FR2939586A1 - Network coding method for wireless mesh communication network, involves constructing part of result packet with combination of expected input packets using momentarily used packets, before end of reception of expected input data packets - Google Patents

Abstract

The method involves detecting a corrupted used packet. A new linear combination of expected input packets permitting to construct a reconstituted result packet using all or part of redundant packets is determined before an end of reception of data packets, when the corrupted used packet is detected. A part of the result packet is constructed with the combination of expected input packets using already correctly received momentarily used packets, before an end of reception of expected input data packets. Independent claims are also included for the following: (1) a computer program product comprising program code instructions for implementing a network coding method (2) a storage medium for storing a computer program comprising instructions for implementing a network coding method (3) a relay node comprised in a mesh network and participating in a network coding method (4) a destination node comprised in a mesh network and participating in a network coding method.

Description

Fast and robust network coding method for transmission losses in a mesh network, relay node, destination node, computer program product and corresponding storage means. FIELD OF THE INVENTION The field of the invention is that of meshed communication networks. More specifically, the invention relates to a network coding technique adapted to the transmission of data packets, in a mesh communication network, from source nodes to destination nodes, via relay nodes retransmitting packets. data from the source nodes and destined for the destination nodes. In accordance with the general principle of network coding, the messages retransmitted by the relay nodes are linear combinations of the messages received by these relay nodes, which makes it possible to increase the data rate and make best use of the network capacity. The invention applies in particular, but not exclusively, in the context of a wireless mesh network. 2. TECHNOLOGICAL BACKGROUND 2.1 Context and problem In the remainder of this document, we will focus on the problem existing in the context of network coding in a wireless mesh network, which the inventors of this patent application. The invention is of course not limited to this particular context of application, but is of interest in all cases of network coding adapted to the transmission, via relay nodes, of data packets from source nodes to destination nodes. , in a mesh communication network.

A wireless mesh communication network consists of a set S of M source nodes and a set Dt of N destination nodes. The transmissions considered are called multicast (the term multicast is sometimes also used), that is to say that each data packet sent by a source node is intended for all the destination nodes of Dt. The other nodes being relay nodes, used to retransmit source packets sent by the source nodes. The topology of the network is assumed to be known, ie all the radio qualities (such as the received radio power) between two communicating nodes are known. The relay nodes conventionally have the function of retransmitting one of the packets they have received as input (routing function). As part of a network coding, these relay nodes have a new feature: they have the ability to issue a resulting packet that is a combination of packets received as input. The concept of network coding was introduced by R. Ahlswede and co. (see article: R. Ahlswede, N. Cai, S. YR Li and RW Yeung "Network Information Flow" IEEE Transactions on Information Theory Vol 46, No. 4, pp 1204-1216, July 2000) and very quickly, many articles have demonstrated the contribution of this new concept, especially in terms of bandwidth gain and in terms of network capacity utilization. In addition, it has been shown that in a multicast framework (each message sent by a source node is destined for the set of destination nodes of Dt), the linear combinations in a sufficiently large field Fq give an optimal result (in terms of gain). In the remainder of the present description, the term network coding scheme is used: • the relay nodes combining the input packets to generate a combined packet called the resulting packet; For these relay nodes, the input packets to be combined among the set of packets received; • Each input packet to combine is associated with a coefficient in Fq. These relay nodes and these packets (corresponding to links) participating in the network coding are considered useful, the others are considered redundant. The destination nodes then receive a plurality of packets (the resulting packets from the relay nodes) which are a linear combination of the source packets (packets sent by the source nodes). They calculate from these received packets a decoding matrix that will decode the source packets (that is, build source packets reconstructed from the received packets). In the context of the invention, the coding scheme used is an optimized coding scheme (described for example in patent application US2005 / 0010675) reducing the number of relay nodes and of useful packets participating in the network coding scheme in order to decrease the number of operations and therefore the CPU time. This scheme is determined at the initialization of the system taking into account the topology of the system. The resulting packets emitted by the relay nodes are therefore predetermined (more precisely their associated linear combination).

But the wireless network is sensitive to masking caused for example by a living being crossing the field of transmission. The loss of links caused by these masks can temporarily modify the topology of the initial network, topology on which the predetermined network coding scheme has been calculated. It is then no longer valid during this period, which can lead to the inability of the destination nodes to decode all the source packets because they are all linked together in the packets received. It is therefore necessary to increase the robustness of the network coding scheme against these link losses (measured in number of source packets decodable by the destination nodes).

In addition, in the context of the invention, the medium access protocol is based on a Time Division Multiple Access (TDMA) protocol where each node of the network has access. to the medium cyclically in a deterministic manner during a predetermined fixed period. A superframe is then defined as being a period during which each node of the network has access to the medium only once during a given time. It should be noted that the relay nodes have, for example, the authorization to combine only data transmitted by the source nodes during the current superframe in order to optimize the latency of the applications considered (video for example). 2.2 Prerequisites and Limits of the State of the Art 2.2.1 The body F3, q = 2s The set of operations carried out in the present invention is carried out in a finite body denoted Fq, consisting of q elements. In the context of the invention, the information sequences sent in the network are in a container called package, which has a fixed size. s consecutive bits of a packet constitute a symbol on the body Fq with q = 2s. For example, a 1400-byte packet contains 1400 symbols if the body size is 28 or contains 700 symbols if the body size is 216. The addition, multiplication, and division operations are then performed symbol by symbol:

> Addition + is done bit by bit with the classic XOR function

- For multiplication. a symbol of s bits, b0 ... bs_1, is transformed into a polynomial: bo + b1X + .. bs_1Xs_1. An irreducible polynomial on Fq is chosen. The multiplication between two symbols is then obtained by the classical multiplication between two polynomials modulo the irreducible polynomial.

- The division is calculated from the Euclidean algorithm.

Implementations are given for example in the document N.R.

Wagner. The laws of Cryptography with Java Code, available on the Internet at: http://www.cs.utsa.edu/ùwagner/laws/FFM.html.

Therefore, in the remainder of this description, when written

Y = with A1 ... A1, 1 input packets and al, .., a, coefficients in Fq, these i = 1

In fact, all of the symbols in the packet operate: yk = .a; `where yk and i = 1 ak are respectively the kth symbol of packets Y and A and the operations + and. take place in Fq.

In the context of real-time operation, in a TDMA environment (framework of the invention), it should be noted that these operations have a significant cost and that the construction of an entire packet, particularly at the Relay node that needs to react quickly, is a problem.

In a TDMA environment (framework of the invention), the construction of a resulting packet by a relay node can be carried out over water. Each useful received packet is multiplied with its associated coefficient and the result is added with the result of the other received packets. For example, if the predetermined resulting packet is alAl + a2A2, upon receiving Al, the relay node performs the multiplication alAl and stores the result Res. Then upon receipt of A2, the relay node performs the operation a2A2 then sum the result with Res and stores the new result in Res. 2.2.2 Network coding

2.2.2.1 Introduction

At a relay node, the linear combination associated with a resulting packet can be seen at two levels, a local level and a global level. To explain these two notions, suppose that a network coding scheme is predetermined for all the nodes and situate us in a useful relay node (also called combining). This relay node Ri must then combine a set of received packets Mi, M2, ..., M, among the packets received. The resulting packet is then equal to y, = l a ~ M; with 1 = 1 belonging to the finite field Fq. This linear combination y, = 1 M; is the local representation of the network coding, hereinafter called local combination. But the bundles to combine received as input can be themselves also packets

resulting from other relays. Let X ~, ... XM be the source packages emitted by the M

source nodes. It is then clear that each packet flowing in the network is a linear combination of X ~, ... XM packets. The previously quoted packet y can be m also thus represented in the following way: y, = g; X; . This representation is the

global representation of the network coding. It takes into account that each packet received M; is also a resulting package that combines source packages. It is called thereafter global combination. It is clear that the coefficients g3 are deduced recursively from the coefficients of o * Notation: the received packets intervening in a local combination are called subsequently the packets associated with the local combination. Source packets that have a nonzero coefficient in a global combination are subsequently called the packets associated with the global combination.

Note: Only one global combination can be associated with a given locale, but not vice versa. Indeed, to a global combination, we can associate several local combinations by playing on the choice of received packets M; to combine.

