Relative signal encoding method

Abstract

A method for encoding a source message via a symbol frame, the source message comprising a first number (l) of initial variables (x0, x1,…,xl-1), each initial variable being discrete and taking values ​​from a finite set (F), the method comprising the steps: 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 includes said coded absolute variables (c0, c1,…, cm -1).Figure from the summary: Figure 3.

Description

Title of the invention: Method for relative encoding of a signal technical field

[0001] The present disclosure falls within the domain of communication systems coupled with error correction mechanisms, and relates more particularly to 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 of the message are implemented in order 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 the received information not by considering estimated absolute values ​​for each received symbol, but relative differences or offsets between symbols.

[0004] An example of relative information representation can be illustrated in a way simple by considering a framework of 5 symbols x2, x3, XJ, each symbol encoding k bits of information and therefore able to take 2k possible values. A relative representation of such a frame can for example be [x0 / ). x1 / 2, x2 / 3, x3 / 4] = [x0-xt, xrx2, x2-x3, x4-x3].

[0005] In another example illustrating a possible context for using a relative representation of information, the so-called CCSK (Cyclic Code Shift Keying) modulation allows two bits (or more, depending on the size of the sequence) of information to be modulated orthogonally to represent a sequence by means of 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 thus makes it possible to encode the information with respect to a reference sequence, so that the symbols are independent of each other. others. In particular, a transmission error affecting a CCSK symbol does not affect subsequent symbols.

[0006] The CCSK modulation implemented then allows the sequence to be represented as a time-frequency frame, called a CCSK-CP-OFDM frame, in which each of the N CCSK symbols of size K 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 by 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: (As / a \ j

[0007] In particular, each coefficient Pyj of such a matrix contains a vector of size K (the size of a CCSK symbol) representing the relative offset 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 offset of symbol 3 with respect to symbol 5 is 0.2, the probability of a one offset of symbol 3 with respect to symbol 5 is 0.3, the probability of a two offset of symbol 3 with respect to symbol 5 is 0.1 and the probability of a three offset 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(P3 / 5) = 3.

[0008] The relative representation of information (for example, obtained by considering relative shift probabilities between CCSK symbols in reception, from a CCSK-CP-OFDM type modulation in transmission, as described above) then offers several advantages, particularly exploitable in information reception. In particular, it allows, during reception processing, for enriching symbol estimation and exploiting information redundancy by leveraging the relationships between the received relative information. For example, the received matrix P reflects symmetry and / or chaining relationships between the coefficients. Typically, Pi / j (relative shift probabilities of symbol i with respect to symbol j) and Pj / j (relative shift probabilities of symbol j with respect to symbol i) are related; Pi / a, Pj, 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 that work with a relative representation of the symbols.

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

[0010] In order to combine the advantages of both the relative representation of information and error correction in message transmission, there is a need to adapt error correction mechanisms to the relative nature of the 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

[0011] The present disclosure therefore addresses such a problem.

[0012] 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: - determine a second set of so-called relative variables, the relative variables being expressed by a change of variable using the initial variables, - encode 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, - determine a fourth number of so-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 includes said coded absolute variables.

[0013] Consequently, 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 (i.e., at the output of the transmission channel) that relies on and / or takes advantage of a relative representation of the information. Such processing in relative space can, for example, correspond to demodulation and / or decoding processes based on relative information. This encoding therefore makes it possible to exploit the advantages (in particular, improved reproduction of the received signal) of the relative representation of information by adapting the signal for this purpose at the encoding stage.

[0014] Furthermore, the proposed encoding process allows for the introduction of redundancy of such relative information by encoding, making it possible to introduce a transmission error correction mechanism within the source frame to be transmitted.

[0015] In particular, the method proposes an encoding that allows relative relationships within the source information to be expressed, while enabling transmission in a transmission channel (and more generally via a communication system) in a generic manner 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 therefore be easily integrated as an encoding component into any existing information transmission structure.

[0016] 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 (particularly 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 allowing, at the receiver, the implementation of processes that specifically exploit relative relationships between elements of the source message.

[0017] The features described in the following paragraphs may optionally be implemented independently of each other or in combination with each other:

[0018] In one embodiment, the first number of initial variables, denoted 1, and the second number of relative variables, denoted k, are related by 1 - 1 < k.

