Method for encoding source data, method for decoding codewords, and corresponding devices and computer program

Abstract

The invention relates to a method for encoding at least one block of K.Z c source data, delivering at least one codeword of size N.Z c , the method implementing a step of encoding the K.Z c source data using a parity matrix H. According to the invention, the parity matrix H is obtained from a base matrix BG' expressed in the form: (I). The extension matrix C comprises at least two blocks of L rows and at least one block of L columns, where L is an integer between 1 and K − 1, each block of L rows comprising at least one matrix (II) obtained by applying a circular rotation coefficient α to a diagonal matrix of size L X L, where α is an integer between 0 and L − 1, the at least one block of L columns comprising at least two matrices (II) obtained by applying a distinct circular rotation coefficient α to the diagonal matrix of size L X L.

Description

[0001]DESCRIPTION Title: Method for encoding source data, method for decoding code words, corresponding devices and computer program. 1. Field of the invention The field of the invention is that of digital communications. More specifically, the invention relates to error-correcting codes, and in particular, but not exclusively, error-correcting codes of the LDPC (Low Density Parity Check) type. The invention finds applications in particular in the field of data storage or transmission, for example via wireless communications (for example by radio waves or unguided optical waves) or wired communications (for example by optical fiber or electric cable). In particular, the invention finds applications in all fields where it is sought to offer good transmission reliability, for example for radio transmissions (Wifi®, 5G, 6G, etc.). 2. Prior art Figure 1 illustrates a transmitter of a digital transmission chain.Such a transmitter uses conventional signal processing modules. Thus, the source data 11, for example binary data from a data-generating source of video type (for example a source of animated images, virtual or augmented reality images, an image sequence source), of audio type (for example voice), of flow control type whether of video or audio type or other, or from a sensor, an actuator, etc., are coded in a channel coding block 12 (applying an error-correcting code) to introduce redundancy. The coded data are then interleaved in an interleaving block 13 (called "external") to mix the coded data. A mapping block 14 (also called "signal binary coding") makes it possible to convert the coded data into constellation points (BPSK, QPSK, 16QAM, etc.).The associated symbols are put into frame 15 and modulated in a single-carrier or multi-carrier modulation block 16, for example of the OFDM (“Orthogonal Frequency-Division Multiplexing”) type. In order to improve the robustness of communications via a communication channel, it is known to use error-correcting codes in the channel coding block 12. For example, LDPC codes, turbo-codes, polar codes, or Reed-Salomon codes offer good performance in terms of error correction. Turbo-codes have been chosen in particular for the 4G mobile telephony standard, and LDPC for the 5G mobile telephony standard. The main characteristics of LDPC codes, as defined in the 5G standard in particular, are recalled below.Conventionally, LDPC codes are defined by three parameters ^^^^, ^^^^ and ^^^^: - ^^^^ corresponds to the size of the source data supplied as input to the LDPC encoder, for example in number of useful bits (or information bits) if we consider binary data, - ^^^^ corresponds to the size of the redundancy data added by the LDPC encoder, for example in number of redundancy bits if we consider binary data, and - ^^^^ corresponds to the size of the data coming from the LDPC encoder, for example in number of coded bits, these coded bits including the useful bits and the redundancy bits. The coding efficiency is conventionally given by ^^^^ = ^^^^ / ^^^^, with the relation ^^^^ = ^^^^ + ^^^^. An LDPC code can in particular be defined by a parity matrix ^^^^, which gives the parity relations between the source data and the data redundancy. An example of a binary parity matrix ^^^^ is given in Figure 2.The parity matrix H consists of M rows (defining M parity equations) and N columns. The values ​​equal to "1" in the parity matrix ^^^^ correspond to the connections (defining the parity equations) between the useful data and the redundancy data. The greater the number of connections (i.e. "1" in the parity matrix ^^^^), the greater the complexity of the decoder will be. As an illustration, following the example of the parity matrix ^^^^ in Figure 2, the parity equation defined in the first line gives the first redundancy data ^^^^(0): ^^^^(0) = ^^^^(0)^^^^^(1)^^^^^(2)^^^^^(3)^^^^^(4)^^^^^(6)^^^^^(7)^^^^^(9)^^^^^(10)^^^^^(11)^^^^^(12)^^^^^(13)with:^^^^(^^^^) = 0 or 1, and^ the "exclusive or" operation. In ETSI TS 138 212 V15.2.0, the 3GPP standardization consortium defined two basic structures or matrices BG1 and BG2 ("Base Graph" in English) allowing to construct 104 parity matrices ^^^^ of LDPC codes (52 matrices constructed from the basic matrix BG1 and 52 matrices constructed from the basic matrix BG2). For example, for 5G, the dimensions of the basic matrices BG1 and BG2 are: -BG1: ^^^^ = 22, ^^^^ = 46, ^^^^ = 68- BG2: either ^^^^^^^^ = 6, ^^^^ = 26, ^^^^ = 32, or ^^^^^^^^ = 8, ^^^^ = 34, ^^^^ = 42, or ^^^^^^^^ = 9, ^^^^ = 38, ^^^^ =47, or ^^^^^^^^ = 10, ^^^^ = 42, ^^^^ = 52. We conventionally use the notation ^^^^^^^^ , instead of ^^^^, for the matrix BG2, with ^^^^^^^^^ = {6,8,9,10}. The matrices of parity ^^^^ are obtained from the basic matrices BG1 or BG2, from an expansion factor ^^^^. ^^^^and a circular rotation ^^^^^^^^ of a diagonal matrix. Such a construction is known as "Protograph" in English and allows to have a compact description of the set of matrices. According to this technique, a parity matrix ^^^^ of size ^^^^.^^^^^^^^ × ^^^^.^^^^^^^^ is obtained by replacing each non-zero element of the base matrix BG1 or BG2 by a diagonal matrix of size ^^^^^^^^ × ^^^^^^^ to which a circular rotation ^^^^^^^^ has been applied (which is not necessarily the same for all non-zero elements of the base matrix). An advantage of this family of LDPC encoders is to easily obtain the set of parity matrices ^^^^ while limiting memory usage.For example, for an expansion factor ^^^^^^^^ = 8 and a circular rotation ^^^^^^^^ = 2, a non-zero element of the basis matrix BG1 or BG2 is replaced by the following matrix: 0 0 1 0 0 0 0 0 0 é0 0 0 ù ê 1 0 0 0 0 0 0 0 0 1 0 ú ê 0 0 0 0 0 ú ê 0 0 0 0 0 0 1 0ú ê0 0 0 0 0 0 0 1ú ê 1 0 0 0 0 0 0 0ú ë0 1 0 0 0 0 00. û According to the ETSI TS 138212 V15.2.0 document, for each basic matrix BG1 or BG2, it is thus possible to construct 52 matrices, classified into eight sub-families according to the value of the expansion factor ^^^^ ^^^^ (between 2 and 384), according to the “ils” index: Ils index Expansion factor ^^^^ ^^^^ 0 2,4,8,16,32,128,256 1 3,6,12,24,48,96,192,384 2 5,10,20,40,80,160,320 3 7,14,28,56,112,224 4 9,18,36,72,144,288 5 11,22,44,88,176,352 6 13,26,52,104,208 7 15,30,60,120,240 Thus, it is possible to encode source data blocks of size ^^^^.^^^^ ^^^^, ranging from 12 bits (from the BG2 base matrix with ^^^^ = ^^^^^^^^ = 6 and the minimum expansion factor ^^^^^^^^ = 2) to 8448 bits (from the BG1 base matrix with ^^^^ = 22 and the maximum expansion factor ^^^^^^^^ = 384). The choice between using the BG1 or BG2 base matrix is ​​made according to the size of the source data to be encoded ^^^^.^^^^ ^^^^and the desired coding efficiency ^^^^. Thus, as illustrated in Figure 3, the BG1 basic matrix is ​​mainly used for high coding efficiencies and large sizes of source data to be coded, for example for eMBB ("enhanced Mobile BroadBand") type applications. The BG2 basic matrix is ​​rather used to code small source data blocks (for example ^^^^.^^^^^^^^ < 292 bits, or ^^^^.^^^^^^^^ < 3824 bits and ^^^^ < 2 / 3, or ^^^^ < 0.25), in particular for URRLC ("Ultra Reliable Low Latency Communications") type applications. These two basic matrices are notably designed to cover the different uses of 5G which may require high throughput and / or high reliability (robustness). Furthermore, according to the 5G standard, the first two columns of the basic matrix BG1 or BG2 are removed before transmission, which means that the basic yields are respectively ^^^^ ^^^^^^^^1=^^^^ / (^^^^ − 2) = 22 / 66 = 1 / 3 and ^^^^^^^^^^^^2 = 10 / 50 = 1 / 5.We also note that the basic matrices BG1 or BG2 used to construct the parity matrix ^^^^ of an LDPC code according to the 5G standard can be represented in the form of six sub-matrices ^^^^, ^^^^, 0, ^^^^, ^^^^ and ^^^^, as described in the document "High Area-Efficient Parallel Encoder with compatible architecture for 5G LDPC codes", Y. Zhu et al., and illustrated in Figure 4: �^^^^ ^^^^ 0^^^^ ^^^^ ^^^^�with: ^^^^ a kernel matrix or Kernel of size 4 × ^^^^^^^^ a matrix having at least one double diagonal of size 4 × 4^^^^ an extension matrix of size (^^^^ − 4) × ^^^^^^^^ an extension matrix, also called an extended matrix, of size (^^^^ − 4) × 40 a zero matrix of size (^^^^ − ^^^^ − 4) × 4^^^^ an identity matrix of size (^^^^ − 4) × (^^^^ − ^^^^ − 4).Although LDPC codes are recognized for their ability to guarantee high-speed transmissions, in particular thanks to the possibility of parallelizing operations at the decoder level, a drawback of these codes is the complexity related to decoding. Indeed, the greater the number of decoding iterations, the greater the number of operations to be performed in reception and the more resource-intensive they are. The decoding block can thus use up to 90% of the receiver's resources. It can be considered the most energy-consuming part of the physical layer, in particular for 5G. There is therefore a need for a new coding technique seeking to reduce the energy consumption of the decoder. 3. Presentation of the invention The invention proposes a new solution in the form of a method for coding at least one block of ^^^^.^^^^. ^^^^ source data, delivering at least one code word of size ^^^^.^^^^ ^^^^ formed from the said ^^^^.^^^^^^^^ source data and ^^^^.^^^^^^^^ redundancy data, ^^^^ = ^^^^ + ^^^^, with ^^^^^^^^ an integer expansion factor, ^^^^^^^^ ≥ 1, said method implementing a step of coding said ^^^^.^^^^ ^^^^ source data using a parity matrix ^^^^ of size (^^^^.^^^^^^^^ × ^^^^.^^^^^^^). According to the invention, the parity matrix ^^^^ is obtained from a base matrix ^^^^^^^^' of size ^^^^ × ^^^^, by replacing each element of said base matrix ^^^^^^^^' by an expansion matrix of size^^^^^^^^ × ^^^^^^^^ , of base ^^^^^^^^' expressed in the form: ^^^^^^^^^' ^^^^ 0with: ^^^^ a kernel matrix of size ^^^^ × ^^^^^^^^ a matrix with at least one diagonal of size ^^^^ × ^^^^^^^^ an extension matrix of size (^^^^ − ^^^^) × ^^^^^^^^ an extension matrix of size (^^^^ − ^^^^) × ^^^^0 a zero matrix of size (^^^^ − ^^^^ − ^^^^) × ^^^^^^^^ an identity matrix of size (^^^^ − ^^^^) × (^^^^ − ^^^^ − ^^^^)Furthermore, the extension matrix ^^^^ comprises at least two blocks of ^^^^ rows and at least one block of ^^^^columns, with ^^^^ an integer between 1 and ^^^^ − 1, each block of ^^^^ rows comprising at least one matrix ^^^^ ^ ^ ^ ^^ ^ ^ ^ obtained by applying a circular rotation coefficient ^^^^ to a diagonal matrix of size ^^^^ × ^^^^, with ^^^^ a between 0 and ^^^^ − 1, said at least one block of ^^^^ columns comprising at least two ^^^^ ^ ^ ^ ^^ ^ ^^ obtained by applying a distinct circular rotation coefficient ^^^^ to said diagonal matrix of size ^^^^ × ^^^^. In other words, the extension matrix ^^^^ comprises, in the same block of ^^^^ columns, at least two matrices obtained by applying a distinct circular rotation to a diagonal matrix of size ^^^^ × ^^^^. Advantageously, the matrix formed from the extension matrix ^^^^ and the extension matrix ^^^^ comprises, in the same block of ^^^^ rows, at least two matrices obtained by applying a circular rotation to a diagonal matrix of size ^^^^ × ^^^^. It is thus sought to avoid the repetition of the same pattern on the different blocks of rows and / or blocks of columns of the extension matrix ^^^^, so as to obtain independence between the rows of the extension matrix ^^^^ and avoid, or at least limit, short cycles.We also seek to distribute the non-zero elements of the extension matrix ^^^^ over its different rows and / or columns, in a substantially homogeneous manner. In particular, it is possible to vary the number of connections per row by choosing the size ^^^^ of the row or column blocks. It is recalled for this purpose that the greater the number of connections (i.e. non-zero elements in the basic matrix BG', and consequently in the parity matrix ^^^^) is, the greater the complexity of the decoder. We therefore seek, according to one embodiment, to achieve a compromise between the number of connections and the decoding performance. The proposed solution thus seeks to improve the structure of an LDPC coder, with the aim of accelerating the convergence of the decoder and therefore reducing the energy consumption in reception associated with the use in transmission of this coding module.In a particular embodiment, the proposed basic matrices correspond to the requirements defined by 3GPP in the document TS 138212 V15.2.0 cited previously in terms of block size to be coded ^^^^.^^^^. ^^^^ and coding efficiency ^^^^. In particular, the coded data (code word formed from ^^^^.^^^^ ^^^^ source data and ^^^^.