In the context of the invention, each relay node stores the global representation of each packet received as input in a matrix, called relay matrix R = (r ,,). al, (12-1, -41>, ..., a Each line represents a received packet, each column a source packet, and each element of the matrix r, i then represents the coefficient of the source packet j of the linear combination The destination node di which receives the packets Y1, Y2,..., Y1 'also stores the global representation of each input packet received in a matrix, called destination matrix D = (d, i). Each line represents a received packet and each column a source packet, and each element of the matrix d, i represents the coefficient of the source packet j of the global linear combination of the received packet Y. The destination node then has to solve the linear system constituted by by the set of linear global combinations m: Y ~ = X; j = 1 ... 1 ', or from a matrix point of view, Y = DX with D the destination matrix, Y the column vector of the received packets and X the column vector of the source packets The resolution of this linear system e is explained in the following section. It should be noted that if the rank of D (in the sense of the linear algebra) is equal to the number of source nodes M then the M source packages are decodable. Otherwise, it is necessary to study more precisely the destination matrix to determine the number of decodable source packets. 2.2.2.2 Construction of a network coding In a mesh network consisting of M sources and N destination nodes, the preliminary step before building a network coding scheme is to ensure that there is a network coding scheme seen the topology of the network. This phase is based on graph theory concepts and in particular on a use of the Ford-Fulkerson algorithm (see "Maximum Flow through a Network" Canadian Journal of Mathematics, 8, pp 399-404, 1956). The network is modeled by a graph G = (V, E), V being a finite set of K nodes (called vertices in English), V = {xi,. . . , xK}, and E c V X V a finite set of edges that connect the nodes. In the context of the invention, the set E is an ordered set of pairs (xi, xi), with x; and xi belonging to v, these pairs being called connected edges, arcs or links (called edges in English). A node of V models a communicating entity in the network (computers, loudspeakers, amplifier) while an arc (xi, xi) indicates for example a sufficiently good radio communication (that is to say above a certain threshold of radio power received) between the two communicating entities x; and xi. Moreover, a path between a node x1 and a node xp is called an ordered set of nodes {x1, x2, .., xp} such that (xi, xi + 1) E E for i = 1,. . . , (pùl). A path can also be written {(x1, x2), .., (x1, x1 + 1), ..., (xp_1, xp)} with (xk, xk + 1) E for k = 1,. .., (pù1). We call k disjoint paths, k sets that do not have two consecutive nodes in common, either from a graphical point of view, two arcs in common. Let T be a set of k disjointed paths. We then define: 1. Let (x, y) EE (a link of the graph), (x, y) AND if and only if there exists a path of T which contains (x, y) 2. Let x EV ( a vertex of the graph), x AND if and only if there exists a path of T that contains x. We call two disjoint paths between a set S and a node d, two ordered sets of nodes {x1, x2, .., xp, d} and {y1, y2, .., yq, d} such that:> (xi , xi + 1) EE for i = 1, ..., (pù1) and (xp, d) EE - (y, y + 1) EE for j = 1, ..., (qù1) and (yq, d) EE - i ES, Y1 ES and x1 ≠ Y1 - Vi = 1 .. (p -1), Vj = 1 .. (q -1), (xi, x1 + 1) ~ (y; 'y; +1) and (xp, d) ~ (Yq, d) The definition is generalized very easily for a set of k disjoint paths. From these notions of graph theory, the state of the art gives the following condition: Let S be a set of M source nodes, if there exist M disjoint paths between S and each destination node of D1, then the M source nodes are able to multicast to D1 if the relay nodes are allowed to linearly combine their incoming packets on a sufficiently large finite field. This result is a direct consequence of the aforementioned article by R. Ahlswede and co. The invention is placed in the context where this condition is verified at the start of the system. On the other hand, during the life of the system, this condition may no longer be respected because of temporary loss of links. In this case, no network coding scheme exists for decoding the M source packets. The destination nodes can no longer decode M source packages. In the state of the art, there are mainly two approaches for the construction of a network coding scheme according to the knowledge or not of the initial topology of the network: for a known topology, a first deterministic diagram of construction of coefficients based on a matrix approach is given in the following article: R. Koetter, M. Medard, "An Algebraic Approach to Network Coding" ACM Transactions on Networking, Vol 11, Nos., October 2003. "The network coding scheme obtained according to this first approach is called a deterministic coding scheme: - For an unknown topology, an on-the-fly construction of the randomly drawn coefficients is given in the following article: "Randomized distributed network coding" - Michelle Effros, Tracey Ho, David Karger, Ralf Koetter, Muriel Medard 20050152391. The network coding scheme obtained according to this second approach is called a random coding scheme. approach, the coefficients are calculated once and for all at the start of the system and thus during the lifetime of the system. Destination nodes and relay nodes have inexpensive operations because they know exactly what they will receive and transmit. In the second approach, the relay nodes randomly pull the coefficients of the resulting packet to be generated, which requires additional processing time. In addition, they are obliged to send the randomly drawn coefficients in the resulting packet so that the other nodes, and more especially the destination nodes, know the linear combinations to decode. But this signaling is even larger than the body is large (each coefficient will be encoded on a larger number of bits), and it is as much lost bandwidth. But in this second approach, the larger the body, the greater the chances of successful decoding of source packages. Hence the contradiction. In the first approach, the decoding is sure to succeed because the construction made at initialization ensures that this is the case. The first approach is therefore more efficient than the second in terms of gain in bandwidth and computing time. On the other hand, the second approach is more efficient than the first on the following points: • it does not require knowledge of the topology of the network. In the context of the present invention, it is assumed that there is a means of recovering the topology of the network, so this disadvantage of the first approach is not taken into account; • it is robust to link losses, unlike the first approach. Indeed, since it generates a resulting packet with a different linear combination with each send, the loss of link is transparent for it (although not guaranteeing the decoding). It indicates a zero coefficient for the packet that was to arrive by this link.

The first approach is, however, strongly affected by link losses because each loss of link modifies the linear combination of the relay node (combination initially fixed) and only the relay node observing this loss is aware of it. The other nodes and especially the destination nodes are not aware of this modification of the topology and believe that everything is happening as usual. The decoding can then be catastrophic and influences all the source packets to be decoded since they are all linked by the linear combinations (unlike a routing where only a source packet would be reached). Considering in particular that the advantages of the first approach are essential in high speed applications as targeted by the invention, it is assumed in the following description that it is the first approach that is used to build a network coding scheme based knowledge of the initial topology of the network. In practice, the method of constructing the commonly used predetermined network coding scheme (according to the first approach) (hereinafter referred to as the optimized version) is that which limits the number of nodes and links participating in the network coding using only the paths disjoint from the existence condition of network encoding: only nodes and links of disjoint paths are useful for building the network encoding scheme. This optimized version is described in particular in the aforementioned US2005 / 0010675 patent application. From this observation, we call a node (respectively link) useful, a node (respectively link) which belongs to the set of disjoint paths and, we call node (respectively link) redundant, a node (respectively link) which n ' does not belong to the set of disjoint paths. This optimized version thus makes it possible to limit the number of operations. But in a wireless LAN, it is likely that these redundant links are numerous, because every time a node sends a packet, all other nodes in the network are likely to receive this packet. This optimized version of the network coding construction is for example used in the context of the present invention. It severely limits operations because only the nodes and links considered useful are used, which reduces the number of operations in the body at the relay node and the destination node. For example, a relay node no longer needs to combine the plurality of packets it receives but only a subset of packets. Same for the destination node that only needs a subset of the packets received to decode the source packets. With this optimized version, at first a network coding scheme is constructed which takes into account only the relay nodes and useful links, according to the following definitions: the relay nodes combining the input packets are the useful relay nodes; for these useful relay nodes, the input packets to be combined among all the packets received are the useful packets; each input packet to combine is associated with a coefficient in Fq. The resulting packets are thus predetermined. In the same way, the destination node then constructs a sub-matrix of the destination matrix D, called the coding matrix (or destination matrix) and denoted C, which only takes into account the useful packets (lines are therefore deleted from D). From C, a square submatrix of dimension (M, M) (the optimized schema assures this property), the destination node calculates the inverse of this one (which exists by construction of the schema), called the decoding matrix and denoted Cl, and thus decodes the source packets: X = C-1Y, with X the column vector of the source packets and Y the column vector of the packets received. In the context of a TDMA access to the medium, the decoding can be carried out over water (same concept as that explained in paragraph 2.2.1 above, for the relay nodes). For each useful received packet, the multiplication between the received packet and its associated coefficients is performed in the matrix C-1 and the result is added together with the result obtained for the other received packets. For example, suppose that two source packets X and Y have been sent and a destination node has the following matrix C-1: C11 C12 ~ C21 C22 On receipt of the first useful packet M1, the destination node already performs the following operations (symbols by symbols) and store them in Xtemp and Ytemp: Xtemp = c11 M1 and Ytemp = c21 Ml. Then, upon receipt of the second useful packet M2, the destination node performs the following operations: Xtemp = Xtemp + c12 M2 and Ytemp = Ytemp + c22 M2 The second packet being the last, Xtemp and Ytemp are equal to x and Y. This decoding is called decoding over water in the following description. 2.2.3 Resolution of a linear system Let a linear system of n equations with p unknowns in Fq: ialipi + + a1pNp ùblan1N1 + + anplp = bn With [(31, ... (3p] the p unknowns of the system , a1i, i = 1..n, j = 1..p the coefficients of the system and [b1, ... bn] the constants of the system To solve this system, one uses for example the method of the pivot of Gauss, also called Gauss-Jordan elimination, which is known to those skilled in the art Other matrix resolutions are possible to solve the system of equation: LU decomposition, QR decomposition, Cholesky method, they are directly applicable to the present invention.