[0019] Consequently, the proposed encoding method makes it possible to preserve all the elements contained in the source information, without loss of information during relative encoding. Indeed, the number of relative variables expressed then makes it possible to express all the information of the initial message, and also to introduce information redundancy (as an error correction mechanism) without loss of information, when this second number is strictly greater than the first number.

[0020] In one embodiment, the change of variable expressing the relative variables and using the initial variables corresponds to:

[0021] yi = xi+1-xo

[0022] where i is a numerical index between 0 and k-1 and x0 is a fixed initial variable.

[0023] In one embodiment, the change of variable expressing the relative variables and using the initial variables corresponds to:

[0024] yi = xi+1 -

[0025] where i is a numerical index between 0 and k-1.

[0026] 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.

[0027] In one embodiment, said initial chaining relation corresponds to x0=c0.

[0028] In one embodiment, the fourth number of coded absolute variables is strictly greater than the first number of initial variables.

[0029] In one embodiment, the change of variable expressing the coded absolute variables and using the coded relative variables corresponds to:

[0030] Z;- = ci +i - c0

[0031] where i' is a numerical index between 0 and n-1 and c0 is a fixed coded absolute variable.

[0032] In one embodiment, the change of variable expressing the coded absolute variables and using the coded relative variables corresponds to:

[0033] Z;- = ci +i - Ci-

[0034] where i' is a numerical index between 0 and n-1.

[0035] In one embodiment, the coded absolute variables are linked together by coding relationships.

[0036] In one embodiment, the coding matrix corresponds to a Hamming code of dimension depending on the second number.

[0037] More generally, the encoding process allows the use of any existing coding matrix.

[0038] According to another aspect, an encoder is proposed comprising at least: - a communication unit configured to receive data relating to a source message comprising an initial set of variables, - at least one processing unit comprising at least one processor configured to implement the proposed process.

[0039] 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 such as the one 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.

[0040] According to another aspect, a computer program is proposed comprising instructions for implementing all or part of a process as defined herein when this program is executed by a processor. According to another aspect, a non-transient, computer-readable recording medium is proposed on which such a program is recorded. Brief description of the drawings

[0041] Other features, details and advantages will become apparent from reading the detailed description below and from analyzing the accompanying drawings, in which: Fig. 1

[0042] [Fig.1] shows a communication system comprising an encoder according to an embodiment of the present. Fig. 2

[0043] [Fig.2] shows steps of an encoding process via a relative space according to a method of implementation of the present. Fig. 3

[0044] [Fig.3] shows an encoding scheme via a relative space according to a mode of implementation of this document. Description of the implementation methods

[0045] Reference is now made to [Fig. 1]. [Fig. 1] schematically illustrates a communication system 10 (e.g., wired or wireless), configured to transmit a sequence of source information, also referred to as the source message (e.g., a 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).

[0046] The encoding entity (also referred to as the encoder) is configured to transform the source information, for example, an analog or digital signal, into so-called coded data. In particular, 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, according to Figures 2 and 3.

[0047] The modulation unit 13 (also referred to as the modulator) is configured to adapt the source information (in particular, encoded information) to the transmission channel 14, for example by adapting the information spectrum to the frequency range suitable for transmission. The modulation implemented by the modulation unit 13 may, for example, consist of transforming the encoded source information into a time-frequency frame composed of CCSK symbols distributed over a plurality of time steps, each CCSK symbol being distributed over a plurality of frequency subcarriers. Such an example of a frame obtained at the output of the modulation unit 13 may, for example, be illustrated as follows: 1] ... —' î]\ [Math. 2] 7; = ...... \ ^©[0] — Cv-iP]

[0048] Such a frame, denoted Ts, comprises here N columns representing N time steps and K rows representing K frequency subcarriers. Each CCSK symbol contained in the frame, denoted c; (i between 0 and Nl), corresponds to a symbol to be transmitted obtained from the output of the encoding entity according to the relative encoding method 200. Each symbol c; has a size K (e.g., is composed of K bits of information). The set of symbols c0,..cN_i thus constitutes a representation of the source information, containing, in particular, information redundancy due to the encoding.

[0049] The modulation unit may in particular correspond to any existing modulator, for example a CCSK-CP-OFDM type modulation unit configured to adapt the symbols at the output of the encoding unit to the transmission channel into a Ts frame, called CCSK-CP-OFDM as illustrated in [Math. 2]. More generally, OFDM modulation may be used for example.