^^^^ ^^^^ redundancy data) can be stored in a memory and / or transmitted from a transmitter to a receiver, via a transmission channel. According to a particular embodiment, at least one of said blocks of lines comprises a succession of at least two matrices ^^^^ ^ ^ ^ ^ ^ ^ ^ ^ by applying a distinct circular rotation coefficient ^^^^ to said diagonal matrix of size ^^^^ × ^^^^. Again, we seek to avoid the repetition of the same pattern within the same block of lines of the extension matrix ^^^^. In particular, the use of distinct circular rotations in the same block of lines makes it possible to avoid, or at least to limit, short cycles of size 4 or 6. It is indeed desirable to limit the number of short cycles, because they limit decoding performance. In particular, such short cycles introduce error floors that do not allow very low block error rates (BLER) to be achieved during decoding as a function of the signal-to-noise ratio, for example of the order of 10 -5 or 10 -6 . According to one embodiment at least one of said blocks of lines comprises a succession of at least two matrices ^^^^ ^ ^ ^ ^ ^ ^ ^ ^obtained by applying the same circular rotation coefficient ^^^^ to said diagonal matrix of size ^^^^ × ^^^^. In this way, it is sought to avoid the repetition of the same pattern within the same block of columns of the extension matrix ^^^^. According to a particular embodiment, ^^^^ ≥ 5. In particular, the use of blocks of ^^^^ ≥ 5 rows makes it possible in particular to avoid, or at least to delimit, short cycles of size 4. According to a particular embodiment, said at least two blocks of ^^^^ rows are consecutive, i.e. no row of zero or non-zero elements is interposed between two blocks of rows. In this way, the non-zero elements of the extension matrix ^^^^ can be distributed homogeneously over the different blocks of rows.According to a first embodiment, the extension matrix ^^^^ also comprises at least one block of ^^^^′ rows, ^^^^′ ≠ ^^^^, with ^^^^′ an integer between 1 and ^^^^ − 1, comprising a succession of matrices^^^^. ^ ^ ^ ^^ ^ ^ ^ ′ obtained by applying the same circular rotation coefficient ^^^^ to a detailed diagonal matrix ^^^^′ × ^^^^′. For example, choosing a number of rows ^^^^′ = 6 for a first block of rows, and ^^^^ = 7 for at least two blocks of rows of the extension matrix ^^^^ makes it possible to avoid short cycles of size 4 or 6. In particular, for at least one of said blocks of rows, said extension matrix ^^^^ comprises a portion of one of said matrices ^^^^ ^ ^ ^ ^^ ^ ^^ obtained by applying a circular rotation coefficient ^^^^ to a diagonal matrix of size ^^^^ × ^^^^, and said extension matrix ^^^^ comprises the extension of said portion. In other words, the matrix formed from said extension matrix C and said extension matrix ^^^^ comprises at least one complete pattern representing the matrix ^^^^ ^ ^ ^ ^ ^ ^ ^ ^ , as well as possibly a partial pattern. For example, said extension matrix ^^^^ is equal to: V2 V1 V3 V4 V1 V1 V2 V3 V2 V2 V0 V3 V3 V1 V3 V3 V0 V2 V2 V2 V2 V3 V0 V1 V4 V1 V0 V2 V4 V2 V0 V2 V1 V1 V0 V3 V2 V2 V3 V3 V4 V3 V3 V2 V0 V0 V2 V3 V1 V4 V4 V1 V0 V1 V0 V2 V3 V3 V2 V2 V4 V3 V3 V3 V4 V1 V2 V3 V1 V2 V3 V0 V4 V1 V1 V3 V4 V3 V3 V1 V3 V3 V3 V1 V3 V4 V1 V1 V1 V2 V1 V1 V1 V2 V1 V4 V3 V1V4 V2 V1 V1 V4 V0 V4 V1 V1 V1 V2 V0 V3 V1 V3 V3 V2 V2 V2 V1 V1 V2 V2 V0 V3 V1 V2 V1 V0 V2 V4 said extension matrix ^^^^ is equal to:V2 V1 V 1 V3 V 4 V3 V1 V1 V1 V3 V1 V3 V 1 V3 V4 V2 V 2 V1 V4 V1 V4 V1 V2 In addition: - each empty or null element of said base matrix ^^^^^^^^' is replaced by a null matrix of size ^^^^^^^^ × ^^^^^^^^ ,- each non-null element of said base matrix ^^^^^^^^' is replaced by an expansion matrix obtained by applying a circular rotation ^^^^^^^^ to an identity matrix of size ^^^^^^^^ × ^^^^^^^^ , such that:Circular rotation ^^^^^^^^ if ^^^^ ^^^^ belongs to^^^^0 = 0 + 4^^^^,^^^^ ∈ [0: 63]{2,4,8,16,32,128,256 } : ^^^^1 = 1 + 4^^^^,^^^^ ∈ [0:63]^^^^2 = 2 + 4^^^^,^^^^ ∈ [0:63]^^^^3 = 3 + 4^^^^,^^^^ ∈ [0:63]^^^^4 = 0 + 4^^^^,^^^^ ∈ [0:63]if ^^^^ ^^^^belongs to^^^^0 = 0 + 5^^^^ + 6^^^^, ^^^^ ∈ [0: 1] and ^^^^ ∈ [0: 63]{3,6,12,24,48,96,192,384} :^^^^1 = 1 + 6^^^^,^^^^ ∈ [0: 63]^^^^2 = 2 + 6^^^^,^^^^ ∈ [0: 63]^^^^3 = 3 + 6^^^^,^^^^ ∈ [0: 63]^^^^4 = 4 + 6^^^^,^^^^ ∈ [0: 63]if ^^^^ ^^^^ belongs to^^^^0 = 0 + 5^^^^,^^^^ ∈ [0: 63]{5,10,20,40,80,160,320} :^^^^1 = 1 + 5^^^^,^^^^ ∈ [0: 63]^^^^2 = 2 + 5^^^^,^^^^ ∈ [0: 63]^^^^3 = 3 + 5^^^^,^^^^ ∈ [0: 63]^^^^4 = 4 + 5^^^^,^^^^ ∈ [0: 63]^^^^0 = 0 + 5^^^^ + 7^^^^, ^^^^ ∈ [0: 1] ^^^^^^^^^ ^^^^ ∈ [0: 31]^^^^1 = 1 + 5^^^^ + 7^^^^, ^^^^ ∈ [0: 1] ^^^^^^^^ ^^^^ ∈ [0: 31] if ^^^^ belongs to^^^^2 = 2 + 7^^^^,^^^^ ∈ [0: 31]{7,14,28,56,112,224 } : ^^^^3 = 3 + 7^^^^,^^^^ ∈ [0:31]^^^^4 = 4 + 7^^^^,^^^^ ∈ [0:31]if ^^^^ ^^^^ belongs to^^^^0 = 0 + 5^^^^ + 9^^^^, ^^^^ ∈ [0: 1] ^^^^^^^^ ^^^^ ∈ [0: 31]{9,18,36,72,144,288 }: ^^^^1 = 1 + 5^^^^ + 9^^^^, ^^^^ ∈ [0: 1]^^^^^^^ ^^^^ ∈ [0: 31]^^^^2 = 2 + 5^^^^ + 9^^^^, ^^^^ ∈ [0: 1] ^^^^^^^ ^^^^ ∈ [0: 31]^^^^3 = 3 + 5^^^^ + 9^^^^, ^^^^ ∈ [0:1] ^^^^^^^ ^^^^ ∈ [0:31]^^^^4 = 4 + 9^^^^,^^^^ ∈ [0:31]if ^^^^ ^^^^ belongs to^^^^0 = 0 + 5^^^^ + 11^^^^, ^^^^ ∈ [0: 2] ^^^^^^^^ ^^^^ ∈ [0: 31]{11,22,44,88,176,352 } : ^^^^1 = 1 + 5^^^^ + 11^^^^, ^^^^ ∈ [0: 1] ^^^^^^^^ ^^^^ ∈ [0: 31]^^^^2 = 2 + 5^^^^ + 11^^^^, ^^^^ ∈ [0: 1] ^^^^^^^^ ^^^^ ∈ [0: 31]^^^^3 = 3 + 5^^^^ + 11^^^^, ^^^^ ∈ [0: 1] ^^^^^^^^ ^^^^ ∈ [0: 31]^^^^4 = 4 + 5^^^^ + 11^^^^, ^^^^ ∈ [0: 1] ^^^^^^^^^ ^^^^ ∈ [0: 31] if ^^^^ ^^^^ belongs to^^^^0 = 0 + 5^^^^ + 13^^^^, ^^^^ ∈ [0: 2] ^^^^^^^^ ^^^^ ∈ [0: 15]{13,26,52,104,208 }: ^^^^1 = 1 + 5^^^^ + 13^^^^, ^^^^ ∈ [0: 2] ^^^^^^^^ ^^^^ ∈ [0: 15]^^^^2 = 2 + 5^^^^ + 13^^^^, ^^^^ ∈ [0: 2] ^^^^^^^^ ^^^^ ∈ [0: 15]^^^^3 = 3 + 5^^^^ + 13^^^^, ^^^^ ∈ [0: 1] ^^^^^^^^ ^^^^ ∈ [0: 15]^^^^4 = 4 + 5^^^^ + 13^^^^, ^^^^ ∈ [0: 1] ^^^^^^^^^ ^^^^ ∈ [0: 15] if ^^^^ ^^^^ belongs to^^^^0 = 0 + 5^^^^ + 15^^^^, ^^^^ ∈ [0: 2] ^^^^^^^^ ^^^^ ∈ [0: 15]{15,30,60,120,240 }: ^^^^1 = 1 + 5^^^^ + 15^^^^, ^^^^ ∈ [0: 2] ^^^^^^^^ ^^^^ ∈ [0: 15]^^^^2 = 2 + 5^^^^ + 15^^^^, ^^^^ ∈ [0: 2] ^^^^^^^^ ^^^^ ∈ [0: 15]^^^^3 = 3 + 5^^^^ + 15^^^^, ^^^^ ∈ [0: 2] ^^^^^^^^ ^^^^ ∈ [0: 15]^^^^4 = 4 + 5^^^^ + 15^^^^, ^^^^ ∈ [0: 2] ^^^^^^^^^ ^^^^ ∈ [0: 15] with ^^^^ and ^^^^ random variables. For example, ^^^^ = 4, ^^^^ = 22 and ^^^^ = 44. We note that the basic matrix BG' proposed according to this first embodiment thus has a format similar to the matrix BG1 defined by the 3GPP with a decomposition into six sub-matrices (^^^^, ^^^^, ^^^^, ^^^^, 0 and ^^^^). However, its size is slightly different from that of the basic matrix BG1. Indeed, for the matrix BG1 defined by the 3GPP, the number ^^^^ of redundancy data is equal to 46, whereas it is equal to 44 in the proposed solution.This is because the first two columns of the BG1 matrix defined by 3GPP are punctured to improve performance in the "waterfall" zone, i.e. in the zone where the decoder's block error rate as a function of the signal-to-noise ratio drops rapidly. Due to this puncturing of the first two columns, source data may not be transmitted. Two rows are therefore added to the basic BG1 matrix to add parity equations and allow the reconstruction of this source data. This solution improves the robustness of the codec, particularly for high throughputs. In particular, the first two columns of the BG1 matrix, which can be punctured, have many non-zero elements, in order to be able to reconstruct the source data. However, this increases the number of connections and therefore the risk of short cycles.According to the invention, the first two columns of the basic matrix BG' are not punctured. It is therefore not necessary to add parity equations or to provide a large number of non-zero elements in the first two columns of the basic matrix BG'. In this way, it is possible according to the invention to reduce the number of connections and therefore to accelerate the convergence of the decoder and to reduce its energy consumption. According to a second embodiment, the extension matrix ^^^^ comprises at least two blocks of ^^^^ lines, each block of lines comprising a matrix ^^^^. ^^^^ ^ ^^^obtenue en appliquant un coefficient derotation circulaire ^^^^ à une matrix diagonale de taille ^^^^ × ^^^^.L'utilisation de matrices diagonales permet ainsi de répartir les éléments non nuls de la matrix de prolongement ^^^^ sur les différences lignes et / ou colonnes de la matrix de prolongement ^^^^.Par exemple, ^^^^ = 4 quelle que soit la valeur de ^^^^.Par exemple, lesdites matrice d'extension ^^^^ et de prolongement D sont égales à : pour K=6 : CD V2 V2 V1 V3 V2 V3 V0 V2 V3 V2 V2 V1 V2 V1 V1 V2 V2 V3 V3 V2 V1 V2 V1 V0 V2 V2 V2 V3 V1 V1 V2 V0 V0 V3 V2 V1 V0 V1 V2 V3 V0 V1 pour K=8 : CD V2 V2 V1 V3 V3 V2 V3 V2 V0 V2 V3 V2 V2 V1 V2 V1 V1 V2 V2 V3 V3 V1 V2 V1 V3 V2 V1 V3 V0 V2 V1 V2 V2 V3 V1 V1 V2 V0 V0 V3 V2 V1 V0 V3 V1 V2 V2 V3 V0 V1 V2 V0 V3 V3 V0 V3 V2 V2 V0 V2 V1 V1 V0 V0 V3 V0 V3 V2 V2 V2 V2 for K=9: CD V2 V2 V1 V3 V3 V2 V3 V2 V0 V2 V1 V3 V2 V2 V1 V1 V2 V1 V1 V2 V1 V2 V2 V3 V3 V1 V2 V1 V3 V2 V1 V3 V0 V2 V1 V2 V1 V3 V1 V2 V1 V3 V2 V1 V3 V0 V2 V1 V2 V1 V3 V1 V2 V0 V0 V0 V3 V2 V1 V0V3 V2 V3 V0 V3 V2 V2 V0 V2 V1 V1 V0 V0 V0 V3 V0 V3 V2 V3 V2 V2 V2 V0 V2 V0 V3 V0 V1 V2 V0 For K=10: CD V2 V2 V1 V3 V3 V2 V3 V2 V0 V2 V1 V3 V2 V2 V2 V1 V1 V2 V1 V2 V1 V2 V2 V3 V3 V1 V2 V1 V3 V2 V1 V3 V0 V2 V1 V2 V2 V1 V3 V1 V3 V1 V2 V0 V0 V3 V2 V1 V0 V3 V1 V2 V2 V3 V0 V0 V1 V2 V1 V0 V3 V2 V3 V0 V0 V3 V2 V2 V0 V2 V1 V1 V0 V0 V0 V3 V0 V3 V2 V3 V2 V2 V2 V2 V0 V2 V0 V3 V0 V1 V2 V0 V2 V1 V0 V2 V0 V1 V2 V3 V1 V2 In addition: - each empty or null element of said base matrix ^^^^^^^^' is replaced by a null matrix of size ^^^^^^^^ × ^^^^^^^^ ,- each non-null element of said base matrix ^^^^^^^^' is replaced by a circular permutation matrix obtained by applying a circular rotation ^^^^^^^^ to an identity matrix of size ^^^^^^^^ × ^^^^^^^^ , as defined previously. For example ^^^^ = 4 and :^^^^ = 6 and ^^^^ = 24, or^^^^ = 8 and ^^^^ = 32, or^^^^ = 9 and ^^^^ = 36 or^^^^ = 10 and ^^^^ = 40. We note that the base matrix BG' proposed according to this secondembodiment has a format similar to the BG2 matrix defined by 3GPP with a decomposition into six sub-matrices (^^^^, ^^^^, ^^^^, ^^^^, 0 and ^^^^). However, its size is slightly different from that of the basic BG2 matrix. Indeed, for the BG2 matrix defined by 3GPP, the number ^^^^ of redundancy data is equal to 26, 34, 38 or 42 depending on the value of K, while it is respectively equal to 24, 32, 36 or 40 in the proposed solution. This is explained by the fact that the first two columns of the BG2 matrix defined by 3GPP are punctured to improve performance in the waterfall area. Due to this puncturing of the first two columns, source data may not be transmitted. Two lines are therefore added to the basic BG2 matrix to add parity equations and allow the reconstruction of this source data. This solution improves the robustness of the codec, particularly for high yields.In particular, the first two columns of the BG1 matrix, which can be punctured, have many non-zero elements, in order to be able to reconstruct the source data. However, this amounts to increasing the number of connections and therefore the risk of short cycles. According to the invention, the first two columns of the basic matrix BG' are not punctured. It is therefore not necessary to add parity equations or to provide a large number of non-zero elements in the first two columns of the basic matrix BG'. In this way, it is possible according to the invention to reduce the number of connections and therefore to accelerate the convergence of the decoder and to reduce its energy consumption. Similarly, the removal of the double diagonal of the matrix B in a proposed embodiment, compared to the basic matrix BG2 defined by the 3GPP, makes it possible to simplify the encoder. In another embodiment, the invention relates to a coding devicecorresponding. Such a coding device, also called an encoder, is particularly suitable for implementing the coding method described above. It may of course include the various characteristics relating to the method according to the invention, which may be combined or taken in isolation. Thus, the characteristics and advantages of the encoder are the same as those of the method described above. Consequently, they are not detailed further. The invention also relates to a corresponding decoding method and device. Such a decoding method is particularly suitable for decoding at least one code word constructed using the coding method described above. It may of course include the various characteristics relating to the coding method according to the invention, which may be combined or taken in isolation. Thus, the characteristics and advantages of the decoding method and the decoder are the same as those of the coding method and the encoderdescribed previously. Consequently, they are not detailed further. In particular, the decoding method can implement a decoding of a parity equation obtained from the last row of the parity matrix ^^^^, then of a parity equation obtained from the previous row of said parity matrix ^^^^, going back row by row to the first row of the parity matrix ^^^^. Such decoding in "reverse" mode offers good performance, in particular for decoding small source data, for example for ^^^^.^^^^^^^^ < 256. The invention also relates to one or more computer programs comprising instructions for implementing a method as described above when this or these programs are executed by at least one processor. The invention also relates to an information medium readable by a computer, and comprising instructions of a computer program as mentioned above. 4.List of figures Other characteristics and advantages of the invention will appear more clearly on reading the following description of a particular embodiment, given as a simple illustrative and non-limiting example, and the appended drawings, among which: - figure 1 illustrates a transmitter of a conventional digital transmission chain; - figure 2 presents an example of a parity matrix ^^^^ for an LDPC code; - figure 3 illustrates selection criteria for the basic matrix BG1 or BG2; - figure 4 illustrates the decomposition of the basic matrix BG1 or BG2 into sub-matrices; - figures 5A and 5B present the main steps implemented by a coding method, respectively decoding method, according to an embodiment of the invention; - figure 6A and figure 6B illustrate the structure of the matrix BG1; - figure 7A and figure 7B illustrate the concept of cycle; - figures 8 to 16 present different structures of thebasic matrices according to different embodiments of the invention; - Figures 17 to 19 illustrate performance curves of an LDPC decoder implementing a decoding of a code word obtained according to an embodiment of the invention; - Figures 20A and 20B present the simplified structure of an encoder, respectively of a decoder, according to an embodiment of the invention. 