To apply the Gaussian method, the following matrix of dimension (n, p + 1) is associated with the system: a, p .b1 ab np n On this matrix, the Gauss-Jordan algorithm performs elementary operations 5 per line to obtain a matrix of the form: 01 0 00000 1 to 1 (r + 1) a1p b1 ar (r + 1) arp br 0 0 br + 1

0 0 bn The system is said to be compatible if it admits at least one solution. Compatibility depends on the value of r with respect to the values of n and p: 1. In the case where r is strictly smaller than n and p, two cases occur: 10 - The coefficients br + 1, ... , bn are void. In this case, the system is compatible and there exists an infinity of solution for the [(31, ... 13p] .The Ut ... 13r] are the main unknowns, the others [(3r + 1, ... (3p) are the secondary unknowns To solve the system, we fix then the [(3r + 1, ... (3p) which become parameters and we determine the main unknowns 15 by solving the linear system starting with 13r then Rr-i '• • • RI> There are coefficients br + 1, ..., bn not null The system is incompatible 2. In the case where r is equal to n and strictly inferior to p, there exists a infinity of solution for [jt ... 13p] The [(3I, ... Rn] are the main unknowns, the others [(3n + l, ... (3p) are the secondary unknowns. the case where r is equal to p and strictly less than n, two cases occur:> The coefficients br + 1, ..., bn are null The system admits a solution 131 = 6,, .., 13p = bp Otherwise the system is incompatible 4. If r equals p and at n, the system admits a unique solution:, .., (3p = bp 2.2.4 Limits of the state of the art In the state of the art, the management of packet losses in a network coding scheme is mainly managed by the random coding scheme (second approach described above), because the latter (unlike the deterministic coding scheme according to the first approach) is robust to link losses (as detailed previously). Indeed, with the random coding scheme, the relay nodes systematically perform expensive operations to combine packets with or without loss of packets.

But, considering that the advantages of the first approach described above (in terms of bandwidth gain and calculation time) are essential in high speed applications (as detailed before), the present invention is placed in the context where it is this first approach that is used (network coding scheme based on knowledge of the initial topology of the network).

However, in the case where the first approach is used, packet loss management consists in looking for robust network coding schemes as soon as they are constructed. This is to ensure that the destination matrices are still able to decode all the source packets sent by the source nodes for a predefined set of broken links. But the relay nodes are obliged to use all the packets they receive, which imposes at the relay nodes a significant and especially systematic calculation time. To solve the problem of packet loss management, in the case where the aforementioned first approach (deterministic coding scheme) is used, it has never been proposed for relay nodes and destination nodes to locally and temporarily modify the predetermined network coding scheme, taking into account redundant packets. A fortiori, it has never been proposed a technique to optimize the latency introduced, in a relay node or a destination node, by the processing time required for this node to modify (locally and temporarily) the predetermined coding scheme ( processing time for reconstructing a reconstituted resulting packet different from the predetermined resulting packet, in the case of a relay node, or processing time for modifying the decoding matrix, in the case of a destination node). However, such an optimization of the latency introduced by this processing time is important in the aforementioned context where the medium access protocol is based on a TDMA protocol. Indeed, this latency must be minimized, especially if the system must operate in real time: • Relay node side, in the case of a real-time system, the question arises as to when the reconstitution of a resulting packet reconstituted must be triggered. If this rebuilding starts as soon as the broken link is detected, it may be that very few redundant packets are already received, which decreases the chances of successful seamless replenishment. If the relay node waits for the reception of all the redundant packets, the reconstitution is done too late to carry out all the operations of a transparent reconstitution and to then build the resulting packet (especially if this transparent reconstruction fails and a non-transparent reconstitution, with a notification, is necessary). There is therefore a problem of optimization of the processing time necessary for the modification of the coding scheme, which this invention proposes to solve; • destination node side, the detection of a useful packet not received or a modified notified useful packet, the destination node is then obliged to recalculate its decoding matrix is no longer valid. A problem of the same nature as for the relay node arises: either the recalculation of the decoding matrix is carried out as soon as the detection is made, at the risk of failing (that is, not to find a matrix decoding all the source packets), or this recalculation takes place on receipt of all the packets received (end of the superframe) which greatly increases the latency introduced by the decoding. OBJECTIVES OF THE INVENTION The invention, in at least one embodiment, has the particular objective of overcoming these various disadvantages of the state of the art. More specifically, in at least one embodiment of the invention, one objective is to provide a network coding technique adapted to the transmission of data packets in a meshed communication network, this technique making it possible to optimize loss management. of packets (ie loss of links) in the case where a deterministic network coding scheme (obtained according to the above-mentioned first approach) is used, while minimizing the processing time (allowing for example a processing in real-time) related to packet loss management in a TDMA environment. Another objective of at least one embodiment of the invention is to provide such a technique which, relying on a new and inventive solution consisting of a given node (relay or destination) to locally and temporarily modify the schema of predetermined network coding, aims to optimize the latency introduced by the processing time required for this node to perform this modification. At least one embodiment of the invention also aims to provide such a technique that is transparent to the source nodes. Another objective of at least one embodiment of the invention is to provide such a technique which is simple to implement and inexpensive. SUMMARY OF THE INVENTION In a particular embodiment of the invention, there is provided a method of network coding in a mesh network comprising at least one relay node which, according to a predetermined network coding scheme, expects receiving as input a plurality of data packets and outputting a predetermined resultant packet obtained in a predetermined linear combination of a portion of said plurality of expected data packets, the data packets belonging to said party being said packets and the data packets not belonging to said portion being said to be redundant packet, each of the expected data packets having an expected source packet composition (s) in accordance with said predetermined network coding scheme. The method is implemented by at least one relay node and comprises the steps of: I) detecting an altered useful packet, defined as a useful packet that is not correctly received or is correctly received but does not have a composition in source package (s) expected; II) if an altered useful packet is detected, determining, before the end of receiving said plurality of data packets, determining a new linear combination of expected input packets for constructing a reconstructed result packet using, in accordance with a scheme modified network coding, all or part of the redundant packets, the packets associated with said new linear combination being said momentarily useful packets; III) With the new linear combination of expected input packets, construct, before the end of the reception of said plurality of expected data packets, at least a portion of said reconstituted resulting packet, using the momentarily useful packets already correctly received. . Thus, at a relay node, this particular embodiment of the invention is based on a completely new and inventive approach allowing, as soon as an altered useful packet is detected, to launch at least one recovery algorithm so that determining a resulting reconstructed packet (resulting from a local and temporary modification of the predetermined network coding scheme) involving new useful packets (already received or to be received), termed as being momentarily useful because they are useful only during a superframe common. Thus, the construction of this resulting reconstructed packet can begin with the momentarily useful packets already received.

This advance subsequently allows the relay node, from its access to the medium, to have the resulting package reconstituted, provided that the construction of the latter has been successful (which depends on the good reception of all momentarily useful packets). Advantageously, said step II) comprises a step IL1) consisting in determining, if it exists, a new linear combination of expected input packets making it possible to construct a reconstituted resulting packet identical to the predetermined resulting packet.