[0050] Once encoded and modulated, the encoded and modulated source information, represented by a symbol frame, can be transmitted via the transmission channel 14. The 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, the transmission channel 14 is particularly likely to affect the transmitted frame Ts, for example, with noise, so that the symbol frame Tr received on the receiving side 15, 16, 17 differs from the transmitted frame Ts. A problem on the receiving side 15, 16, 17 is then the demodulation and decoding of the received frame Tr in order to reconstruct the source information as faithfully as possible.In particular, consideration is given here to certain demodulators 15 and / or decoders 16, 17 configured to implement processes relying specifically on a relative representation of the information received.

[0051] The demodulation unit 15 (also referred to as the demodulator) is configured to perform an operation inverse to that of the modulator, namely to extract the received symbols from the frequency subcarriers of the received frame Tr.

[0052] 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 received frame Tr to be represented as a matrix (or tensor) P of probability distributions of relative offsets between symbols of the received frame Tr, as shown in [Math.1]. Such an equalization unit and its process for obtaining the matrix P is illustrated, for example, in document [DFTLink]. In other examples, any receiving processing that enables a differential representation of the received frame to be obtained, in particular in the form of data relating to differences between symbols of the received frame, may be used.

[0053] In such an embodiment, the demodulation unit 15 then allows the processing of data relating to the received frame Tr, corresponding for example to the matrix P, so as to obtain a demodulated frame (containing coded demodulated symbols). For this purpose, the demodulation unit 15 used, at least in part, may be that described in document [GLAD].

[0054] 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.

[0055] 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 the symbols from the received frame relies on a probabilistic decision.

[0056] In another example, regardless of the demodulation method implemented, the decoding entity can also take advantage of a frame received at the output of the transmission channel encoded by the relative encoding process. For example, the decoding entity can correspond to a so-called hard decoder, using a parity matrix H for decoding and calculating syndromes, that is, vectors obtained by multiplying data relative to the received coded elements (i.e., the symbols encoded in the received frame Tr, 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.

[0057] 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 [Fig. 1].

[0058] Reference is now made to [Fig. 2]. [Fig. 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 [Fig. 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 that takes 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].

[0059] At a step S200, the encoder receives a source message to be transmitted via the communication system 100. Such a source message may, for example, consist of a sequence of initial variables x0, Xi,...,Xn. Each initial variable x; (i being a numerical index between 0 and 1-1) is discrete and can take values ​​from a A set of values ​​in a finite field FK of size K. For example, when the initial variables x0, xb, ..., Xn correspond to bits, i.e., binary values ​​(i.e., 0s and 1s), Fk - 2 is a binary field. Thus, x0, xb, ..., ¾ ∈ FK*.

[0060] At a step S210, the encoder defines k new variables called relative variables, y0, yb..., yk.b, the relative variables y0, yb..., yk.i being expressed by a change of variable using the initial variables x0, xb..., xi_b

[0061] The number k of relative variables can in particular be related to the number 1 of initial variables x0, xb...,xn by 1 - 1 < k, so that all the initial variables x0, xb...,xu are represented and contained in the relative variables y0, yb..., yk.b

[0062] The change of variable implemented in step S210 can for example be:

[0063] [Math. 3] y; = x; +[ - x0,

[0064] where i is a numeric index between 0 and k-1 and x0 is the first initial variable.

[0065] 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 x0.

[0066] 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:

[0067] [Math. 4]y; = Xi +1 - x;,

[0068] where i is a numerical index between 0 and k-1.

[0069] Consequently, the change of variable implemented in step S210 introduces a relative representation (i.e., in a relative space) of the elements constituting the source message. The information processed at this stage is therefore no longer absolute information (namely, values ​​of the initial variables x0, xb...,xn directly reflecting the content, e.g., the words, of the source message) but relative information, here typically the offset between two elements constituting the source message.

[0070] At step S220, the relative variables y0, yb..., 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 y0, yb..., yk i) and redundancy (e.g., relationships between the source message elements). Furthermore, the number n of coded elements (i.e., the size of the coded message or word) can be defined, n being greater than k. Thus, the efficiency of the encoding implemented at step S220 can be defined as k / n.