5. Description of an embodiment of the invention 5.1 General principle The general principle of the invention is based on a clever distribution of the connections (i.e. non-zero elements) in a basic matrix ^^^^^^^^', seeking to distribute the connections in a substantially homogeneous manner and / or to limit the number of short cycles. Consequently, a parity matrix ^^^^ obtained from the modified basic matrix ^^^^^^^^' has a particular structure. Such a structure makes it possible to improve the performance of error-correcting codes, in particular by reducing the complexity of thedecoding. Figure 5A illustrates the main steps of a coding method according to an embodiment of the invention. During a first step 51, a basic matrix ^^^^^^^^' of size ^^^^ × ^^^^ is obtained. Such a basic matrix ^^^^^^^^' can be decomposed into six sub-matrices ^^^^, ^^^^, 0, ^^^^, ^^^^, ^^^^, and expressed in the form: ^^^^^^^^' ^^^^ 0 with: ^^^^ a kernel matrix of size ^^^^ × ^^^^^^^^ a matrix having at least one diagonal of size ^^^^ × ^^^^^^^^ an extension matrix of size (^^^^ − ^^^^) × ^^^^^^^^ an extension matrix of size (^^^^ − ^^^^) × ^^^^0 a zero matrix of size (^^^^ − ^^^^ − ^^^^) × ^^^^^^^^ an identity matrix of size (^^^^ − ^^^^) × (^^^^ − ^^^^ − ^^^^)In particular, the extension matrix ^^^^ has a particular structure and comprises at least two blocks of ^^^^ rows and at least one block of ^^^^ columns, with ^^^^ an integer included between 1 and ^^^^ − 1, each block of ^^^^ lines comprising at least one ^^^^ matrix ^ ^ ^ ^^ ^ ^ ^ obtained by applying a circular rotation coefficient ^^^^ to a diagonal matrix of size ^^^^ × ^^^^, with ^^^^ an integer between 0 and ^^^^ − 1, said at least one block of ^^^^ columns comprising at least two matrices ^^^^ ^ ^ ^ ^^ ^ ^^ obtained by applying a distinct circular rotation coefficient ^^^^ to said diagonal matrix of size ^^^^ × ^^^^. During a second step 52, a parity matrix ^^^^ is obtained from the basic matrix ^^^^^^^^'. To do this, we replace each element of the base matrix ^^^^^^^^' with an expansion matrix of size ^^^^^^^^ × ^^^^^^^^ , with ^^^^^^^^ an integer expansion factor, ^^^^^^^^ ≥ 1. More precisely, each zero or empty element of the base matrix ^^^^^^^^' is replaced by a zero matrix of size ^^^^^^^^ × ^^^^^^^^, and each non-zero or non-empty element of the base matrix ^^^^^^^^' is replaced by a circular permutation matrix, obtained by applying a circular rotation ^^^^^^^^ to an identity matrix of size ^^^^^^^^ × ^^^^^^^^ . During a third step 53, at least one block of ^^^^.^^^^ ^^^^source data is coded using the parity matrix ^^^^ of size (^^^^.^^^^^^^^ × ^^^^.^^^^^^^^), so as to obtain at least one code word of size ^^^^.^^^^^^^ formed from the ^^^^.^^^^^^^^ source data and ^^^^.^^^^^^^^ redundancy data, ^^^^ = ^^^^ + ^^^^. Such a code word may in particular be stored in a memory of the encoder or transmitted by a transmitter to a receiver. Figure 5B illustrates the main steps of a decoding method according to an embodiment of the invention. During a first step 54, a basic matrix ^^^^^^^^' of size ^^^^ × ^^^^ is obtained. This step is similar to the first step 51 implemented by the coding method. In a second step 55, a parity matrix ^^^^ is obtained from the basic matrix ^^^^^^^^'. This step is similar to the second step 52 implemented by the coding method. In a third step 56, at least one code word of size ^^^^.^^^^ ^^^^formed from ^^^^.^^^^ ^^^^source data and ^^^^.^^^^^^^^ redundancy data, ^^^^ = ^^^^ + ^^^^ is decoded using the parity matrix ^^^^of size (^^^^.^^^^^^^^ × ^^^^.^^^^^^^^), so as to reconstruct at least one block of ^^^^.^^^^^^^^ source data.5.2 Basic matrix BG1 In order to better understand the invention, we recall in Figure 6A the structure of the basic matrix BG1 as defined in the document ETSI TS 138212 V15.2.0, formed of the matrices ^^^^, ^^^^, ^^^^ and ^^^^. The sub-matrices ^^^^ and ^^^^ are omitted for the sake of simplification. The “1” elements of the basic matrix BG1 represent the connections of the different parity equations. The number of connections per column and per row has been added in Figure 6A. Thus, the first column of the matrices ^^^^ and ^^^^ includes 30 connections, the second column includes 28 connections, the third column includes 7 connections, etc.The first column of the ^^^^ and ^^^^ matrices has 12 connections, the second column has 5 connections, etc. The first four rows of the ^^^^ and ^^^^ matrices each have 19 connections. The first row of the ^^^^ and ^^^^ matrices has 2 connections, the second row has 7 connections, etc. If we ignore the null ^^^^ and identity ^^^^ matrices, the minimum number of connections per row is 2 and the maximum number of connections per row is 19. The minimum number of connections per column is 4 and the maximum number of connections per column is 30. There is therefore a large disparity in the number of connections per row and / or per column in the BG1 matrix. The kernel matrix ^^^^ has, in proportion, many connections, i.e. many non-zero elements, because it is the kernel of the BG1 matrix. This allows the decoder, on reception, to find the source data.Note also that the first two columns of matrix BG1, which correspond to the untransmitted data, also have many connections ("1"). As an example, Figure 6B illustrates the circular rotation factors ^^^^ for matrix BG1 in Figure 6A, for an expansion factor ^^^^^^^^ = 256. The parity matrix ^^^^ is constructed by replacing each non-zero element of matrix BG1 with an identity matrix of size ^^^^^^^^ × ^^^^^^^^ , and applying a circular rotation ^^^^ according to the factors illustrated in Figure 6B. Thus, the element "1" in the first row / first column of matrix BG1 in Figure 6A is replaced by an identity matrix of size 256 × 256 to which a circular rotation ^^^^ = 250 is applied.The element "1" in the first row / second column of matrix BG1 in Figure 6A is replaced by an identity matrix of size 256 × 256 to which a circular rotation is applied ^^^^ = 69, and so on.5.3 Basis Matrix BG2 Similarly, ETSI TS 138212 V15.2.0 describes the structure of the basis matrix BG2, which can be decomposed into sub-matrices ^^^^, ^^^^, ^^^^, ^^^^, ^^^^ and ^^^^. The sub-matrices ^^^^ and ^^^^ are omitted hereafter for simplification. In particular, 3GPP proposed to decompose the BG2 basis matrix into four sub-matrices whose dimension depends on the parameter K. This parameter depends on the size of the source data to be encoded (K=6, 8, 9 or 10). The sub-matrices C and D of the BG2 basis matrix can be represented in a nested form. 5.4 Proposed basic matrices The position of the connections in the basic matrices BG1 or BG2, as well as the rotation factors to be used, are specified in the 5G 3GPP standard. However, as previously indicated, it remains desirable to improve the performance of error-correcting codes, in particular by reducing the complexity of decoding. We therefore propose below new basic matrices adapted in particular to the requirements of 5G (in terms of block size to be coded ^^^^.^^^^. ^^^^and coding efficiency ^^^^) and future developments, providing good performance while reducing decoding complexity, for example by reducing the number of decoding iterations. The proposed solution thus makes it possible to reduce the energy consumption of the LDPC codec. Of course, the invention, although presenting a preferred application in the context of 3GPP standards, is not limited to this use and can be envisaged in other contexts, for example for other networks or more generally for other communication systems using LDPC codes. According to a particular embodiment, the structure of the proposed basic matrices is defined so as to have a low disparity in the number of connections per row and / or per column. Indeed, if we consider an LDPC coder for example, we recall that LDPC decoding is based on the bases of the probabilities of having transmitted a value equal to "1" or "0".It is therefore desirable to distribute the number of connections evenly, so that the number of connections in rows, and especially in columns, is substantially constant or equally distributed, so as to obtain better performances for a reduced number of iterations. The structure of the proposed basic matrices is also defined so as to limit the number of short cycles, and if possible to avoid short cycles ("Girth" in English). Indeed, such short cycles limit the performances of error-correcting codes, in particular LDPC codes, especially for small source data, for example of the order of ^^^^.^^^^^^^^ = 256 bits or less. To better understand this principle, Figures 7A and 7B illustrate the loop phenomena with an expansion factor ^^^^^^^^^ = 4.According to Figure 7A, we apply an expansion factor ^^^^^^^^ = 4 with the same rotation factor ^^^^1 = ^^^^2 = ^^^^3 = ^^^^4 = 0 to the elements "1" located at (^^^^, ^^^^), (^^^^ + 7, ^^^^), (^^^^, ^^^^ + 7) and (^^^^ + 7, ^^^^ + 7). We obtain a loop, illustrated by the arrows. According to. 7 B,we apply an expansion factor ^^^^^^^^ = 4 with the same rotation factor ^^^^1 = ^^^^2 = ^^^^4 = 0 to the elements "1" located in position (^^^^, ^^^^), (^^^^ + 7, ^^^^) and (^^^^ + 7, ^^^^ + 7), and a rotation factor ^^^^3 = 1 to the element located in position (^^^^, ^^^^ + 7). In this case, there is no loop. Changing the rotation factor of one of the elements of the matrix therefore makes it possible to eliminate the loops. The inventor was thus able to define a particular rule for the "Protograph" matrices concerning short cycles of length 4: if (^^^^0 − ^^^^3 + ^^^^4 − ^^^^2) ^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^ = 0, then this configuration causes a short cycle of length 4 (or the alternation of signs corresponds to the passage from an elementary block (greyed out in figures 7A and 7B) to another elementary block on the same line (sign "+") or on the same column (sign "-") in the loop).This equation makes it possible, according to one embodiment of the invention, to choose the value of the circular rotation coefficients making it possible to guarantee that the basic matrix BG' does not have a cycle of length 4, the limit or the degree of freedom being given by the value of ^^^^. ^^^^. Furthermore, we present below different solutions to obtain a low disparity in the number of connections per row and / or per column of the modified basic matrix and / or to limit (or even avoid) short cycles. In order to limit the number of short cycles, we first propose to no longer puncture the first two columns of the new kernel ^^^^ and extension ^^^^ matrices at transmission, whereas the first two columns of the kernel ^^^^ and extension ^^^^ matrices are conventionally punctured in the basic matrices BG1 and BG2 according to 3GPP. Indeed, such a puncturing technique requires a large number of connections in the first two columns and can therefore lead to a large number of short cycles. In addition, it reduces the convergence speed of the decoder. We therefore seek to overcome it. We also seek to improve the distribution of connections in the extension matrix ^^^^.Indeed, the extension matrix ^^^^ is generally the largest in terms of its size. For the basic matrix BG1 according to the 3GPP for example, the extension matrix ^^^^, excluding its first two columns intended to be punctured, has a size of 40 × 22. For the basic matrix BG2 according to the 3GPP, the extension matrix ^^^^, excluding its first two columns, has a size of: 22 × 4 for ^^^^^^^^ = 630 × 6 for ^^^^^^^^ = 834 × 7 for ^^^^^^^^ = 9 and 38 × 8 for ^^^^^^^^^ = 10. To ensure a good distribution of the connections according to an embodiment of the invention, the connections can be distributed on diagonals in the extension matrix ^^^^. Thus, all the parity equations are distinct from each other. For example, if we consider a block of 10 rows and 20 columns, as illustrated in Figure 8, it is possible to have two occurrences of a 10 × 10 diagonal matrix on the block of 10 rows, i.e. two row connections and one column connection.According to another example, if we consider two blocks of 5 rows and 20 columns as illustrated in Figure 9, it is possible to have four occurrences of a 5 × 5 diagonal matrix on each block of 5 rows, i.e. four connections in rows and one in columns per block. It is thus possible to vary the number of connections per row according to the size of the diagonals or blocks of rows. Note, however, that the configuration illustrated in Figure 9 can introduce short cycles of size 4. To overcome this problem, it is possible to perform a circular rotation per "elementary block", as illustrated in Figure 10, in. technique described in relation to figures 7A and 7B. By introducing a new variable ^^^^^^ ^^^ ^^^ which defines an identity matrix of size ^^^^ × ^^^^ and ^^^^ a circular rotation coefficient, the two blocks of 5 rows and 20 columns illustrated in Figure 10 can be represented more compactly in the following form: ^^^^0 5 ^^^^0 5 ^^^^0 5 ^^^^0 5 ^^^^0 5 ^^^^1 5 ^^^^2 5 ^^^^3 5With this new representation, it is possible to determine the different circular rotation coefficients ^^^^ which ensure the minimum number of cycles of length 4, 6 … for all the extension matrices C and extension D. 5.4.1 Optimization of the extension matrices C and extension D according to a first example We present a first example of structure for the extension matrices ^^^^ and extension ^^^^, which can be used in particular in 5G with ^^^^ = 4. According to this example, illustrated in figure 11, the extension matrix ^^^^ has a size (^^^^ − ^^^^) × ^^^^ = 40 × 22 and the extension matrix ^^^^ has a size (^^^^ − ^^^^) × ^^^^ = 40 × 4. Such a structure makes it possible to limit the number of short cycles of size 4 and to obtain a homogeneous number of connections for the proposed basic matrix, denoted BG1', substantially equivalent to the basic matrix BG1 proposed by 3GPP.As illustrated in Figure 11, the proposed extension matrix ^^^^ thus comprises at least two blocks of ^^^^ rows, for example four blocks of ^^^^ = 7 rows, referenced 111, 112, 113 and 114, and at least one block of ^^^^ columns, for example three blocks of ^^^^ = 7 columns, referenced 121, 122 and 123. Each block of ^^^^ rows comprises at least one matrix ^^^^. ^ ^ ^ ^^ ^ ^ ^ obtained by applying a circular rotation coefficient ^^^^ to a diagonal matrix of size ^^^^ × with ^^^^ an integer between 0 and ^^^^ − 1 (i.e. at least one complete pattern). For example, the first block 111 includes three occurrences of a matrix ^^^^0 7 , corresponding to the identity matrix of size 7. The first block of lines 111 thus comprises a succession of at least two matrices ^^^^ ^ ^ ^ ^ ^ ^ ^ ^obtained by applying the same circular rotation coefficient ^^^^ to said diagonal matrix of size ^^^^ × ^^^^. The second block 112 comprises an occurrence of a matrix ^^^^6 7 , an occurrence of a matrix ^^^^1 7 and an occurrence of a matrix ^^^^3 7 . The third block 113 includes an occurrence of a matrix ^^^^2 7 , an occurrence of a matrix ^^^^3 7 and an occurrence of a matrix ^^^^4 7 . The fourth block 114 includes an occurrence of a matrix ^^^^1 7 , an occurrence of a matrix ^^^^0 7 and an occurrence of a matrix ^^^^6 7 . The line blocks 112, 113 and 114 thus each comprise a succession of at least two matrices ^^^^ ^ ^ ^ ^^ ^ ^^ obtained by applying a distinct circular rotation coefficient ^^^^ to the diagonal matrix of size ^^^^ × ^^^^. According to the example illustrated, the blocks of ^^^^ rows are consecutive, i.e. no row of zero or non-zero elements is interposed between two blocks of rows. Furthermore, at least one block of ^^^^ columns includes at least two ^^^^ matrices ^ ^ ^ ^^ ^ ^ ^ obtained by applying a distinct circular