In other words, if it is possible, the value of the coefficients associated with the momentarily useful packets is chosen in such a way that the reconstituted resulting packet is identical to the predetermined resulting packet. In this way, the operation performed in the given relay node (construction of the resulting reconstructed packet instead of the predetermined resulting packet) is transparent to all other downstream relay nodes as well as to the destination nodes. In addition, as soon as a corrupted useful packet is detected, the relay node can know whether the predetermined resulting packet can be reconstructed with the already received packets and especially the packets to be received. In the positive case, the construction of the resulting reconstituted packet starts with the momentarily useful packets already received. In the negative case, it is not very wise to wait for the packets to be received and, as detailed below, it is better to launch a new less restrictive recovery algorithm (which does not try to reconstruct exactly the resulting packet). predetermined). Advantageously, said step IL1) comprises a step of testing whether said corrupted user packet can be replaced by a redundant packet received or to be received by said given relay node. Thus, the transparent reconstitution operation of the resulting reconstituted packet is fast and inexpensive. According to an advantageous characteristic, said step IL1) comprises an execution of a complete recovery mechanism, comprising the steps of: determining a predetermined linear combination of source packets, associated with said predetermined linear combination of packets expected at the input, and allowing to obtain said predetermined resulting packet; constructing a linear system A (3 = g, where 13 is a column vector of the coefficients of said new linear combination of expected input packets to be determined, where g is a column vector of the coefficients of said predetermined linear combination of source packets, and where A is a matrix of dimension (M, S), with M the number of source packets and S the number of packets expected at input by said given relay node, the matrix A being defined as follows: * each line of the matrix A is associated with a source packet, each column of matrix A is associated with an expected packet as input, each element a; i of matrix A represents: - the coefficient of the source packet i in a composition in actual source packet (s) of the expected packet j, if the expected packet has already been received, - or the coefficient of the source packet i in a source packet composition (s) expected from package expected j, s the expected packet has not yet been received; - resolving said linear system by a predetermined resolution method, storing, at each iteration k of said predetermined resolution method, operations and a temporary matrix A (k); if the linear system admits a solution, determining said new linear combination of expected packets as input, according to the column vector 13 of said solution. Thus, the transparent reconstitution operation of the resulting reconstituted packet is optimized and allows to achieve a systematic way if the linear system considered admits a solution. Advantageously, at each reception of one of the momentarily useful packets, the method comprises the steps of: detecting a momentarily useful altered packet, defined as a momentarily useful packet that is not correctly received or is correctly received but does not does not have a composition in source packet (s) expected; - If a corrupted momentarily useful packet is detected, perform a partial recovery mechanism, comprising the steps of: * determining the expected packet (s) expected, including said momentarily useful packet corrupted received since a last run of the partial recovery mechanism or since an execution of the full recovery mechanism, an altered expected packet being defined as an expected packet that is not correctly received or is correctly received but does not have a composition in source package (s) expected; * in the temporary matrix A (11-1) stored at a (tl-1) th iteration of said predetermined resolution method, modify the altered column (s) corresponding to the expected packet (s) altered, where t1 is the rank of the first of the expected packet (s) altered in a predetermined sequence defining the order in which said plurality of expected data packets are expected, as well as that the order in which the columns of said matrix A are classified, the altered column (s) being modified by the operations stored during the (tl-1) first iterations of said predetermined resolution method; resuming resolution of said linear system at the iteration of said predetermined resolution method, storing, at each iteration k of said predetermined resolution method, operations and a temporary matrix A); if the linear system admits a solution, determining said second linear combination of expected packets as input, according to the column vector 13 of said solution. Thus, if a momentarily useful packet is received in an altered form (reception not correct or with a composition modified in source packets), it is not necessary to implement again the whole of the complete recovery mechanism. A partial recovery mechanism, corresponding to only a part of it, can be implemented. This requires fewer operations since some of the operations performed during the full recovery mechanism remain valid and therefore these operations are not performed again. Thus, even if the packets to be received are not the ones expected, the complete recovery mechanism has not been in vain, its previous execution made it possible to lighten the operations of the partial recovery mechanism and to optimize the end date of recovery. Advantageously, in case of failure of said step IL1), said step II) comprises a step IL2) of determining a new linear combination of expected packets as input to construct a nearest reconstituted resulting packet, in at least one determined criterion, of the predetermined resulting packet.

In this way, as soon as the relay node knows that, even with the packets to be received, the predetermined resulting packet can not be reconstructed identically, the relay node launches an algorithm to determine the momentarily useful packets (received or to be received ) that will send the best resulting package reconstituted, that is to say the one that will impact the network as little as possible. Executing this algorithm before all packets are received is very advantageous because it is a comprehensive algorithm that tests all of the resulting reconstructed possible packets. This early execution thus makes it possible to test more possibilities and therefore to increase the robustness of the network (increase of the number of source packets decodable by all the destination nodes). Advantageously, at each reception of one of the momentarily useful packets, the method comprises the steps of: detecting a momentarily useful altered packet, defined as a momentarily useful packet that is not correctly received or is correctly received but does not does not have a composition in source packet (s) expected; if a momentarily useful, corrupted packet is detected, repeat steps IL2) and III). Thus, if a momentarily useful packet is received in an altered form (reception not correct or with a composition modified source packets), the relay node can immediately restart the aforementioned algorithm to determine the momentarily useful packets (received or to receive) that will send the best resulting package restored. Advantageously, said step IL2) comprises the steps of: a) determining a new linear combination of expected input packets making it possible to construct a reconstituted resulting packet containing source packets not contained in the predetermined resulting packet; b) obtaining relative information, for at least one other node participating in the predetermined network coding scheme, to a modified network coding scheme that would result from sending the reconstituted resulting packet mentioned in step a); c) based on the information obtained in step b), selecting the new linear combination determined in step a) or repeating step a) to determine another new linear combination. In this way, the operation performed in the given relay node (sending the reconstructed resultant packet instead of the predetermined resulting packet) is not transparent (for all other downstream relay nodes, as well as for the destination nodes), but it has no impact on the capacity of the network (ie the number of source packets decodable by all the destination nodes). In other words, if a transparent reconstruction is not feasible, the relay node tries to reconstruct a resulting packet that has no influence on the network, that is to say that does not decrease the number source packages that can decode the destination nodes. This reconstruction is also based on the use of redundant packets. On the other hand, in this case, the relay node must notify the other nodes that the resulting packet that it sends is not based on the predetermined linear combination.

Advantageously, step a) comprises the steps of: i) determining a predetermined linear combination of source packets, to obtain said reconstituted resulting packet containing source packets not contained in the predetermined resulting packet; ii) constructing a linear system A (3 = g, where 13 is a column vector of the coefficients of said new linear combination of expected input packets to be determined, where g is a column vector of the coefficients of said predetermined linear combination of source packets, and where A is a matrix of dimension (M, S), with M the number of source packets and S the number of packets expected to be input by said given relay node, the matrix A being defined as follows: * each line of the matrix A is associated with a source packet, * each column of the matrix A is associated with an expected packet as input, * each element a; i of the matrix A represents: - either the coefficient of the source packet i in a composition in actual packet (s) of the expected packet j, if the expected packet ja has already been received, - or the coefficient of the source packet i in a source packet composition (s) expected from the expected packet j, if the attentive package has not yet been received; iii) resolving said linear system by a predetermined resolution method; iv) if the linear system admits a solution, determining said new linear combination of expected packets as input according to the column vector 13 of said solution, otherwise repeating step i) with another predetermined linear combination of source packets. Thus, the operation (non-transparent but without impact) of reconstitution of the resulting reconstituted packet allows to achieve a systematic way if one of the linear systems, considered during successive iterations, admits a solution. Advantageously, in step b), said information relating to the modified network coding scheme, which would result from sending the reconstituted resulting packet mentioned in step a), is the sum of the number of decodable source packets by the set destination nodes of the network if the resulting reconstructed packet mentioned in step a) is assumed to be sent. In step c), the new linear combination determined in step a) is selected if said information relating to the modified network coding scheme is equal to the number of source nodes in the network multiplied by the number of destination nodes in the network. .