[0071] To this end, step S220 defines an encoding relation for the relative variables y0, yb ..., yk_i which can be expressed as follows:

[0072] [Math. 5] z = yx G

[0073] where G corresponds to the coding matrix, y corresponds to a matrix y = [y0, yb..., yk.i] containing the relative variables y0, yb..., yk.b and z corresponds to the coded elements obtained, called coded relative variables, denoted z0, zb..., zn_b

[0074] 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 y0, yb..., yk.b and n corresponds to the number of coded relative variables z0, zb..., zn_b

[0075] The number of coded relative variables z0, zb..., zn i is greater than the number of relative variables y0, yb..., yk.b

[0076] For example, considering a number 1 = 5 of initial variables x0, xb.. .,x4 and a yield code of k / n = 4 / 8, we define k=4 relative variables y = [y0, yb y2, y4] resulting in n=8 coded relative variables, z = [z0, zb..., z7].

[0077] The S220 encoding step can then use a code-generating matrix, corresponding to a Hamming code C(8,4), as follows:

[0078] [Math. 6] ■1 0 0 0 1 1 1 0' 0 10 0 110 1 0 0 10 10 11 .0 0 0 1 0 1 1 1.

[0079] In another embodiment, any other type of existing code-generating matrix may also be used.

[0080] In such an example, the encoding relation defined in [Math. 5] is expressed as follows: Fl [Math. 7]: [zo, zi,..., z?] ” [yos yt, yz, ysl x 0 1 0 0 0 U 1 0 0. 1 1 1 0' 0 1 1 0 1 0 1 0 1 1 1 0 1 1 1.

[0081] Such a relation [Math. 7] can then be translated into a system of equations linking the relative and relative variables coded as follows: [Math.. 8]:

[0082] Step S220 then makes it possible 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 (i.e., the first four coded relative variables z0, zb, z2, z3 contain the source information, resulting in an identity relationship between the relative variables and the coded relative variables), and - the introduction of redundancy of source information due to coding (i.e., the last four coded relative variables z4, z5, z6, z7, resulting in relationships between the relative variables).

[0083] The number n = 8 of coded relative variables therefore makes it possible to quantify the coding and thus the amount of redundancy introduced in step S220.

[0084] At step S230, a second change of variable linked to the first change of variable is implemented on the relative variables coded z0, zb..., zn.b so as to determine m so-called absolute variables coded c0, cb..., cm.b. Such a second change of variable corresponds in particular to the same change of variable used in step S210 to obtain the relative variables y0, yb..., yk.b

[0085] 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 c0, cb..., cm_i as follows:

[0086] [Math. 9]: z; = Ci +[ - U,

[0087] where i is a numerical index between 0 and n-1.

[0088] Applying relation [Math. 9] to the previous example with expression [Math. 8] of the coded relative variables z0, zb..., zn b, we obtain a new system of equations following at step S230, defining new coded absolute variables c0, cb..., cm_ i to be transmitted: Xi - = >0 = X ~ lu fe ~ Ci) = = Ji = (X2 — 10] ui I LÉ = Z3 = e4 = Ys - y0 = (x4 - x3) + + y2 - ,(cc - c7) = Z? = ¾ +■ y2 + ya = (¾ -Xj + C .¾ - x2) + (x4 -

[0089] In particular, the number m of coded absolute variables c0, cb..., cm.i then follows directly from the number n of coded relative variables z0, zb..., zn_i and the change of variable used, here m = n+1 (as illustrated in [Fig.3] with the n+1 variables c0, cb cn).

[0090] Following step S230, process 200 then allows the introduction of m coded absolute variables c0, cb..., cm_i formatted for transmission via the communication system 100. In particular, such coded absolute variables allow both: - to visualize the source information in a relative form (i.e., the initial variables x0, xb...,xn of the source message appear as relative relations), and - to introduce information redundancy due to coding (i.e., the m=8 coded absolute variables allow 4 new variables to appear, where the source message only contains 4 initial variables).

[0091] The S230 step then allows the expression of absolute symbols coded c0, cb..., cm_i for transmission via the communication system.

[0092] At a step S240, the values ​​of such m coded absolute variables c0, cb..., cm_i are determined for transmission. To this end, the coded absolute variables c0, cb..., cm_i are successively determined, step by step, from: - the change of variable expressing the absolute variables coded c0, cb..., cm i and using the relative variables coded z0, zb..., zn b and - of an (initial) chaining relation between a first absolute variable coded c0 and a first initial variable x0. Such a chaining relation can also link other variables, according to the change of variable relation used in step S210.