rotation coefficient ^^^^ to said diagonal matrix of size ^^^^ × ^^^^. For example, the first block 121 comprises an occurrence of a matrix ^^^^0 7 , an occurrence of a matrix ^^^^6 7 , an occurrence of a matrix ^^^^2 7 and an occurrence of a matrix ^^^^1 7 . The second block 122 comprises an occurrence of a matrix ^^^^0 7 , an occurrence of a matrix ^^^^1 7 , an occurrence of a matrix ^^^^3 7and an occurrence of a matrix ^^^^0 7 . The third block 123 includes an occurrence of a matrix ^^^^0 7 , an occurrence of a matrix ^^^^3 7 , an occurrence of a matrix ^^^^4 7 and an occurrence of a matrix ^^^^6 7 The intersection of a block of rows and a block of columns corresponds to an elementary block formed by a matrix ^^^^ ^ ^ ^ ^ ^ ^ ^ ^ . It is further noted that said extension matrix ^^^^ also comprises at least one block of ^^^^ ′ lines, ^^^^′ ≠ ^^^^, with ^^^^′ an integer between 1 and ^^^^ − 1 comprising a succession of matrices ^^^^^^ ^^ ^^ ^^′ obtained by applying the same circular rotation coefficient ^^^^ to a diagonal matrix size^^^^′ × ^^^^′. For example, such a block of ^^^^′ = 6 rows is referenced 110 in Figure 11. Such a block of rows comprises a succession of matrices ^^^^0 6 . The structure of the extension matrix ^^^^ can in particular be extended onto the extension matrix ^^^^. Thus, for at least one block of lines, the extension matrix ^^^^ comprises a portion of a matrix ^^^^ ^ ^ ^ ^^ ^ ^ ^ and the extension matrix ^^^^ includes the extension of the portion of the matrix ^^^^ ^ ^ ^ ^^ ^ ^ ^. For example, returning to Figure 11, if we consider the first block of 7 rows 111, with the first 22 columns belonging to the extension matrix ^^^^ and the last 4 columns belonging to the continuation matrix ^^^^, the extension matrix ^^^^ includes three "complete" patterns each corresponding to the matrix ^^^^0 7. The fourth pattern is partial and extends into the extension matrix ^^^^. The extension matrix ^^^^ thus allows "to extend the diagonals" and consequently to increase the overall performance of the LDPC. The matrices ^^^^ ^ ^ ^ ^^ ^ ^ ^ thus be used to decompose the extension matrices ^^^^ and continuation ^^^^. As already indicated, the exponent ^^^^ gives the dimension of the identity matrix (^^^^ rows, ^^^^ columns), and the subscript ^^^^ gives the coefficient of circular rotation applied to the identity matrix to obtain this matrix ^^^^ ^ ^ ^ ^^ ^ ^ ^. In particular, if the last matrices ^^^^ ^ ^ ^ ^ ^ ^ ^ ^of a row or a column exceed the dimensions of the extension matrices ^^^^ and continuation matrices ^^^^, then they can be truncated. Circular rotations make it possible in particular to minimize the number of short cycles of size 4 and 6 for matrices of the same dimension, for example matrices of dimension (6,6) and (7,7) according to the example in Figure 11. Using the compact notation proposed above, the extension and continuation matrices in Figure 11 can be expressed in the following form: ^^^^0 6 ^^^^0 6 ^^^^0 6 ^^^^0 6 ^^^^0 6 ^^^^0 7 ^^^^0 7 ^^^^0 7 ^^^^0 7 ^^^^6 7 ^^^^1 7 ^^^^3 7 ^^^^6 7 ^^^^2 7 ^^^^3 7 ^^^^4 7 ^^^^6 7 ^^^^1 7 ^^^^0 7 ^^^^6 7 ^^^^6 7 ^^^^3 7 ^^^^1 7 ^^^^6 7 ^^^^4 7Returning to Figure 11, the number of connections per row and per column is indicated on the right and at the bottom of the figure. By using diagonal matrices to which a circular rotation is applied, we see that the number of connections per row and / or per column in the proposed extension ^^^^ and extension ^^^^ matrices is substantially homogeneous (for example, between 3 and 5 for the number of connections per row and between 5 and 6 for the number of connections per column). Such homogeneity makes it possible to optimize the performance of LDPC codecs for a limited number of decoder iterations (less than 10 iterations for example). In the examples above, the extension ^^^^ and extension ^^^^ matrices are optimized to reduce short cycles. However, if we take into account the basic matrix BG1' formed by the kernel matrices ^^^^, ^^^^, spreading ^^^^ and extension ^^^^,short cycles may remain. The kernel matrix A may be identical to or different from that proposed for the BG1 base matrix according to 3GPP. Advantageously, the kernel matrix A comprises approximately 75% of connections (i.e. non-zero elements) per row. For example, the kernel matrix ^^^^ is equal to: V0 V0 V1 V3 V4 V3 V2 V1 V1 V1 V1 V4 V0 V4 V2 V2 V3 V2 V2 V2 V2 V3 V0 V0 V3 V4 V3 V0 V1 V2 V1 V0 V3 V4 V0 V1 V4 V0 V4 V0 V2 V2 V0 V0 V3 V4 V3 V1 V0 V4 V1 V2 V1 V3 V4 V0 V4 V2 V2 V2 V0 V0 V0 Similarly, matrix B, which includes the start of the redundancy part associated with kernel matrix A, can be the same as or different from that proposed for the basic matrix BG1 according to 3GPP. For example, the matrix ^^^^ having at least one diagonal is equal to: V1 V0 V0 V0 V0 V0 V0 V1 V0 As illustrated in figure 7B, taking into account the rotation factors makes it possible in particular to reduce, or even avoid,short cycles. It is therefore possible to increase the diversity of the proposed basis matrix and thus to decrease the number of short cycles by taking into account the rotation factors. In other words, for each connection identified by a value "1" in the matrices ^^^^, ^^^^, ^^^^ and ^^^^, another circular rotation operation ^^^^^^^^ is implemented, allowing to minimize the number of short cycles of size 4 and size 6 for the whole of the proposed basis matrix BG1'. It is possible to increase the number of rotation factors to increase the diversity of the basis matrix ^^^^^^^^1'. For example, five rotation factors denoted V0 to V4 are chosen. Of course, a different number of rotation factors can be chosen, which leads to a different structure for the matrices ^^^^, ^^^^,^^^^ and ^^^^. In particular, it is possible to define the equations that define the rotation factors V0 to V4 as a function of the index "ils" according to the 5G 3GPP standard. Index "they" Circular Rotation ^^^^^^^^ ^^^^0 = 0 + 4^^^^,^^^^ ∈ [0: 63]^^^^1 = 1 + 4^^^^,^^^^ ∈ [0: 63]0^^^^2 = 2 + 4^^^^,^^^^ ∈ [0: 63]^^^^3 = 3 + 4^^^^,^^^^ ∈ [0: 63]^^^^4 = 0 + 4^^^^,^^^^ ∈ [0: 63]^^^^0 = 0 + 5^^^^ + 6^^^^, ^^^^ ∈ [0: 1] and ^^^^ ∈ [0: 63]^^^^1 = 1 + 6^^^^,^^^^ ∈ [0: 63]1^^^^2 = 2 + 6^^^^,^^^^ ∈ [0: 63]^^^^3 = 3 + 6^^^^,^^^^ ∈ [0: 63]^^^^4 = 4 + 6^^^^,^^^^ ∈ [0: 63]^^^^0 = 0 + 5^^^^,^^^^ ∈ [0: 63]^^^^1 = 1 + 5^^^^,^^^^ ∈ [0: 63]2^^^^2 = 2 + 5^^^^,^^^^ ∈ [0: 63]^^^^3 = 3 + 5^^^^,^^^^ ∈ [0: 63]^^^^4 = 4 + 5^^^^,^^^^ ∈ [0:63]^^^^0 = 0 + 5^^^^ + 7^^^^, ^^^^ ∈ [0:1] ^^^^^^^^ ^^^^ ∈ [0:31]^^^^1 = 1 + 5^^^^ + 7^^^^, ^^^^ ∈ [0:1] ^^^^^^^^ ^^^^ ∈ [0:31]3^^^^2 = 2 + 7^^^^,^^^^ ∈ [0:31]^^^^3 = 3 + 7^^^^,^^^^ ∈ [0:31]^^^^4 = 4 + 7^^^^,^^^^ ∈ [0:31]^^^^0 = 0 + 5^^^^ + 9^^^^,^^^^ ∈ [0: 1] ^^^^^^^^ ^^^^ ∈ [0: 31]^^^^1 = 1 + 5^^^^ + 9^^^^, ^^^^ ∈ [0: 1]^^^^^^^^ ^^^^ ∈ [0: 31]4^^^^2 = 2 + 5^^^^ + 9^^^^, ^^^^ ∈ [0: 1] ^^^^^^^^ ^^^^ ∈ [0: 31]^^^^3 = 3 + 5^^^^ + 9^^^^, ^^^^ ∈ [0: 1] ^^^^^^^^ ^^^^ ∈ [0: 31]^^^^4 = 4 + 9^^^^,^^^^ ∈ [0: 31]^^^^0 = 0 + 5^^^^ + 11^^^^, ^^^^ ∈ [0: 2] ^^^^^^^^ ^^^^ ∈ [0: 31]^^^^1 = 1 + 5^^^^ + 11^^^^, ^^^^ ∈ [0: 1] ^^^^^^^^ ^^^^ ∈ [0: 31]5^^^^2 = 2 + 5^^^^ + 11^^^^, ^^^^ ∈ [0: 1] ^^^^^^^^ ^^^^ ∈ [0: 31]^^^^3 = 3 + 5^^^^ + 11^^^^, ^^^^ ∈ [0: 1] ^^^^^^^^ ^^^^ ∈ [0: 31]^^^^4 = 4 + 5^^^^ + 11^^^^, ^^^^ ∈ [0: 1] ^^^^^^^^ ^^^^ ∈ [0: 31]^^^^0 = 0 + 5^^^^ + 13^^^^, ^^^^ ∈ [0: 2] ^^^^^^^^ ^^^^ ∈ [0: 15]^^^^1 = 1 + 5^^^^ + 13^^^^, ^^^^ ∈ [0: 2] ^^^^^^^^ ^^^^ ∈ [0: 15]6^^^^2 = 2 + 5^^^^ + 13^^^^, ^^^^ ∈ [0: 2] ^^^^^^^^ ^^^^ ∈ [0: 15]^^^^3 = 3 + 5^^^^ + 13^^^^, ^^^^ ∈ [0: 1] ^^^^^^^^ ^^^^ ∈ [0: 15]^^^^4 = 4 + 5^^^^ + 13^^^^, ^^^^ ∈ [0: 1] ^^^^^^^^ ^^^^ ∈ [0: 15]^^^^0 = 0 + 5^^^^ + 15^^^^,^^^^ ∈ [0:2] ^^^^^^^^^ ^^^^ ∈ [0:15]^^^^1 = 1 + 5^^^^ + 15^^^^, ^^^^ ∈ [0:2] ^^^^^^^^ ^^^^ ∈ [0:15]7^^^^2 = 2 + 5^^^^ + 15^^^^, ^^^^ ∈ [0:2] ^^^^^^^^ ^^^^ ∈ [0:15]^^^^3 = 3 + 5^^^^ + 15^^^^, ^^^^ ∈ [0:2] ^^^^^^^^ ^^^^ ∈ [0:15]^^^^4 = 4 + 5^^^^ + 15^^^^, ^^^^ ∈ [0: 2] ^^^^^^^^ ^^^^ ∈ [0: 15] with ^^^^ and ^^^^ random variables whose interval is given in the table above. Figure 12 gives an example of a basic matrix BG1' proposed according to the invention, for an expansion factor ^^^^^^^^ = 256, in which the matrices ^^^^ and ^^^^ are constructed from identity matrices of length 6 or 7 to which circular rotations have been applied (^^^^, ^ 6 ^ ^^ or ^^^^ ^ 7 ^ ^^). We recall that the matrices 0 and I are not illustrated for the sake of simplification. From the basic matrix BG1' thus obtained, it is possible to obtain a parity matrix ^^^^, by replacing each empty or zero element of the basic matrix ^^^^^^^^1' by a zero matrix of size^^^^^^^^ × ^^^^^^^^ and each non-zero element of the basic matrix ^^^^^^^^1' by an expansion matrix obtained by applying a circular rotation ^^^^^^^^ to an identity matrix of size ^^^^^^^^ × ^^^^^^^^ . The parity matrix ^^^^ thus obtained can be used by an encoder to encode at least one block of ^^^^.^^^^ ^^^^source data. The structure illustrated in Figure 12 makes it possible in particular to reduce short cycles for small source data, for example for ^^^^.^^^^^^^^ < 256. Figure 13 gives another example of a basic matrix BG1' proposed according to the invention, for an expansion factor ^^^^^^^^ = 256, an index ^^^^^^^^^^^^ = 0, and ^^^^ = 50, with a new structure for the matrix ^^^^. 5.4.2 Optimization of the extension matrices C and extension D according to a second example We present below a second example of structure for the extension matrices ^^^^ and extension ^^^^, which can also be used in 5G with ^^^^ = 4. According to this example, illustrated in Figure 14, the extension matrices ^^^^ and extension ^^^^ have a size that depends on ^^^^ = ^^^^^^^^ = {6, 8, 9, 10}. In particular, the matrices ^^^^,^^^^ and ^^^^ have a nested structure depending on the value of ^^^^.If ^^^^ = 6, the extension matrix ^^^^ has size (^^^^ − ^^^^) × ^^^^ = 20 × 6 and the continuation matrix ^^^^ has size (^^^^ − ^^^^) × ^^^^ = 20 × 4. If ^^^^ = 8, the extension matrix ^^^^ has size (^^^^ − ^^^^) × ^^^^ = 28 × 8 and the continuation matrix ^^^^ has size (^^^^ − ^^^^) × ^^^^ = 28 × 4. If ^^^^ = 9, the extension matrix ^^^^ has size (^^^^ − ^^^^) × ^^^^ = 32 × 9 and the extension matrix ^^^^ a size (^^^^ − ^^^^) × ^^^^ = 32 × 4. If ^^^^ = 10, the extension matrix ^^^^ has a size (^^^^ − ^^^^) × ^^^^ = 34 × 10 and the extension matrix ^^^^ a size (^^^^ − ^^^^) × ^^^^ = 34 × 4. Such a structure makes it possible to limit the number of short cycles of size 4 and to obtain a homogeneous number of connections for the proposed basic matrix, denoted BG2', substantially equivalent to the basic matrix BG2 proposed by 3GPP. The case where ^^^^ = 10 is described below.A similar description could be made for the other values ​​of ^^^^. As illustrated in Figure 14, the proposed extension matrix ^^^^ comprises at least two blocks of ^^^^rows, for example five blocks of ^^^^ = 5 rows, referenced 141, 142, 143, 144 and 145, and at least one block of ^^^^ columns, for example two blocks of ^^^^ = 5 columns. Each block of ^^^^ rows comprises at least one matrix ^^^^. ^ ^ ^ ^^ ^ ^ ^ obtained by applying a coefficient of circular rotation ^^^^ to a diagonal matrix of size ^^^^ × ^^^^, with ^^^^ an integer between 0 and ^^^^ − 1 (i.e. at least one complete pattern). For example, the first block 141 includes two occurrences of a matrix ^^^^0 5 , corresponding to the identity matrix of size 7. The first block of lines 141 thus comprises a succession of at least two matrices ^^^^ ^ ^ ^ ^ ^ ^ ^ ^obtained by applying the same circular rotation coefficient ^^^^ to the diagonal matrix of size ^^^^ × ^^^^. The second block 142 includes an occurrence of a matrix ^^^^4 5 and an occurrence of a ^^^^3 5 . The third block 143 includes an occurrence of a matrix ^^^^0 5 and an occurrence of a matrix ^^^^1 5 . The fourth block 144 includes an occurrence of a matrix ^^^^2 5 and an occurrence of a matrix ^^^^0 5 . The fifth block 145 includes an occurrence of a matrix ^^^^1 5 and an occurrence of a matrix ^^^^3 5 . The blocks of lines 141 to 145 thus each comprise a succession of at least two matrices ^^^^ ^ ^ ^ ^^ ^ ^^ obtained by applying a distinct circular rotation coefficient ^^^^ to the detailed diagonal matrix ^^^^ × ^^^^. According to the example illustrated, the blocks of ^^^^ rows are consecutive, i.e. no row of zero or non-zero elements is interposed between two blocks of rows. Furthermore, at least one block of ^^^^ columns comprises at least two matrices ^^^^ ^ ^ ^ ^^ ^ ^ ^ obtained by applying a distinct circular rotation coefficient ^^^^ to said diagonal matrix of size ^^^^ × ^^^^. For example, the first block of ^^^^ = 5 columns includes an occurrence of a matrix ^^^^5 0, une occurrence of a matrix ^^^^4 5 , an occurrence of a matrix ^^^^0 5 , and an occurrence of a matrix ^^^^2 5 and an occurrence of a matrix ^^^^51. The second block of ^^^^ = 5 columns includes an occurrence of a matrix ^^^^0 5 , an occurrence of a matrix ^^^^3 5, an occurrence of a matrix ^^^^1 5 , an occurrence of a matrix ^^^^0 5 and an occurrence of a matrix ^^^^3 5 The intersection of a block of rows and a block of columns corresponds to an “elementary block” formed by a matrix ^^^^ ^ ^ ^ ^ ^ ^ ^ ^ . It is further noted that said extension matrix ^^^^ also comprises at least one block of ^^^^ ′ lines, ^^^^′ ≠ ^^^^, with ^^^^′ an integer between 1 and ^^^^ − 1 comprising a succession of matrices ^^^^^^ ^^ ^^ ^^′ obtained by applying the same circular rotation coefficient ^^^^ to a diagonal matrix size^^^^′ × ^^^^′. For example, such a block of ^^^^′ = 7 rows is referenced 146 in Figure 14. Such a block of rows comprises a succession of matrices ^^^^0 7. According to the embodiment illustrated in Figure 14, the extension matrix ^^^^ comprises at least two blocks of ^^^^ lines, each block of lines comprising a matrix ^^^^ ^^^^ ^ ^^^ obtained by applying a circular rotation coefficient ^^^^ to a diagonal matrix of size ^^^^ × ^^^^. For example, the extension matrix ^^^^ comprises nine blocks of 4 rows each comprising the matrix ^^^^2 4 . The structure of the matrix ^^^^ can notably be extended to the extension matrix ^^^^. For example, returning to Figure 14, the block formed by the last two rows of the matrix ^^^^ and the first two rows of the extension matrix D forms a "complete" pattern corresponding to an identity matrix. The extension matrix ^^^^ thus allows "the diagonals to be extended" and consequently the overall performance of the LDPCs to be increased. The matrices ^^^^ ^ ^ ^ ^^ ^ ^^ can thus be used to decompose the extension matrices ^^^^ and continuation matrices ^^^^. In particular, if the last matrices ^^^^ ^ ^ ^ ^ ^ ^ ^ ^ of a row or a column exceed the dimensions of the extension matrices ^^^^ and continuation ^^^^, then they can be truncated. Circular rotations make