Thus, the information test (relative to the modified network coding scheme) makes it possible to ensure that the (non-transparent) operation has no impact on the capacity of the network (that is to say the number of source packets). decodable by the set of destination nodes). Advantageously, in case of failure of steps a), b) and c), said step IL2) further comprises the steps of: - determining a first new linear combination of expected packets as input, making it possible to construct a first resulting packet reconstituted different from the predetermined resulting packet but containing only source packets included in the predetermined resulting packet; obtaining a first relative information, for at least one other node participating in the predetermined network coding scheme, to a modified network coding scheme that would result from sending the first reconstructed resultant packet, the first new linear combination being associated with said first information on the modified network coding scheme; among the new linear combination (s) not selected in step c), selecting a second new linear combination of packets expected at the input, according to said information, obtained at step b) for each new linear combination not selected in step c), on the modified network coding scheme, the second new linear combination being associated with a second piece of information relating to the modified network coding scheme; selecting between the first and second new linear combinations, according to the first and second information relating to the modified network coding scheme. In this way, the operation performed in the given relay node (sending the resulting reconstructed packet instead of the predetermined resulting packet) is not transparent and has an impact on the network capacity, but this impact is minimized. In other words, if no rebuilding, which does not impact the network, is possible, the relay node rebuilds the packet that has the least impact on the network, that is, say the one that degrades the network the least (always in number of decodable source packets for all the destination nodes). In this case, the relay node must also notify the other nodes that the resulting packet that it sends is not based on the predetermined linear combination. Advantageously, said step IL2) comprises a step of determining a new linear combination of expected input packets for constructing a reconstituted resulting packet different from the predetermined resultant packet but containing only source packets included in the predetermined resulting packet. In this variant, if a transparent operation is not possible, the given relay node directly performs an operation that has an impact on the capacity of the network, but this impact is minimized. In this case, the relay node must also notify the other nodes that the resulting packet that it sends is not based on the predetermined linear combination. In another embodiment, the invention relates to a network coding method in a mesh network comprising at least one destination node which, according to a predetermined network coding scheme, expects to receive as input a plurality of data packets and should output at least one predetermined source packet obtained in a predetermined linear combination of a portion of said plurality of expected data packets, the data packets belonging to said portion being said useful packets and the data packets n ' not belonging to said part being said redundant packet, each of the data packets expected input having a composition in source packet (s) expected, according to said predetermined network coding scheme. The method is implemented by at least one destination node and comprises the steps of: I) detecting an altered useful packet, defined as a useful packet that is not correctly received or is correctly received but does not have a composition in source package (s) expected; II) if an altered useful packet is detected, determining, before the end of receiving said plurality of data packets, at least one new linear combination of expected input packets for constructing at least one reconstituted source packet using according to a modified network coding scheme, all or part of the redundant packets, the packets associated with said at least one new linear combination being said momentarily useful packets; III) with said at least one new linear combination of expected input packets, constructing, before the end of receiving said plurality of expected data packets at the input, at least a portion of said at least one reconstituted source packet, using the momentarily useful packets already correctly received. Thus, at a destination node, this particular embodiment of the invention is based on a completely new and inventive approach allowing, as soon as an altered useful packet is detected, to launch at least one (modification) algorithm. of the decoding matrix) for decoding at least one source packet, i.e., determining at least one reconstituted source packet (resulting from a local and temporary modification of the predetermined network coding scheme) involving new packets useful (already received or to be received), qualified as momentarily useful because they are useful only during a current superframe. Thus, the decoding of the source packets can begin with the momentarily useful packets already received. This advance allows the relay node to finish the decoding earlier and the source packets are sent earlier to the application, provided that the decoding of the latter has been successful (which depends on the good reception of all packages momentarily useful). Advantageously, said step II) comprises a step IL1) of determining, if it exists, a new decoding matrix identical to a predetermined decoding matrix, making it possible to construct a set of reconstituted source packets identical to a set of all the source packets. predetermined, each line of said new decoding matrix defining a new linear combination of expected input packets for constructing a reconstituted source packet identical to one of the predetermined source packets. In other words, if it is possible, we build a new decoding matrix to decode all the source packages. As soon as a corrupted useful packet is detected, the destination node can know whether this is possible or not, with the packets already received and the packets to be received. In the positive case, the construction of the new decoding matrix starts with the momentarily useful packets already received. In the negative case, it is not very wise to wait for the packets to be received and, as detailed below, it is better to launch a new algorithm of less binding determination (which tries to obtain a new decoding matrix not not allowing to decode all source packages). Advantageously, said step IL1) comprises an execution of a complete recovery mechanism, comprising the steps of: constructing a matrix D 'of dimension (S, M), with S the number of packets expected as input by said node given destination and M the number of source packets, the matrix D 'being defined as follows: * each row of the matrix D' is associated with an expected packet as input, * each column of the matrix D 'is associated with one source packet, * each element d, i of the matrix D 'represents: - either the coefficient of the source packet j in a composition in source packet (s) of the expected packet i, if the expected packet has already been received or - the coefficient of the source packet j in a source packet composition (s) expected from the expected packet i, if the expected packet i has not yet been received, - constructing a resultant matrix T from of the matrix D ', by a method of triangulation predetermined pattern taking into account the lines one after the other, storing, at each iteration k of said predetermined triangulation method, operations and a temporary matrix A (k); if the resulting matrix T has M non-zero lines, constructing said new decoding matrix from the resulting matrix T. Thus, with this complete recovery mechanism, the determination of the new decoding matrix is optimized and makes it possible to to succeed systematically. Advantageously, at each reception of one of said packets momentarily useful, the method comprises the steps of: detecting a momentarily useful altered packet, defined as a momentarily useful packet which is not correctly received or is correctly received but does not possess not a composition in source packet (s) expected; - If a corrupted momentarily useful packet is detected, perform a partial recovery mechanism, comprising the steps of: * determining the expected packet (s) expected, including said momentarily useful packet corrupted received since a last run of the partial recovery mechanism or since an execution of the full recovery mechanism, an altered expected packet being defined as an expected packet that is not correctly received or is correctly received but does not have a composition in source package (s) expected; In the temporary matrix A (tl - "stored at one (tl-1) th iteration of said predetermined resolution method, modify the altered column (s) corresponding to the (x) package (s) expected (s) altered, where t1 is the rank of the first one of the expected packet (s) altered in a predetermined sequence defining the order in which said plurality of expected data packets are inputted; expected, as well as the order in which the rows of said matrix D 'are classified, the altered line (s) being modified by the stored operations during (tl-1) first iterations of said triangulation method predetermined: * resume the construction of the resulting matrix T at the iteration of said predetermined triangulation method, by storing, at each iteration k of said predetermined triangulation method, operations and a temporary matrix Au; * if the resulting matrix T has M nonzero lines, constructing said new decoding matrix from the resulting matrix T. Thus, if a momentarily useful packet is received in an altered form (reception not correct or with a composition modified in source packages) it is not necessary to re-implement the entire full recovery mechanism. A partial recovery mechanism, corresponding to only a part of it, can be implemented. This requires fewer operations since some of the operations performed during the full recovery mechanism remain valid and therefore these operations are not performed again. Thus, even if the packets to be received are not the ones expected, the complete recovery mechanism has not been in vain, its previous execution made it possible to lighten the operations of the partial recovery mechanism and to optimize the end date of recovery. Advantageously, in case of failure of said step IL1), said step II) comprises a step IL2) of determining a new decoding matrix different from a predetermined decoding matrix, but making it possible to construct a maximum number of reconstructed source packets identical to predetermined source packets, each line of said new decoding matrix defining a new linear combination of expected input packets for constructing a reconstituted source packet identical to one of the predetermined source packets. In this way, as soon as the destination node knows that, even with the packets to be received, it will not be able to decode all the source packets, the destination node launches an algorithm to determine a new decoding matrix making it possible to decode the largest number of source packages. Running this algorithm before all packets are received is very advantageous because it is a comprehensive algorithm that tests a set of new decoding matrices. This early execution therefore makes it possible to greatly reduce the latency of the decoder.