[0093] For example, with reference to the example illustrated above, the absolute variables coded c0, cb..., cm i are determined with the following rule:

[0094] Thus, at step S240, the m absolute coded variables c0, cb..., cm4 to be transmitted can all be determined in an absolute way.

[0095] In particular, by definition of the absolute coded variables c0, cb..., cm_b, parity relations (or coding relations) S exist between them 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: [Math. 12]: S Æcs - c4) = (q | (¾ — ^s) = (A (c7 - Q) = (q 1(¾ “ ¾) = (¾ - £«) + (¾ - -¾) + (¾ - ¾) q) + (Q - WHERE - + (¾ ~ £3) + (¾ ~ C2 ? + (¾ -¾) -¾) q = -q + ​​c3 + c4 Q - - q 4- c2 + q - q 4- c5 C7 “ Q — ^0 — ^2 c4 cs = -€1 4- e4 4- q

[0096] At step S250, a frame Ts of coded 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 c0, cb..., cm_b

[0097] It should be noted that such absolute variables coded c0, cb..., cm1 can be interpreted in a conventional manner by any communication system, and in particular can be processed by any modulator 13, for the purpose of transmitting a source frame Ts. Such absolute variables coded c0, cb..., cm1 nevertheless contain information that can be interpreted in a relative manner by any downstream process (demodulation and / or decoding) based on a relative representation of the information.

[0098] The process 200 as described in [Fig. 2] is schematically summarized in [Fig. 3]. [Fig. 3] illustrates the specific processing method proposed, working on both absolute and relative spaces (i.e., spaces representing values, variables, and symbols), both to introduce relative relationships between the variables of the source message and to allow generic, absolute transmission by any communication system 100 (in particular, any modulation unit 13, any transmission channel 14). Such an encoding process can therefore be introduced into any communication system 100, 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 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 (i.e., the coded symbols in the received frame Tr) by the parity matrix H. Such a matrix H can be defined by:

[0100] [Math. 14] : GHT=0

[0101]

[0102]

[0103]

[0104]

[0105]

[0106]

[0107]

[0108]

[0109]

[0110] [Math. 15]: H = where G corresponds to the coding matrix used in the encoding process at step S220. 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: 3 3 3 0 1 0 0 0' 3 3 0 3 0 1 0 0 3 0 3 3 0 0 1 0 0 3 3 3 0 0 0 1. The syndrome denoted s can then be defined as: [Math. 16] : s = 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. Here, due to the chosen encoding, the received coded elements are not directly vectors of received symbols directly translating the source information, but relative virtual symbols calculated at reception (for example via the algorithm described in the [DFTLink] document or any other process allowing calculation of relative relationships between received symbols) based on the symbols actually received. Thus, if the received symbols are denoted Ph, the relative symbols can be calculated as differences between received symbols and denoted P^j = P, " Pj. Similarly, the error ei actually suffered by the physical symbol 1 of the source frame is not the same as the error perceived by the decoding mechanism which works on the relative symbols and therefore errors, themselves relative eijj = ei ' eJ. Considering z = [z0, zb..., zn], where J is the vector of coded relative values ​​obtained previously in step S220, P / is the corresponding vector of relative symbols calculated at reception, and ete / is the vector of relative errors experienced by the system, we see that: [Math. 17]: s = p?HT = (z + e^H1, = (yG + e?.)HT = yGHT + e / HT = e;HT 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: [Math. 18]: z = pz - é} = p7 — f(s) = - f(p;HT)

[0111] 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(g) 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

[0112] - 10: communication system

[0113] - 11: Signal encoding unit

[0114] - 12: transmission channel encoding unit

[0115] - 13: modulation unit

[0116] - 14: transmission channel

[0117] - 15: demodulation unit

[0118] - 16: transmission channel decoding unit

[0119] - 17: signal decoding unit

[0120] -1: (first) number of initial variables

[0121] - x0, Xi,...,Xn: initial variables

[0122] - Fk: finite field of size K

[0123] - k: (second) number of relative variables

[0124] - y0, yi,..., yn: relative variables

[0125] - y: matrix of relative variables

[0126] - n: (third) number of coded relative variables

[0127] - z0, Zi,..zn i : coded relative variables

[0128] - z: matrix of coded relative variables

[0129] - m: (fourth) number of coded absolute variables

[0130] - c0, Ci,..., cm4 : coded absolute variables

[0131] - G: coding matrix List of documents cited Patent documents

[0132] For the avoidance of doubt, the following patent documents are cited:

[0133] - [DFTLink]: FR 23 06540

[0134] - [GLAD]: FR 23 14765.