it possible in particular to minimize the number of short cycles of size 4 and 6 for matrices of the same dimension, for example matrices of dimension (5,5) and (7,7) according to the example in figure 14. Using the compact notation proposed above, the extension matrix C in figure 14 can be expressed in the following form: ^^^^0 5 ^^^^0 5 ^^^^4 5 ^^^^3 5 ^^^^0 5 ^^^^1 5 ^^^^2 5 ^^^^0 5 ^^^^1 5 ^^^^3 5 ^^^^0 7 ^^^^0 7 ^^^^6 7 ^^^^5 7And the extension matrix ^^^^ of figure 14 in the following form: ^^^^2 4 ^^^^2 4 ^^^^2 4 ^^^^2 4 ^^^^2 4 ^^^^2 4 ^^^^2 4 ^^^^2 4 ^^^^2 4 Another example of an extension matrix ^^^^ is given below: ^^^^0 4 ^^^^0 4 ^^^^0 4 ^^^^0 4 ^^^^0 4 ^^^^0 4 ^^^^0 4 ^^^^0 4 ^^^^0 4Other circular rotations can be applied to the ^^^^ extension matrix. Returning to Figure 14, the number of connections per row and per column is indicated on the right and at the bottom of the figure. By using diagonal matrices to which a circular rotation is applied, we see that the number of connections per row and / or per column in the proposed ^^^^ extension and ^^^^ extension matrices is substantially homogeneous (for example, between 2 and 3 for the number of connections per row, and between 9 and 10 for the number of connections per column for the ^^^^ extension matrix, and between 10 and 12 for the number of connections per column for the ^^^^ extension matrix). As already indicated, such homogeneity makes it possible to optimize the performance of LDPC codecs for a limited number of decoder iterations (less than 10 iterations for example).In the above examples, the extension matrices ^^^^ and extension ^^^^ are also optimized to reduce short cycles. However, as mentioned earlier, if we consider the basis matrix BG2' formed by the kernel matrices ^^^^, ^^^^, spreading ^^^^ and extension ^^^^, short cycles may remain. The kernel matrix A may be the same as or different from the one proposed for the basis matrix BG2 according to 3GPP. For example, depending on the value of ^^^^, said kernel matrix ^^^^ is equal to: for K=10 for K=9 for K=8 for K=6 V1 V0 V3 V2 V1 V4 V3 V2 V4 V0 V3 V2 V4 V2 V3 V0 V2 V0 V3 V4 V2 V3 V1 V1 V3 V4 V4 Matrix B, which includes the start of the redundancy part associated with kernel matrix A, can also be identical to or different from that proposed for the basic matrix BG2 according to 3GPP.For example, said matrix ^^^^ is equal to: V0 V0 V0 V0 V1 V0 V0 V0 V0 As illustrated in Figure 7B, taking into account the rotation factors makes it possible to reduce, or even avoid, short cycles. It is therefore possible to increase the diversity of the proposed basic matrix and therefore to reduce the number of short cycles by taking into account the rotation factors. In other words, for each connection identified by a value "1" in the matrices ^^^^, ^^^^, ^^^^ and ^^^^, another circular rotation operation ^^^^^^^^ is implemented, making it possible to minimize the number of short cycles of size 4 and size 6 for the entire proposed basic matrix BG2'. It is possible to increase the number of rotation factors to increase the diversity of the basic matrix ^^^^^^^^2'. For example, we choose five rotation factors denoted V0 to V4, as defined above for the proposed basic matrix BG1'.Of course, a different number of rotation factors can be chosen, which leads to a different structure for the matrices ^^^^, ^^^^, ^^^^ and ^^^^. In particular, it is possible to define the equations that define the rotation factors V0 to V4 as a function of the index "ils" according to the 5G 3GPP standard defined previously. Figure 15 gives an example of a basic matrix BG2' proposed according to the invention, for an expansion factor ^^^^^^^^ = 256, in which the extension matrix ^^^^ is constructed from five identity matrices of length 5 and two identity matrices of length 7 to which circular rotations (^^^^) have been applied. ^ 5 ^ ^^ or ^^^^ ^ 7 ^ ^^ ) and the extension matrix ^^^^ is constructed from identity matrices of length recalls that the matrices 0 and I are not illustrated for the sake of simplification. According to the example illustrated in Figure 15, the matrices ^^^^,^^^^ and ^^^^ have a nested structure according to the value of ^^^^. From the base matrix BG2' thus obtained, it is possible to obtain a parity matrix ^^^^, by replacing each empty or zero element of the base matrix ^^^^^^^^2' by a zero matrix of size^^^^^^^^ × ^^^^^^^^ and each non-zero element of the base matrix ^^^^^^^^2' by an expansion matrix obtained by applying a circular rotation ^^^^^^^^ to an identity matrix of size ^^^^^^^^ × ^^^^^^^^ . The parity matrix ^^^^ thus obtained can be used by an encoder to encode at least one block of ^^^^.^^^^ ^^^^source data. The structure illustrated in Figure 15 makes it possible in particular to reduce short cycles for small source data, for example for ^^^^.^^^^^^^^ < 256. Figure 16 gives another example of a basic matrix BG2' proposed according to the invention, for an expansion factor ^^^^^^^^ = 256, an index ^^^^^^^^^^^^ = 0, and ^^^^ = 50, with a new structure for the matrix ^^^^. 5.5 Decoding The use of basic matrices according to the different embodiments described above makes it possible in particular to improve the decoding performance of LDPC codes. In the embodiment described here, the implementation of a decoding in “reverse” mode is further considered, according to which the parity matrix is ​​decoded from bottom to top (i.e., the parity equations obtained from the last lines of the parity matrix are first sought to be resolved before those obtained from the first lines of the parity matrix).Such decoding in "reverse" mode offers good performance, especially for decoding small source data, for example for ^^^^.^^^^^^^^ < 256. More generally, starting the decoding with the rows of the parity matrix having the fewest connections (bottom of the parity matrix, corresponding to the last rows of the extension matrices ^^^^ and extension ^^^^) and ending with the rows of the parity matrix having the most connections (top of the parity matrix, corresponding to the kernel matrix ^^^^ and the matrix ^^^^) in "reverse" mode allows the decoder to converge more quickly. Such a decoder therefore requires fewer decoding iterations to achieve similar performance to that obtained for a conventional decoder using the basic matrices BG1 and BG2 according to 3GPP.In particular, MinSum decoders, as described in the document “A fully parallel LDPC decoder architecture using probabilistic minsum algorithm for high-throughput applications”, C.-C. Cheng et al., IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 61, no. 9, pp. 2738–2746, Sep. 2014, conventionally used to decode LDPC codes, have better performance if the decoding starts from the end of the parity matrix. It is therefore particularly advantageous to implement a “reverse” decoding to decode LDPC codes constructed from the basic matrices according to the invention or the basic matrices according to 3GPP. However, the use of a “standard” decoding from the top to the bottom of the parity matrix, or in another order, is also possible. 5.6 Performance curves We now present, in relation to Figure 17, the decoding performances obtained in terms of block error rate (BLER) as a function of the signal-to-noise ratio (SNR in dB), for LDPC decoders, after encoding source data using a parity matrix obtained either from the BG1 base matrix as defined by the 3GPP for the 5G standard, or from a BG1' base matrix according to an embodiment of the invention. These performances are obtained for code lengths of 330 bits (^^^^ = 22, ^^^^^^^^ = 15) and a throughput of 1 / 3.The decoder algorithm is for example the MinSum, with an alpha parameter equal to 0.7, in “reverse” mode for decoding the data obtained using a parity matrix constructed from a basic matrix BG1' according to an embodiment of the invention, and in “classical” mode for decoding the data obtained using a parity matrix constructed from a basic matrix BG1 according to the 3GPP. Curve 171 illustrates the decoding performance using the basic matrix BG1' according to an embodiment of the invention after 20 iterations of the decoder. Curve 172 illustrates the decoding performance using the basic matrix BG1 after 20 iterations of the decoder. Curve 173 illustrates the decoding performance using the basic matrix BG1' according to an embodiment of the invention after 10 iterations of the decoder.Curve 174 illustrates the decoding performance using the basic matrix BG1 after 10 iterations of the decoder. Curve 175 illustrates the decoding performance using the basic matrix BG1' according to one embodiment of the invention after 5 iterations of the decoder. Curve 176 illustrates the decoding performance using the basic matrix BG1 after 5 iterations of the decoder. It is noted that the structure proposed according to at least one embodiment of the invention makes it possible to improve the performance of the LDPC decoder according to the 5G standard. The difference is even greater with a lower number of iterations of the decoder.Finally, in relation to Figures 18 and 19, the decoding performances obtained in terms of block error rate (BLER) as a function of the signal-to-noise ratio (SNR in dB) are presented for LDPC decoders, after encoding source data using a parity matrix obtained either from the BG2 base matrix as defined by the 3GPP for the 5G standard, or from a BG2' base matrix according to an embodiment of the invention. The performances illustrated in Figure 18 are obtained for code lengths of 720 bits (^^^^ = 10, ^^^^^^^^ = 72) and an efficiency of 1 / 5.The decoder algorithm is for example the MinSum, with an alpha parameter equal to 0.7, in “reverse” mode for decoding the data obtained using a parity matrix constructed from a BG2' base matrix according to an embodiment of the invention, and in “classical” mode for decoding the data obtained using a parity matrix constructed from a BG2 base matrix according to the 3GPP. Curve 181 illustrates the decoding performance using the BG2' base matrix according to an embodiment of the invention after 20 iterations of the decoder. Curve 182 illustrates the decoding performance using the BG2 base matrix after 20 iterations of the decoder. Curve 183 illustrates the decoding performance using the BG2' base matrix according to an embodiment of the invention after 10 iterations of the decoder.Curve 184 illustrates the decoding performance using the BG2 base matrix after 10 iterations of the decoder. Curve 185 illustrates the decoding performance using the BG2' base matrix according to an embodiment of the invention after 5 iterations of the decoder. Curve 186 illustrates the decoding performance using the BG2 base matrix after 5 iterations of the decoder. The performance illustrated in FIG. 19 is obtained for small code sizes, a rate of 1 / 5 and five decoding iterations. The decoder algorithm is the MinSum in “classic” mode with an alpha parameter equal to 0.7. The decoding performances of a 12-bit length code (K = 6,^^^^^^^^ = 2) are illustrated by curve 191 for a codec using the basic matrix BG2' according to an embodiment of the invention and by curve 192 for a codec using the basic matrix BG2.The decoding performance of a code of length 18 bits (K = 6,^^^^^^^^^ = 3) is illustrated by curve 193 for a codec using the basic matrix BG2' according to an embodiment of the invention and by curve 194 for a codec using the basic matrix BG2. The decoding performance of a code of length 30 bits (K = 6,^^^^^^^^^ = 5) is illustrated by curve 195 for a codec using the basic matrix BG2' according to an embodiment of the invention and by curve 196 for a codec using the basic matrix BG2. The decoding performance of a code of length 42 bits (K = 6,^^^^^^^^^ = 7) is illustrated by curve 197 for a codec using the basic matrix BG2' according to an embodiment of the invention and by curve 198 for a codec using the BG2 base matrix. 5.7 Variants Examples with particular values ​​for ^^^^, ^^^^ and ^^^^ have been described above.These are, however, simple examples, and other values ​​for ^^^^, ^^^^ and ^^^^ may be considered, in particular for other transmission standards (Wifi®, 6G, etc.). Similarly, basic matrices with five rotation factors V0 to V4 have been proposed. However, a different number of rotation factors may be chosen. Other forms of the matrix ^^^^ may also be used. In this case, the position of the connections and / or the values ​​of the rotation factors may be updated to take into account the structure of the matrix ^^^^. An LDPC code has also been taken as an example. The invention may also be extended to other error-correcting codes using a parity matrix. 5.8 Coding and decoding devices Finally, in relation to Figures 20A and 20B, the simplified structures of an encoder and a decoder according to at least one embodiment described above are presented.As illustrated in Figure 20A, an encoder comprises at least one memory 201, at least one processing unit 202, equipped for example with a programmable computing machine or a dedicated computing machine, for example a processor P, and controlled by the computer program 203, implementing steps of the coding method according to at least one embodiment of the invention. At initialization, the code instructions of the computer program 203 are for example loaded into a RAM memory before being executed by the processor of the processing unit 202. The processor of the processing unit 202 implements steps of the coding method described above, according to the instructions of the computer program 203, to code the ^^^^.^^^^. ^^^^ source data using a parity matrix ^^^^ of size (^^^^.^^^^^^^^ × ^^^^.^^^^^^^^), and deliver at least one codeword of size ^^^^.^^^^ ^^^^ formed from ^^^^.^^^^ ^^^^source data and ^^^^.^^^^ ^^^^ redundancy data. As illustrated in Figure 20B, a decoder comprises at least one memory 204, at least one processing unit 205, equipped for example with a programmable computing machine or a dedicated computing machine, for example a processor P, and driven by the computer program 206, implementing steps of the decoding method according to at least one embodiment of the invention. At initialization, the code instructions of the computer program 206 are for example loaded into a RAM memory before being executed by the processor of the processing unit 205. The processor of the processing unit 205 implements steps of the decoding method described previously, according to the instructions of the computer program 206, to decode at least one code word of size ^^^^.^^^^ ^^^^ formed from ^^^^.^^^^ ^^^^ source data and ^^^^.^^^^ ^^^^redundancy data, using a parity matrix ^^^^ of size (^^^^.^^^^^^^^ × ^^^^.^^^^^^^^), and reconstruct the ^^^^.^^^^^^^ source data.

