), at least one processing unit comprising at least one processor configured to implement the method according to one of the preceding claims.

12. Communication system (1) configured to transmit a source message via a transmission channel (14), said communication system (1) comprising at least: an encoder according to claim 1 1 , a decoder configured to process a received symbol frame, said frame comprising symbols reflecting relative parity relations linking initial variables (xo, xi,... ,xi-i) contained in the source message.

13. Computer program comprising instructions for carrying out the method according to any one of claims 1 to 10 when this program is executed by a processor.

14. A non-transient, computer-readable recording medium on which a program is recorded for the implementation of the method according to any one of claims 1 to 10 when this program is executed by a processor.

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