Claims

Demands

1. A method (200) for encoding a source message to be transmitted over a transmission channel via a symbol frame, the source message comprising a first number (1) of initial variables (x0, xb..., Xi_i), each initial variable being discrete and taking values ​​from a finite set (F), the method comprising the following steps: - (S210) determining a second number (k) of so-called relative variables (y0, yb..., yk_i), the relative variables (y0, yb...yk_i) being expressed by a change of variable using the initial variables (x0, xb..., xu), - (S220) encoding the relative variables (y0, yb..., yk_i) using a predefined coding matrix (G), said encoding resulting in a third number (n) of so-called coded relative variables (z0, zb..., zn), the third number (n) being greater than the second number (k), - (S230) determine a fourth number (m) of so-called absolute coded variables (c0, cb..., cm 4), the coded absolute variables (c0, cb..., cm J being expressed by the change of variable using the coded relative variables (z0, zb..., Zn -1), and in which the symbol frame to be transmitted (Ts) includes said coded absolute variables (c0, cb..., cm i).

2. Method (200) according to claim 1, wherein the first number (1) of initial variables (x0, xb...,xki) and the second number (k) of relative variables (y0, yb..., yk-i) are related by 1 - 1 < k, where i is the first number and k is the second number.

3. Method (200) according to claim 2, wherein the change of variable expressing the relative variables (y0, yb..., yk.i) and using the initial variables (x0, xb...,xki) corresponds to: yi = Xi +i - x0 where y; is a relative variable, x; +[ is an initial variable, i is a numeric index between 0 and k-1 and x0 is a fixed initial variable.

4. A method (200) according to claim 2, wherein the change of variable expressing the relative variables (y0, yb..., yki) and using the initial variables (x0, xb..., xki) corresponds to: Yi = Xi +1 - where y; is a relative variable, x; and xi+i are initial variables and i is a numerical index between 0 and k-1.

5. Method (200) according to any one of the preceding claims, wherein the coded absolute variables (c0, cb..., cm 4) are successively determined from: - the change of variable expressing the coded absolute variables (c0, cb..., cm i) and using the coded relative variables (z0, zb..., zn 4), and - an initial chaining relation between a first coded absolute variable (c0) and a first initial variable (xo).

6. Method (200) according to claim 5, wherein said initial chaining relation corresponds to x0=c0, where xo is the first initial variable and co is the first coded absolute variable.

7. Method (200) according to any one of the preceding claims, wherein the fourth number (m) of coded absolute variables is strictly greater than the first number (1) of initial variables (x0, Xb...,Xu).

8. Method (200) according to claim 3, wherein the change of variable expressing the coded absolute variables (c0, cb..., cm .1) and using the coded relative variables (z0, zb..., zn .1) corresponds to: zi ' = ci ' +1 — c0 where Z;- is a coded relative variable, ci +i is a coded absolute variable, i' is a numeric index between 0 and n-1 and c0 is a fixed coded absolute variable.

9. Method (200) according to claim 4, wherein the change of variable expressing the coded absolute variables (c0, cb..., cm .1) and using the coded relative variables (z0, zb..., zn .1) corresponds to: Zi' = Ci- +1 - Ci' where Z, is a coded relative variable, cr and ci +i are coded absolute variables and i' is a numeric index between 0 and n-1.

10. Method (200) according to any one of the preceding claims, wherein the coded absolute variables (c0, cb..., cm .1) are related to each other 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 (1) of initial variables (x0, Xi,...,Xn), - at least one processing unit comprising at least one processor configured to implement the method (200) 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 11, - a decoder configured to process a received symbol frame, said frame comprising symbols reflecting relative parity relations linking initial variables (x0 , Xi,...,Xu) contained in the source message.

13. Computer program comprising instructions for carrying out the method (200) 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 is recorded a program for implementing the method (200) according to any one of claims 1 to 10 when this program is executed by a processor.