Claims

CLAIMS 1. Method for coding at least one block of ^^^^.^^^^ ^^^^ source data, delivering at least one code word of size ^^^^.^^^^^^^^ formed from said ^^^^.^^^^^^^^ source data and ^^^^.^^^^^^^^ redundancy data, ^^^^ =^^^^ + ^^^^, with ^^^^^^^^ an integer expansion factor, ^^^^^^^^ ≥ 1, said method implementing a step of coding (53) said ^^^^.^^^^ ^^^^ source data using a parity matrix ^^^^ of size (^^^^.^^^^^^^^ × ^^^^.^^^^^^^^), characterized in that said parity matrix ^^^^ is obtained (52) from a base matrix ^^^^^^^^' of size ^^^^ × ^^^^, by replacing each element of said base matrix ^^^^^^^^' by an expansion matrix of size ^^^^^^^^ × ^^^^^^^^, said base matrix ^^^^^^^^' being expressed in the form: ^^^^^^^^' ^^^^ 0with: ^^^^ a kernel matrix of size ^^^^ × ^^^^^^^^ a matrix having at least one diagonal of size ^^^^ × ^^^^^^^^ an extension matrix of size (^^^^ − ^^^^) × ^^^^^^^^ an extension matrix of size (^^^^ − ^^^^) × ^^^^0 a zero matrix of size (^^^^ − ^^^^ − ^^^^) × ^^^^^^^^ an identity matrix of size (^^^^ − ^^^^) × (^^^^ − ^^^^ − ^^^^)and in that said extension matrix ^^^^ comprises at least two blocks of ^^^^ rows and at least one block of ^^^^ columns, with ^^^^ an integer between 1 and ^^^^ − 1, each block of ^^^^ rows comprising at least one matrix ^^^^ ^ ^ ^ ^^ ^ ^ ^ obtained by applying a circular rotation coefficient ^^^^ to a diagonal matrix of size ^^^^ × ^^^^, with ^^^^ a between 0 and ^^^^ − 1, said at least one block of ^^^^ columns comprising at least two ^^^^ ^ ^ ^ ^^ ^ ^^ obtained by applying a separate circular rotation coefficient ^^^^ to said diagonal matrix of size ^^^^ × ^^^^.