Advantageously, at each reception of one of said momentarily useful packets, said method comprises the steps of: detecting a momentarily useful corrupted packet, defined as a momentarily useful packet which is not correctly received or is correctly received but does not possess not a composition in source packet (s) expected; if a momentarily useful, corrupted packet is detected, repeat steps IL2) and III). Thus, if a momentarily useful packet is received in an altered form (reception not correct or with a composition modified in source packets), the destination node can immediately restart the aforementioned algorithm for determining a new decoding matrix for decoding the most large number of source packages. In another embodiment, the invention relates to a computer program product downloadable from a communication network and / or recorded on a computer readable medium and / or executable by a processor. This computer program product includes program code instructions for carrying out the aforesaid method (in any one of its various embodiments), when said program is run on a computer. In another embodiment, the invention relates to a computer readable storage means, possibly totally or partially removable, storing a computer program comprising a set of instructions executable by a computer to implement the aforementioned method (in any of its different embodiments). In another embodiment, the invention relates to a relay node included in a mesh network and participating in a network coding method in said mesh network, said relay node, according to a predetermined network coding scheme, expecting to receive in inputting a plurality of data packets and outputting a predetermined resultant packet obtained according to a predetermined linear combination of a portion of said plurality of expected data packets, the data packets belonging to said portion being said to be useful packets and the data packets not belonging to said part being said to be redundant packet, each of the expected data packets having an expected source packet composition (s), in accordance with said predetermined network coding scheme. Said relay node comprises: - detection means, for detecting an altered useful packet, defined as a useful packet that is not correctly received or is correctly received but does not have a source packet composition (s) expected; determination means, activated if an altered useful packet is detected, making it possible to determine, before the end of the reception of said plurality of data packets, a new linear combination of expected input packets making it possible to construct a resulting packet reconstituted using, in accordance with a modified network coding scheme, all or part of the redundant packets, the packets associated with said new linear combination being said momentarily useful packets; means of construction, making it possible to construct, with the new linear combination of expected packets as input, and before the end of the reception of said plurality of expected data packets, at least a portion of said reconstituted resulting packet, using momentarily useful packets already correctly received. In another embodiment, the invention relates to a destination node included in a mesh network and participating in a network coding method in said mesh network, said destination node, according to a predetermined network coding scheme, expecting to receiving as input a plurality of data packets and to output at least one predetermined source packet obtained in a predetermined linear combination of a portion of said plurality of input data packets, the data packets belonging to said portion being said useful packets and the data packets not belonging to said part being said to be redundant packet, each of the expected data packets having an expected source packet composition (s), according to said predetermined network coding scheme. Said destination node comprises: - detection means, for detecting an altered useful packet, defined as a useful packet that is not correctly received or is correctly received but does not have a source packet composition (s) expected; determination means, activated if an altered useful packet is detected, determining, to determine, before the end of the reception of said plurality of data packets, at least one new linear combination of packets expected at the input allowing constructing at least one reconstituted source packet using, in accordance with a modified network coding scheme, all or part of the redundant packets, the packets associated with said at least one new linear combination being said momentarily useful packets; means for constructing, with said at least one new linear combination of packets expected as input, and before the end of the reception of said plurality of data packets expected at the input, at least a part of said at least one reconstituted source package, using momentarily useful packets already correctly received. More generally, the relay node and the destination node according to the invention comprise means for implementing the methods as described previously (in any one of their various embodiments). 5. LIST OF FIGURES Other features and advantages of the invention will become apparent on reading the following description, given by way of indicative and nonlimiting example, and the appended drawings, in which: FIG. 1 represents an example wireless mesh network in which the network coding technique of the invention can be implemented; FIG. 2 represents the architecture of a device (relay node or destination node) according to a particular embodiment of the invention; FIG. 3 describes the structure of a packet notifying a modification of the predetermined coding scheme, according to a particular embodiment of the invention; FIGS. 4a, 4b and 4c describe algorithms, implemented in a central node, a relay node and a destination node respectively, of construction of a predetermined network coding scheme, at the start of the system; FIG. 5 presents a main algorithm for processing a received packet, implemented by a relay node in a particular embodiment of a network coding method according to the invention; FIG. 6 describes an algorithm for reconstituting a local combination (of a relay node affected by a loss of link), corresponding to step 565 of FIG. 5; FIG. 7 describes an algorithm for determining a new local combination from a global combination, corresponding to step 625 of FIG. 6; FIG. 8 describes an algorithm for selecting the overall linear combination that has the least impact on the network, corresponding to step 555 of FIG. 5 and step 1145 of FIG. 11; FIG. 9 describes an algorithm for reconstituting a local combination associated with a global combination close to the predetermined overall combination that has the least impact on the network, corresponding to step 815 of FIG. 8; FIG. 10 depicts an algorithm for solving a linear system based on the Gauss-Jordan algorithm for determining a new local combination from a global combination corresponding to step 715 of FIG. 7 and FIG. step 915 of Figure 9; FIG. 11 describes an algorithm for resuming the reconstitution of a local combination (of a relay node affected by a loss of link), corresponding to step 570 of FIG. 5; FIG. 12 describes an algorithm for resuming the resolution of the linear system linked to the recovery algorithm of the reconstitution of a local combination, corresponding to step 1115 of FIG. 11; FIG. 13 describes an algorithm for assigning a confidence index to a local linear combination, corresponding to step 930 of FIG. 9; FIG. 14 describes an algorithm for selecting the overall linear combination that has the least impact on the network, corresponding to step 965 of FIG. 9; FIG. 15 describes an algorithm for reconstituting a local combination associated with a global combination closest to another global combination, corresponding to step 820 of FIG. 8; FIG. 16 presents a main algorithm for processing a received packet, implemented by a destination node in a particular embodiment of a network coding method according to the invention; FIG. 17 describes an algorithm for modifying the decoding matrix corresponding to step 1655 of FIG. 16; FIG. 18 describes an algorithm for resuming the modification of the decoding matrix, corresponding to step 1660 of FIG. 16; FIG. 19 describes an algorithm for determining the number of decodable source packets, and consequently for determining the associated decoding matrix, corresponding to step 1715 of FIG. 17 and step 1645 of FIG. 16. DETAILED DESCRIPTION In all the figures of this document, the elements and identical steps are designated by the same numerical reference. FIG. 1 represents an example of a wireless mesh network in which the network coding technique of the invention can be implemented. The medium access protocol is of the TDMA (Time Division Multiple Access) type, where for a fixed period, called superframe, each node of the network has 10 15 20 a single access to the medium during a fixed speaking time called time slot (or slot in English). This network is composed of three source nodes, named respectively NS 1, NS 2 and NS 3, and six nodes which are both relay nodes and destination nodes, named NR / D 1,..., NR / D 6. Each communication link is represented by an arrow indicating the direction of the transmission. The four full-line communications links (as for example between the nodes NS1 and NR / D1) represent packets consisting solely of a source packet from the node NS 1.

The three small dotted communication links (as for example between the nodes NS2 and NR / D4) represent packets consisting solely of a source packet from the node NS2. The two large dotted communications links (such as between the NS3 and NR / D2 nodes) represent packets consisting solely of a source packet from the NS3 node. The other five communication links (for example between the nodes NR / D1 and NR / D3) represent packets which have undergone network coding and therefore contain a linear combination of at least two source packets. Communications links are not represented which are either victims of permanent masking or not usable due to the TDMA protocol and the successive speech times given to each node, the source nodes emitting first in the order of their numbering and then all the relay nodes also in the order of their numbering. FIG. 2 represents the architecture of a device (relay node or destination node) according to a particular embodiment of the invention. This device is represented by the block 210, blocks 230 (application) and 240 (Radio Frequency transmitter / receiver) corresponding to the environment of this device. The Man / Machine interface 212 allows the user to give the graph representing the network in order to calculate the reference network coding scheme with the Ford-Fulkerson algorithm. This network coding scheme will then be shared between all the nodes of the network.

The data memory 216 makes it possible to store the different copies of the data transmitted by the source nodes and the different relay nodes. This data is received by the Radio Frequency transmitter / receiver 240 and passes through the radio packet receiver 215. This memory 216 also makes it possible to store the matrices of the various nodes involved in the network coding process. The network coding packet management module, referenced 217, which is segmented into four sub-modules, manages, both at the relay nodes and the destination nodes, the network coding packets. The first sub-module 218 is a notification analyzer that makes it possible to know if the received packet corresponds to the expected packet or if coefficients related to the network coding have been modified. The second sub-module 219 allows it to update the network coding coefficients to be used either for retransmission or for decoding, in place of the reference coefficients stored in the data memory 216. The updating of these coefficients is performed after the analysis of a notification corresponding to a received packet. The third sub-module 220, encoded packet production, is used by the relay nodes. It makes it possible to generate the resulting package that must be sent. This resulting packet is a function (linear combination) of some received packets and their associated coefficients. Once produced, the resulting packet is stored in data memory to be transmitted by the radio packet transmitter 214. The fourth sub-module 221 is used during the decoding phase. It makes it possible to construct a decoding matrix according to the received packets and their associated coefficients (stored in the data memory), and to extract from this matrix the different source packets. Once decoded, the source packets are transmitted to the application 230 by the CPU 213. FIG. 3 describes the structure of a packet notifying a modification of the predetermined network coding scheme. In a stable regime where no packet loss is detected, a packet consists only of a given part 310, in which part the information transmitted by the source nodes or the relay nodes is contained. In the context of the present invention, this given part 310 is a linear combination of the source packets sent by the source nodes, linear combination predetermined at the initialization of the system. If the data portion 310 does not contain this predetermined linear combination of source packets (because of link loss), a notification portion 305 is added to indicate the coefficients of the linear combination that have been modified. It should therefore be noted that this notification part 305 is not systematically present in the packet. For each modified coefficient, information is introduced in the notification part 305. This information contains an identifier 315 (respectively 325) of the source packet associated with the coefficient, as well as the new value of the coefficient 320 (respectively 330). In the particular case where a source packet is missing, the value of the coefficient is set to zero. FIGS. 4a, 4b and 4c describe algorithms, implemented in a central node, a relay node and a destination node respectively, of construction of a predetermined network coding scheme, at the start of the system. The central node, which is one of the nodes present in FIG. 1 (for example one of the source nodes), has the function of constructing the predetermined network coding scheme and of distributing it to all the other nodes (as described in FIG. Figure 4a). On receipt of this network coding scheme by the other nodes of the network, the relay nodes store the latter (as described in FIG. 4b) and the destination nodes as well (as described in FIG. 4c). We now present, in relation with Figure 4a, the algorithm implemented in the central node. At system initialization (step 405), the central node retrieves (step 410) the topology of the network (i.e., recovers the quality of the communications between the nodes), the list of source nodes, and the list of the nodes. destination nodes. This topology can be known from the nodes of the network by construction, if the network is fixed and if the number of nodes is constant. It is also certain that this information can be introduced by the user after the installation of a system. Then, in step 415, the central node constructs the network graph G from the network topology. If the quality of a transmission between two entities is considered good, for example if the signal-on-noise ratio (in English Signal Noise Ratio) or the power of the signal received (in English Radio Signal Strength Indication) is higher than a given threshold ( depending on the type of radio used), the transmission is considered valid, if not invalid. The graph is then constructed in the following way: each communicating entity is modeled by a node of the graph and each communication considered valid between two entities is modeled by a link between two nodes (and therefore each communication considered invalid is not modeled in the graph). Then, in step 420, the central node determines the predetermined network coding scheme. The method is explained in the patent application US2005 / 0010675 and repeated in many articles of the state of the art. The steps are as follows:> Find the disjoint paths Uj between the set S of the source nodes and each destination node Dj; - Construction of the subgraph G 'of G containing only vertices and links belonging to at least one set Uj; - Determine the coefficients of the linear combinations in such a way that the set of destination matrices is of rank equal to the number of source nodes. Then, in step 425, the central node diffuses the coefficients according to a predetermined diffusion protocol. Several dissemination techniques are known to those skilled in the art for broadcasting information in a mesh network (for example data flood type in a mesh protocol, English flooding protocol). For a relay node (FIG. 4b), at the end of the diffusion step (425) by the central node, that is to say on reception (step 430) by the relay node of the coefficients of the linear combinations of the set of nodes of the network, the relay node keeps in memory its local combination cmb_loc_pred, which it will later use to build a predetermined resulting packet, and builds a relay matrix and a destination matrix (step 435). The relay matrix contains the global combinations of the resulting packets of the source nodes or relay nodes that had access to the medium, during the superframe, before the date of access to the medium of the relay node considered. The other packets, that is to say those sent by nodes which had access to the medium after the relay node considered, are not taken into account because they are not usable (because of the constraint that the combinations only occur with data sent during the current superframe). In addition, the lines corresponding to the packets involved in the combination cmb_loc_pred, that is to say the useful packets, are marked and are considered useful. The destination matrix contains the set of global combinations of the resulting packets received by the destination nodes. These two matrices are explained above in the section titled Network Encoding. For a destination node (FIG. 4c), at the end of the broadcasting step (425) by the central node, that is, at the reception (step 440) by the destination node of the coefficients of the linear combinations of the set of nodes of the network, the destination node constructs a destination matrix (step 445). From this destination matrix and from the Gauss Jordan algorithm, the destination node defines (step 450) a square submatrix of dimension (M, M) of D, denoted C, invertible, such that we have : Y '= CX, with Y' a subvector of the column vector Y of the packets received and X the vector of the source packets, the subvector Y 'incorporating only the received packets taken into account in C (the useful packets). From this equation, we deduce: X = C_ 'Y'. The destination node stores in memory the inverse of C, a matrix called a decoding matrix that it will use directly on receiving the packets. After this initialization phase, each source node starts sending the source packets on the network, each relay node performs its local combination and each destination node decodes the source packets from its decoding matrix. FIG. 5 describes the main algorithm for processing a received packet, implemented by a relay node in a particular embodiment of a network coding method according to the invention. The input parameters are as follows: • an expected p packet, to be received; The predetermined local combination of the relay node, denoted cmb_loc_pred (combination of a predetermined subset of packets among the plurality of packets to be received); The relay matrix R, containing global combinations of the packets received before access to the medium of this relay node. This algorithm launches for each expected packet p (step 510). In step 515, it is checked whether the expected packet p is available. This means is based for example on radio information, such as the signal-to-noise ratio (SNR) or the signal strength received (RSSI for Radio Signal Strength Indication in English). If these variables exceed a predefined threshold, the packet is considered available and proceed to step 520, otherwise the packet is considered unavailable and proceed to step 525.