2. Method according to claim 1, characterized that at least one of said blocks of lines comprises a succession of at least two matrices ^^^^ ^ ^ ^ ^ ^ ^ ^ ^ obtained by applying a distinct circular rotation coefficient ^^^^ to said diagonal matrix of size ^^^^ × ^^^^.

3. Method according to any one of claims 1 and 2, characterized in that at least one of said blocks of lines comprises a succession of at least two matrices ^^^^ ^ ^ ^ ^ ^ ^ ^ ^obtained by applying the same circular rotation coefficient ^^^^ to said diagonal matrix of size ^^^^ × ^^^^.

4. Method according to any one of claims 1 to 3, characterized in that ^^^^ ≥ 5.

5. Method according to any one of claims 1 to 4, characterized in that said at least two blocks of ^^^^ lines are consecutive.

6. Method according to any one of claims 1 to 5, and in that said extension matrix ^^^^ also comprises at least one block of ^^^^′ rows, ^^^^′ ≠ ^^^^, with ^^^^′ an integer between 1 and ^^^^ − 1, comprising a succession of matrices ^^^^ ^ ^ ^ ^ ^ ^ ^ ^′obtained by applying the same circular rotation coefficient ^^^^ to a diagonal matrix of size ^^^^′ × ^^^^′.

7. Method according to any one of claims 1 to 6, characterized in that for at least one of said blocks of lines, said extension matrix ^^^^ comprises a portion of one of said matrices ^^^^ ^ ^ ^ ^^ ^ ^ ^ obtained by applying a circular rotation coefficient ^^^^ to a diagonal matrix of size^^^^ × ^^^^, and in that said extension matrix ^^^^ comprises the extension of said portion.

8. Method according to any one of the preceding claims, characterized in that said extension matrix ^^^^ is equal to: V2 V1 V3 V4 V1 V1 V2 V3 V2 V2 V0 V3 V3 V1 V3 V3 V0 V2 V2 V2 V2 V3 V0 V1 V4 V1 V0 V2 V4 V2 V0 V2 V1 V1 V0 V3 V2 V2 V3 V3 V4 V3 V3 V2 V0 V0 V2 V3 V1 V4 V4 V1 V0 V1 V0 V2 V3 V3 V2 V2 V4 V3 V3 V3 V4 V1 V2 V3 V1 V2 V3 V0 V4 V1 V1 V3V4 V3 V3 V1 V3 V3 V3 V1 V3 V4 V1 V1 V1 V2 V1 V1 V1 V2 V1 V4 V3 V1 V4 V2 V1 V1 V4 V0 V4 V1 V1 V1 V2 V0 V3 V1 V3 V3 V2 V2 V2 V1 V1 V2 V2 V0 V3 V1 V2 V1 V0 V2 V4said extension matrix ^^^^ is equal to:V2 V1 V 1 V3 V 4 V3 V1 V1 V1 V3 V1 V3 V 1 V3 V4 V2 V 2 V1 V4 V1 V4 V1 V2 and in that: - each empty or null element of said basic matrix ^^^^^^^^' is replaced by a null matrix of size ^^^^^^^^ × ^^^^^^^^ ,- each non-null element of said basic matrix ^^^^^^^^' is replaced by a circular permutation matrix obtained by applying a circular rotation ^^^^^^^^ to an identity matrix of size ^^^^^^^^ × ^^^^^^^^ , such that:Circular rotation ^^^^^^^^ if ^^^^ ^^^^ belongs to^^^^0 = 0 + 4^^^^,^^^^ ∈ [0: 63]{2,4,8,16,32,128,256 } : ^^^^1 = 1 + 4^^^^,^^^^ ∈ [0:63]^^^^2 = 2 + 4^^^^,^^^^ ∈ [0:63]^^^^3 = 3 + 4^^^^,^^^^ ∈ [0:63]^^^^4 = 0 + 4^^^^,^^^^ ∈ [0:63]if ^^^^^^^^ belongs to^^^^0 = 0 + 5^^^^ + 6^^^^, ^^^^ ∈ [0: 1] and ^^^^ ∈ [0: 63]{3,6,12,24,48,96,192,384} :^^^^1 = 1 + 6^^^^,^^^^ ∈ [0: 63]^^^^2 = 2 + 6^^^^,^^^^ ∈ [0: 63]^^^^3 = 3 + 6^^^^,^^^^ ∈ [0: 63]^^^^4 = 4 + 6^^^^,^^^^ ∈ [0: 63]if ^^^^ ^^^^ belongs to^^^^0 = 0 + 5^^^^,^^^^ ∈ [0: 63]{5,10,20,40,80,160,320} :^^^^1 = 1 + 5^^^^,^^^^ ∈ [0: 63]^^^^2 = 2 + 5^^^^,^^^^ ∈ [0: 63]^^^^3 = 3 + 5^^^^,^^^^ ∈ [0: 63]^^^^4 = 4 + 5^^^^,^^^^ ∈ [0: 63]if ^^^^ belongs to^^^^0 = 0 + 5^^^^ + 7^^^^, ^^^^ ∈ [0: 1] ^^^^^^^^^ ^^^^ ∈ [0:31]{7,14,28,56,112,224 } : ^^^^1 = 1 + 5^^^^ + 7^^^^, ^^^^ ∈ [0: 1] ^^^^^^^ ^^^^ ∈ [0: 31]^^^^2 = 2 + 7^^^^,^^^^ ∈ [0: 31]^^^^3 = 3 + 7^^^^,^^^^ ∈ [0:31]^^^^4 = 4 + 7^^^^,^^^^ ∈ [0:31]if ^^^^ ^^^^ belongs to^^^^0 = 0 + 5^^^^ + 9^^^^, ^^^^ ∈ [0: 1] ^^^^^^^^ ^^^^ ∈ [0: 31]{9,18,36,72,144,288 }: ^^^^1 = 1 + 5^^^^ + 9^^^^, ^^^^ ∈ [0: 1]^^^^^^^ ^^^^ ∈ [0: 31]^^^^2 = 2 + 5^^^^ + 9^^^^, ^^^^ ∈ [0: 1] ^^^^^^^ ^^^^ ∈ [0: 31]^^^^3 = 3 + 5^^^^ + 9^^^^, ^^^^ ∈ [0:1] ^^^^^^^ ^^^^ ∈ [0:31]^^^^4 = 4 + 9^^^^,^^^^ ∈ [0:31]if ^^^^ ^^^^ belongs to^^^^0 = 0 + 5^^^^ + 11^^^^, ^^^^ ∈ [0: 2] ^^^^^^^^ ^^^^ ∈ [0: 31]{11,22,44,88,176,352 } : ^^^^1 = 1 + 5^^^^ + 11^^^^, ^^^^ ∈ [0: 1] ^^^^^^^^ ^^^^ ∈ [0: 31]^^^^2 = 2 + 5^^^^ + 11^^^^, ^^^^ ∈ [0: 1] ^^^^^^^^ ^^^^ ∈ [0: 31]^^^^3 = 3 + 5^^^^ + 11^^^^, ^^^^ ∈ [0: 1] ^^^^^^^^ ^^^^ ∈ [0: 31]^^^^4 = 4 + 5^^^^ + 11^^^^, ^^^^ ∈ [0: 1] ^^^^^^^^ ^^^^ ∈ [0: 31] if ^^^^ ^^^^ belongs to^^^^0 = 0 + 5^^^^ + 13^^^^, ^^^^ ∈ [0: 2] ^^^^^^^^ ^^^^ ∈ [0: 15]{13,26,52,104,208 }: ^^^^1 = 1 + 5^^^^ + 13^^^^, ^^^^ ∈ [0: 2] ^^^^^^^^ ^^^^ ∈ [0: 15]^^^^2 = 2 + 5^^^^ + 13^^^^, ^^^^ ∈ [0: 2] ^^^^^^^^ ^^^^ ∈ [0: 15]^^^^3 = 3 + 5^^^^ + 13^^^^, ^^^^ ∈ [0: 1] ^^^^^^^^ ^^^^ ∈ [0: 15]^^^^4 = 4 + 5^^^^ + 13^^^^, ^^^^ ∈ [0: 1] ^^^^^^^^^ ^^^^ ∈ [0: 15] if ^^^^ ^^^^ belongs to^^^^0 = 0 + 5^^^^ + 15^^^^, ^^^^ ∈ [0: 2] ^^^^^^^^ ^^^^ ∈ [0: 15]{15,30,60,120,240 }: ^^^^1 = 1 + 5^^^^ + 15^^^^, ^^^^ ∈ [0: 2] ^^^^^^^^ ^^^^ ∈ [0: 15]^^^^2 = 2 + 5^^^^ + 15^^^^, ^^^^ ∈ [0: 2] ^^^^^^^^ ^^^^ ∈ [0: 15]^^^^3 = 3 + 5^^^^ + 15^^^^, ^^^^ ∈ [0: 2] ^^^^^^^^ ^^^^ ∈ [0: 15]^^^^4 = 4 + 5^^^^ + 15^^^^, ^^^^ ∈ [0: 2] ^^^^^^^^^ ^^^^ ∈ [0: 15] with ^^^^ and ^^^^ random variables.

9. Method according to any one of the preceding claims, characterized in that ^^^^ = 4,^^^^ = 22 and ^^^^ = 44.

10. Method according to any one of claims 1 to 5, characterized in that said extension matrix ^^^^ comprises at least two blocks of ^^^^ lines, each block of lines comprising a matrix ^^^^ ^^^^ ^ ^^^obtained by applying a circular rotation coefficient ^^^^ to a detailed diagonal matrix ^^^^ × ^^^^.

11. Method according to any one of claims 1 to 5 or 10, characterized in that, depending on the value of ^^^^, said extension matrix ^^^^ and continuation matrix D are equal to: for K=6: CD V2 V2 V1 V3 V2 V3 V0 V2 V3 V2 V2 V1 V2 V1 V1 V2 V2 V3 V3 V2 V1 V2 V1 V0 V2 V2 V2 V3 V1 V1 V2 V0 V0 V3 V2 V1 V0 V1 V2 V3 V0 V1 for K=8: CD V2 V2 V1 V3 V3 V2 V3 V2 V0 V2 V3 V2 V2 V1 V2 V1 V1 V2 V2 V3 V3 V1 V2 V1 V3 V2 V1 V3 V0 V2 V1 V2 V2 V3 V1 V1 V2 V0 V0 V3 V2 V1 V0 V3 V1 V2 V2 V3 V0 V1 V2 V0 V3 V3 V0 V3 V2 V2 V0 V2 V1 V1 V0 V0 V0 V3 V0 V3 V2 V2 V2 V2 for K=9: CD V2 V2 V1 V3 V3 V2 V3 V2 V0 V2 V1 V3 V2 V2 V1 V1 V2 V1 V1 V2 V2 V3 V3 V1 V2 V1 V3 V2 V1 V3 V0 V2 V1 V2 V2 V1 V3 V1 V2 V0 V0 V3 V2 V1 V0 V3 V1 V2 V2 V3 V0 V0 V1 V2 V0 V3 V2 V3 V0 V3 V2 V2 V0 V2 V1 V1 V0 V0 V0 V3 V0 V3 V2 V2 V0 V2 V1 V1 V0 V0 V3 V0 V3 V2 V3 V2 V2 V2 V0 V2 V0 V2 V0 V3 V0 V1 V2 V0 For K=10: CD V2 V2 V1 V3 V3 V2 V3 V2 V0 V2 V1 V3 V2 V2 V2 V1 V1 V2 V1 V2 V1 V2 V2 V3 V3 V1 V2 V1 V3 V2 V1 V3 V0 V2 V1 V2 V2 V1 V3 V1 V3 V1 V2 V0 V0 V3 V2 V1 V0 V3 V1 V2 V2 V3 V0 V0 V1 V2 V1 V0 V3 V2 V3 V0 V0 V3 V2 V2 V0 V2 V1 V1 V0 V0 V0 V3 V0 V3 V2 V3 V2 V2 V2 V2 V0 V2 V0 V3 V0 V1 V2 V0 V2 V1 V0 V2 V0 V1 V2 V3 V1 V2 and in that: - each empty or zero element of said base matrix ^^^^^^^^' is replaced by a zero matrix of size ^^^^^^^^ × ^^^^^^^^ ,- each element non-zero of said base matrix ^^^^^^^^' is replaced by a circular permutation matrix obtained by applying a circular rotation ^^^^^^^^ to an identity matrix of size ^^^^^^^^ × ^^^^^^^^ , such that: Circular Rotation ^^^^^^^^ ^^^^0 = 0 + 4^^^^,^^^^ ∈ [0: 63]^^^^1 = 1 + 4^^^^,^^^^ ∈ [0: 63]^^^^2 = 2 + 4^^^^,^^^^ ∈ [0: 63] if ^^^^^^^^3 = 3 + 4^^^^,^^^^ ∈ [0:63] ^^^^ belongs to^^^^4 = 0 + 4^^^^,^^^^ ∈ [0: 63]{2,4,8,16,32,128,256} : if ^^^^^^^^0 = 0 + 5^^^^ + 6^^^^, ^^^^ ∈ [0: 1] and ^^^^ ∈ [0: 63] ^^^^belongs to^^^^1 = 1 + 6^^^^,^^^^ ∈ [0: 63]{3,6,12,24,48,96,192,384 } : ^^^^2 = 2 + 6^^^^,^^^^ ∈ [0:63]^^^^3 = 3 + 6^^^^,^^^^ ∈ [0:63]^^^^4 = 4 + 6^^^^,^^^^ ∈ [0:63]if ^^^^^^^^0 = 0 + 5^^^^,^^^^ ∈ [0:63] ^^^^ belongs to^^^^1 = 1 + 5^^^^,^^^^ ∈ [0: 63]{5,10,20,40,80,160,320} :^^^^2 = 2 + 5^^^^,^^^^ ∈ [0: 63]^^^^3 = 3 + 5^^^^,^^^^ ∈ [0: 63]^^^^4 = 4 + 5^^^^,^^^^ ∈ [0: 63]if ^^^^ belongs to^^^^0 = 0 + 5^^^^ + 7^^^^, ^^^^ ∈ [0: 1] ^^^^^^^^^ ^^^^ ∈ [0: 31] ^^^^ ient to^^^^1 = 1 + 5^^^^ + 7^^^^, ^^^^ ∈ [0: 1] ^^^^^^^^ ^^^^ ∈ [0: 31]{7,14,28,56,112,224} :^^^^2 = 2 + 7^^^^,^^^^ ∈ [0: 31]^^^^3 = 3 + 7^^^^,^^^^ ∈ [0: 31]^^^^4 = 4 + 7^^^^,^^^^ ∈ [0: 31]if ^^^^ belongs^^^^0 = 0 + 5^^^^ + 9^^^^, ^^^^ ∈ [0: 1] ^^^^^^^^^ ^^^^ ∈ [0: 31] ^^^^t to^^^^1 = 1 + 5^^^^ + 9^^^^, ^^^^ ∈ [0: 1]^^^^^^^^ ^^^^ ∈ [0: 31]{9,18,36,72,144,288} :^^^^2 = 2 + 5^^^^ + 9^^^^, ^^^^ ∈ [0: 1] ^^^^^^^^ ^^^^ ∈ [0: 31]^^^^3 = 3 + 5^^^^ + 9^^^^, ^^^^ ∈ [0: 1] ^^^^^^^^ ^^^^ ∈ [0: 31]^^^^4 = 4 + 9^^^^,^^^^ ∈ [0: 31]if ^^^^ belongs to^^^^0 = 0 + 5^^^^ + 11^^^^, ^^^^ ∈ [0: 2] ^^^^^^^^ ^^^^ ∈ [0: 31]^^^^ ^^^^1 = 1 + 5^^^^ + 11^^^^, ^^^^ ∈ [0: 1] ^^^^^^^^ ^^^^ ∈ [0: 31]{11,22,44,88,176,352} :^^^^2 = 2 + 5^^^^ + 11^^^^, ^^^^ ∈ [0: 1] ^^^^^^^^ ^^^^ ∈ [0: 31]^^^^3 = 3 + 5^^^^ + 11^^^^, ^^^^ ∈ [0: 1] ^^^^^^^ ^^^^ ∈ [0:31]^^^^4 = 4 + 5^^^^ + 11^^^^, ^^^^ ∈ [0:1] ^^^^^^^^ ^^^^ ∈ [0:31]if ^^^^^^^^0 = 0 + 5^^^^ + 13^^^^, ^^^^ ∈ [0:2] ^^^^^^^ ^^^^ ∈ [0:15] ^^^^belongs to^^^^1 = 1 + 5^^^^ + 13^^^^, ^^^^ ∈ [0:2] ^^^^^^^^ ^^^^ ∈ [0:15]{13,26,52,104,208} :^^^^2 = 2 + 5^^^^ + 13^^^^, ^^^^ ∈ [0:2] ^^^^^^^^ ^^^^ ∈ [0:15]^^^^3 = 3 + 5^^^^ + 13^^^^, ^^^^ ∈ [0:1] ^^^^^^^^ ^^^^ ∈ [0:15]^^^^4 = 4 + 5^^^^ + 13^^^^, ^^^^ ∈ [0:1] ^^^^^^^^ ^^^^ ∈ [0:15]if ^^^^ appa^^^^0 = 0 + 5^^^^ + 15^^^^, ^^^^ ∈ [0:2] ^^^^^^^ ^^^^ ∈ [0:15] ^^^^ retains to^^^^1 = 1 + 5^^^^ + 15^^^^, ^^^^ ∈ [0: 2] ^^^^^^^^ ^^^^ ∈ [0: 15]{15,30,60,120,240} :^^^^2 = 2 + 5^^^^ + 15^^^^, ^^^^ ∈ [0: 2] ^^^^^^^^ ^^^^ ∈ [0: 15]^^^^3 = 3 + 5^^^^ + 15^^^^, ^^^^ ∈ [0: 2] ^^^^^^^^ ^^^^ ∈ [0: 15]^^^^4 = 4 + 5^^^^ + 15^^^^, ^^^^ ∈ [0: 2] ^^^^^^^^ ^^^^ ∈ [0: 15]with ^^^^ and ^^^^ random variables.

12. Method according to any one of claims 1 to 5 or 10 to 11, characterized in that ^^^^ =4 and :^^^^ = 6 and ^^^^ = 24, or^^^^ = 8 and ^^^^ = 32, or^^^^ = 9 and ^^^^ = 36 or^^^^ = 10 and ^^^^ = 40.

13. Device for coding at least one block of ^^^^.^^^^ ^^^^source data, delivering at least one code word of size ^^^^.^^^^^^^^ formed from said ^^^^.^^^^^^^^ source data and ^^^^.^^^^^^^^ redundancy data, ^^^^ =^^^^ + ^^^^, with ^^^^^^^^ an integer expansion factor, ^^^^^^^^ ≥ 1, comprising at least one processing unit configured to code said ^^^^.^^^^ ^^^^ source data using a parity matrix ^^^^ of size ( ^^^^.^^^^^^^^ × ^^^^.^^^^^^^^ ) , said parity matrix ^^^^ being obtained from a base matrix ^^^^^^^^' of size ^^^^ ×^^^^, by replacing each element of said base matrix ^^^^^^^^' by an expansion matrix of size^^^^^^^^ × ^^^^^^^^ , said base matrix ^^^^^^^^' being expressed in the form: ^^^^^^^^' =�^^^^ ^^^^ 0^^^^ ^^^^ ^^^^�with: ^^^^ a kernel matrix of size ^^^^ × ^^^^^^^^ a matrix having at least one diagonal of size ^^^^ × ^^^^^^^^ an extension matrix of size (^^^^ − ^^^^) × ^^^^^^^^ an extension matrix of size (^^^^ − ^^^^) × ^^^^0 a zero matrix of size (^^^^ − ^^^^ − ^^^^) × ^^^^^^^^ an identity matrix of size (^^^^ − ^^^^) × (^^^^ − ^^^^ − ^^^^)said extension matrix ^^^^ comprising at least two blocks of ^^^^ rows and at least one block of ^^^^columns, with ^^^^ an integer between 1 and ^^^^ − 1, each block of ^^^^ lines comprising at least one ^^^^ matrix ^ ^ ^ ^^ ^ ^ ^obtained by applying a circular rotation coefficient ^^^^ to a diagonal matrix of size ^^^^ × ^^^^, with ^^^^ an integer between 0 and ^^^^ − 1, said at least one block of ^^^^ columns comprising at least two ^^^^ ^ ^ ^ ^^ ^ ^^ obtained by applying a separate circular rotation coefficient ^^^^ to said diagonal matrix of size ^^^^ × ^^^^.

14. Method for decoding at least one code word of size ^^^^.^^^^ ^^^^ formed from ^^^^.^^^^ ^^^^ source data and ^^^^.^^^^^^^^ redundancy data, ^^^^ = ^^^^ + ^^^^, with ^^^^^^^^ an integer expansion factor, ^^^^^^^^ ≥ 1,said method implementing a step of decoding (56) said at least one code word of size^^^^.^^^^^^^ using a parity matrix ^^^^ of size (^^^^.^^^^^^^^ × ^^^^.^^^^^^^^),characterized in that said parity matrix ^^^^ is obtained (55) from a base matrix ^^^^^^^^' of size ^^^^ × ^^^^, by replacing each element of said base matrix ^^^^^^^^' by an expansion matrix of size ^^^^^^^^ × ^^^^^^^^, the said basic matrix ^^^^^^^^' being expressed ^^^^^^^^^' =�^^^^ ^^^^ 0^^^^ ^^^^ ^^^^�with:^^^^ a kernel matrix of size ^^^^ × ^^^^^^^^ a matrix having at least one diagonal of size ^^^^ × ^^^^^^^^ an extension matrix of size (^^^^ − ^^^^) × ^^^^^^^^ an extension matrix of size (^^^^ − ^^^^) × ^^^^^0 a zero matrix of size (^^^^ − ^^^^ − ^^^^) × ^^^^^^^^ an identity matrix of size (^^^^ − ^^^^) × (^^^^ − ^^^^ − ^^^^)and in that said extension matrix ^^^^ comprises at least least two blocks of ^^^^ rows and at least one block of ^^^^ columns, with ^^^^ an integer between 1 and ^^^^ − 1, each block of ^^^^ rows comprising at least one matrix ^^^^ ^ ^ ^ ^^ ^ ^ ^ obtained by applying a circular rotation coefficient ^^^^ to a diagonal matrix of size ^^^^ × ^^^^, with ^^^^ an integer between 0 and ^^^^ − 1, said at least one block of ^^^^ columns comprising at least two matrices ^^^^ ^ ^ ^ ^^ ^ ^^ obtained by applying a distinct circular rotation coefficient ^^^^ to said diagonal matrix size ^^^^ × ^^^^.

15. Method according to claim 14, characterized in that said decoding step implements a decoding of a parity equation obtained from the last line of said parity matrix ^^^^, then of a parity equation obtained from the previous line of said parity matrix ^^^^, going up line by line to the first line of the parity matrix ^^^^.

16. Device for decoding at least one code word of size ^^^^.^^^^ ^^^^ formed from ^^^^.^^^^ ^^^^ source data and ^^^^.^^^^^^^^ redundancy data, ^^^^ = ^^^^ + ^^^^, with ^^^^^^^^ an integer expansion factor, ^^^^^^^^ ≥1, comprising at least one processing unit configured to decode said at least one code word of size ^^^^.^^^^ ^^^^ using a parity matrix ^^^^ of size ( ^^^^.^^^^^^^^ ×^^^^.^^^^ ^^^^ ) ,said parity matrix ^^^^ being obtained from a base matrix ^^^^^^^^' of size ^^^^ × ^^^^, by replacing each element of said base matrix ^^^^^^^^' by an expansion matrix of size^^^^^^^^ × ^^^^^^^^ ,said base matrix ^^^^^^^^' being expressed in the form: ^^^^^^^^' =�^^^^ ^^^^ 0^^^^ ^^^^ ^^^^�with: ^^^^ a kernel matrix of size ^^^^ × ^^^^^^^^ a matrix having at least one diagonal of size ^^^^ × ^^^^^^^^ an extension matrix of size (^^^^ − ^^^^) × ^^^^^^^^ an extension matrix of size (^^^^ − ^^^^) × ^^^^0 a zero matrix of size (^^^^ − ^^^^ − ^^^^) × ^^^^^^^^ an identity matrix of size (^^^^ − ^^^^) × (^^^^ − ^^^^ − ^^^^) said extension matrix ^^^^ comprising at least two blocks of ^^^^ rows and at least one block of ^^^^columns, with ^^^^ an integer between 1 and ^^^^ − 1, each block of ^^^^ rows comprising at least one matrix ^^^^ ^^ ^ ^^ ^ ^ ^ obtained by applying a circular rotation coefficient ^^^^ to a diagonal matrix of size ^^^^ × ^^^^, with ^^^^ an integer between 0 and ^^^^ − 1, said at least one block of ^^^^ columns comprising at least two matrices ^^^^ ^ ^ ^ ^^ ^ ^ ^ obtained by applying a separate circular rotation coefficient ^^^^ to said diagonal matrix of size ^^^^ × ^^^^.

17. Computer program comprising instructions for implementing a method according to any one of claims 1 to 12, 14 or 15 when this program is executed by a processor.

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