In step 520, it is checked whether the received packet p is actually the predetermined linear combination of source packets. For this, it is detected whether the packet received p includes a notification or not (see Figure 3). If yes, proceed to step 525, otherwise step 530. In step 525, the new combination of the received packet is stored. For this, we use a temporary relay matrix R '= r', i, valid only for the execution of this algorithm in the current superframe. If this is the first modification detection of a packet during the current superframe, the matrix R 'is created otherwise it is updated. The creation of the matrix R 'is characterized by the following steps: - Initialization of the value of the coefficients r', i of the matrix R 'to the value of the coefficients r, i of the predetermined relay matrix; If the received packet is unavailable (test of step 515), the line corresponding to this packet becomes a null line (all the coefficients of the line are set to zero); If the packet received does not consist of the predetermined linear combination (test of step 520), the line corresponding to this packet is modified and takes into account the modifications of the notification: a modified element r ', i means the package associated with this line has been modified. Package i was received with a notification. Column j corresponds to the identifier (315) of the source packet indicated in the notification. The new value of r ', i corresponds to the coefficient indicated in the notification (320).

In step 525, the position of the relay node is also stored in the superframe which sent the packet p, which information may be useful if the recovery algorithm is resumed (step 570, FIG. 12). Then, in step 530, it is checked whether p is a packet considered useful (momentarily or not). If yes, proceed to step 540, otherwise end of the algorithm (step 535). In step 540, it is checked again if p had a notification or not (test of step 520) or if p is unavailable (test of step 515). If yes, proceed to step 550, otherwise step 545. In step 545, the received packet is concatenated with the other received useful packets (momentarily or not) to form part of the resulting packet. The concatenation is explained in section 2.2.1 above. In step 550, it is checked whether the final recovery algorithm has already been started or not during the current superframe. If so, proceed to step 555, where the algorithm is re-started because a momentarily useful packet has been modified. The final recovery algorithm is described in FIG. 8. If no, the next step is the test step 560. In the test step 560, it is checked whether the intermediate recovery algorithm is in progress during the test. current superframe. The algorithm is running when it has been started and the last momentarily useful packet needed has not yet been received. If yes, proceed to step 570, otherwise step 565.

At step 565, the intermediate recovery algorithm is started. This algorithm is described in FIG. 6. At step 570, the intermediate recovery algorithm is restarted. This algorithm is described in Figure 11. It should be noted that if p is the last momentarily useful packet to combine to build the resulting packet, or that pa triggered a recovery (transparent or not) in such a way that all the momentarily useful packets have been received, a notification, described in Figure 3, is then constructed (if necessary) notifying the differences between the predetermined combination and the sent combination, indicated by the recovery algorithm. The resulting packet built with the notification is then put into the send buffer, ready to be sent to the next medium access of the relay node. Note also that if the local combination cmb_loc_nouv is the null combination, the relay node does not send a resulting packet. FIG. 6 describes an algorithm for reconstituting a local combination (of a relay node affected by a loss of link), corresponding to step 565 of FIG. 5. The input parameters are as follows:> The combination predetermined local relay node, noted cmb_loc_pred; The temporary relay matrix R ', containing global combinations of the packets received before access to the medium of this relay node. The output parameter is the new combination cmb_loc_nouv, and the associated received packets (called momentarily useful packets). As stated in section 2.2.1 above, a combination of local (packets received) is associated with a single global combination (linked to the source packets). Note cmb_glob_pred the predetermined global combination associated with the predetermined local combination cmb_loc_pred. On the contrary, in a global combination it is possible to associate several local combinations. The purpose of the algorithm of Figure 6 is then to find a new local combination cmb_loc_nouv corresponding to cmb_glob_pred (because cmb_loc_pred is no longer available). We can summarize the concept as follows: from a local combination cmb_loc_pred, we determine its global combination cmb_glob_pred and from it, we determine a new local combination cmb_loc_nouv. The determination of cmb_loc_nouv is based on both the packets already received and the packets to receive. Indeed, the packets to be received are logically constituted of a linear combination of source packets which is predetermined at the creation of the network coding scheme, during the initialization of the system (FIG. 4). If this hypothesis is false, the algorithm of FIG. 5 will not restart the algorithm described in this FIG. 6 again, but a recovery algorithm described in FIG. 11, which is much lighter in operations because it uses the calculated calculations. by this algorithm of FIG. 6. In step 605, it is checked whether each source packet of cmb_glob_pred is at least in a packet received or to be received, a necessary condition to hope to reconstruct the global combination cmb_glob_pred with the received packets. For this, it is verified that no column of the temporary relay matrix R '(see step 525, FIG. 5) corresponding to a source packet of cmb_glob_pred is zero (all its coefficients zero). If the test is positive (test of step 610), proceed to step 620 if not step 615. In step 620, it is checked whether rapid reconstitution of cmb_glob_pred is possible by a new local combination. For this, this step determines whether the modified line of R (change between R and R ', in step 525) is present in R' at another line position. If so, the new line is called a successor line. The new local combination assigned, cmb_loc_nouv, is constructed in the following way: the values of the coefficients are not modified but the coefficients are no longer attributed to the same received packets. The package associated with the substitute line is now marked momentarily useful. It should be noted that this momentarily useful packet can be a packet to receive. If the test in step 620 is negative, go to step 625, if it is positive go to step 640.

Step 625 is the step of reconstituting a local combination cmb_loc_nouv. At step 625, an attempt is first made to find a local combination corresponding to the predetermined overall combination. This algorithm is explained in FIG. 7. If the attempt is successful (positive result of the test of step 630), the reconstitution is local and is transparent for the other nodes of the network and one proceeds to step 640. Otherwise (negative result from the test of step 630), proceed to step 615. In step 640, store the new local combination cmb_loc_nouv, update the momentarily useful packets and notify the difference for the construction of the notification (if necessary).

In step 645, all the momentarily useful packets already received are concatenated to constitute a part of the resulting packet. This allows us to start in advance the construction of the new resulting package to be sent (also called the resulting reconstituted package). If we arrive at step 615, this means that even with the packets to be received we will not be able to determine a new local combination cmb_loc_nouv associated with the global combination cmb_glob_pred. The final recovery algorithm explained in Figure 8 is then launched to find a new local combination cmb_loc_nouv associated with a global combination close to cmb_glob_pred. The sooner this one is executed, the better it is because being based on exhaustive tests, it is very expensive in computing time.

FIG. 7 describes an algorithm for determining a new local combination cmb_loc_nouv from a global combination, corresponding to step 625 of FIG. 6. The input parameters are as follows:> The predetermined local combination cmb_loc_pred of relay node and the associated predetermined global combination cmb_glob_pred, given by the network encoding scheme on initialization; The temporary relay matrix R ', containing global combinations of the packets received before access to the medium of this relay node. In step 710, one builds from packets received and receive a linear system to determine the coefficients to be assigned to these packets. Note (31, .., (3s these coefficients with S the number of packets received and to receive.) First, we try to build a new local combination cmb loc new associated with cmb_glob_pred.For each source packet X; the coefficient associated with it in cmb_glob_pred g; is found in the sum of the packets received from s cmb_loc_nouv, that is to say we must have the relation 1 Ri r'i; = gi for each packet i = 1 source, with S the number of packets received and to be received, so we have a linear system: A (3 = g, with 13 the column vector of [(31, .., 13s], g = [gi, .., gM] the column vector of cmb_glob_pred and A a dimension matrix (M, S) of which each coefficient aii is equal to r'i, remember that, by definition, g; is zero (respectively non-zero) if the associated source package is not (respectively is) in cmb_glob_pred.

In step 715, the linear system created in step 710 is solved. This algorithm is explained in FIG. 10. Then in test step 720, it is verified that the system is compatible or not (that is, ie admits a solution or not) (see paragraph 2.2.3 above). If yes, proceed to step 730, otherwise step 725 (failure and end of the algorithm).

At step 730, the values of [3 ,, .., (3s] given by the Gauss-Jordan algorithm are then assigned If the system admits an infinity of solutions, the value of the coefficients 13i which are unknowns secondary is assigned to zero, which is to say that the associated packets are considered redundant, then the success of the algorithm is stored and end of the algorithm (step 735) Figure 8 describes a selection algorithm of the combination overall linear pattern that has the least impact on the network, corresponding to step 555 of FIG. 5 and step 1145 of FIG. 11 The input parameters are:> The predetermined global combination cmb_glob pred given by the network coding scheme at initialization; temporary relay matrix R 'containing global combinations of packets received before access to the medium of this relay node; in step 805 it is checked whether each source packet of cmb_glob_pred is at least in a re package received or received (a necessary condition to hope to reconstruct the global combination cmb_glob_pred with received packets). For that, one checks that no column of the matrix R 'corresponding to a source package of cmb_glob_pred is null (all its null coefficients). If the test of step 810 is positive, proceed to step 815 if not to step 820. In step 815, a new local combination cmb_loc_new associated with a closest overall combination is determined (according to a first definition) of cmb_glob_pred. This algorithm is described in FIG. 9. Then, we go to step 835, in which we create a notification that indicates the source packets that are missing or modified with respect to cmb_glob_pred. Then, we go to step 840, in which we concatenate all the momentarily useful packets already received to form part of the resulting packet. In step 820, a new local combination cmb_loc_nouv associated with a closest overall combination (in a second finish) of cmb_glob_pred is determined. This algorithm is described in FIG. 15. Then, we go to step 825, in which we create a notification that indicates the source packets that are missing or modified with respect to cmb_glob_pred. Then, we go to step 840, in which we concatenate all the momentarily useful packets already received to form part of the resulting packet. It is worth noting the difference between steps 815 and 820 on the concept of the closest. In step 820, the global combination closest to cmb_glob_pred is the global combination containing the most source packages contained in cmb_glob_pred, prohibiting the source packages not contained in cmb_glob_pred. In step 815, we do not have this constraint, packets not associated with cmb_glob_pred can be present in cmb_loc_nouv (more precisely, in its associated overall combination). But in this case, all the associated packages of cmb_glob_pred must be present in cmb_loc_nouv. In this case, the closest overall combination of cmb_glob_pred is the overall combination that has the least impact on the network. FIG. 9 describes an algorithm for reconstituting a new local combination cmb_loc_nouv associated with a global combination cmb_glob_nouv close to the predetermined global combination cmb_glob_pred which has the least impact on the network. This algorithm corresponds to step 815 of FIG. 8. The input parameters are as follows:> The predetermined global combination cmb_glob pred given by the network coding scheme at initialization; The temporary relay matrix R ', containing global combinations of the packets received before access to the medium of this relay node. At step 910, one builds from packets received and receive a linear system in order to determine the coefficients to be assigned to these packets, (31, .., (3s these coefficients with S the number of packets received or It is known that we can not reconstruct a local combination cmb_loc_nouv associated with cmb_glob_pred, so we will try to determine a local combination associated with a global combination other than cmb_glob_pred, then we assign a new value for g; sources not associated with cmb_glob_pred For the associated packets, we keep the coefficients of the global linear combination We then have, as in step 710, a linear system: A (3 = g, with 13 the vector column of unknowns [ (31, .., (3s], has a matrix of dimension (M, S) of which each coefficient a; i is equal to r'i, (coefficients of the matrix R ') and g = [gi, .., gM] the column vector representing a global combination close to cmb_gl ob_pred, containing at least this one. The assignment of a value to this vector g consists of assigning at least one non-zero value to a coefficient g; corresponding to the T source packages not associated with cmb_glob_pred (which have a null value in it). Several implementations are possible:> Random: One draws randomly the value of the T coefficients g; corresponding to the T unassociated packages on the body Fq by verifying that at least one non-zero value is drawn. A pseudo-random generator is therefore implemented in this case; - Deterministic: an initial deterministic value is attributed to the T coefficients. Assigning the values of g will be explained in more detail in step 955. Then proceed to step 915.

In step 915, the linear system created in step 910 is solved. The Gauss-Jordan algorithm is used. This is described in Figure 10 but in the case of the final reconstruction, there is no need to memorize operations and matrices. In step 920, it is verified that the system is compatible or not (i.e. admits a solution or not) (see paragraph 2.2.3 above). If so, proceed to step 925, otherwise step 960. In step 925, the values of g, .., (3s) given by the Gauss-Jordan algorithm are then assigned. system admits an infinity of solutions, the value of the coefficients 13i which are secondary unknowns is assigned to zero, then, in step 930, it is verified that the source packets added in the new local combination which are not in cmb_glob_pred (the linear system 920 was not solved at the first iteration) have an impact or not on the network This test is described precisely in figure 13. If this addition has no impact, we go to step 935 otherwise in step 950. In step 935, the coefficients of the different source packets are notified between the vector g and the global combination cmb_glob_pred, and then step 940.

At step 940, the new local combination cmb_loc_nouv given by definition by the values of [(3 ~, .., (31] is kept in memory and the utility or not of the packets received or to be received (the packets associated with the coefficients g, non-zero are marked momentarily useful, the others are marked redundant).

In step 950, in a list called Scand, the tested local combination is memorized (storage of [(3 ~, .., (3s]) and the overall linear combination (storage of [g1, .., gM] ) associated, as well as the confidence index associated with this combination given by the test of step 930. Then, go to step 955. In step 955, new values are given for the corresponding g; to source packets not associated with cmb_glob_pred This step is associated with step 960 which determines whether searching for global combinations not affecting the network should be stopped or not, and of course at step 910 which gave a first value to the vector g To determine a new value for the vector g: • either we randomly draw again the value of the T coefficients g, corresponding to the T unassociated packages on the body Fq, by checking that we draw at least one value null: • in a deterministic way, we choose a new value The stopping condition for step 960 is based on either a maximum number of trials or a stopping time. This stop time may be for example the start time of a predetermined period before the date of access to the medium by the relay node. It is considered that after this moment of stopping, the search for global combinations that do not impact the network has lasted long enough and it is now necessary to conclude and find at least one resulting packet that has the least possible impact on the network. So in step 960, if the maximum number of tests or the stopping time are reached, the test is negative and we go to step 965, otherwise the test is positive and we go back to step 955. It should be noted that the number of values tested for the vector g is highly optimized. Indeed, the fact of triggering the algorithm before the reception of all the packets makes it possible to test many more combinations for g (that is to say, makes it possible to increase the maximum number of tests or, by definition, increase the test period between the trigger date and the stop time) and therefore increase the robustness of the network because it is more likely to find a global combination that does not impact the network. In step 965, a default local combination is selected, associated with a global combination that will impact the network as little as possible. This algorithm is described precisely in FIG. 14. Then, we go to step 975, in which we create a notification that indicates the source packets that are missing or modified with respect to cmb_glob_pred. In step 970, the new local combination is stored in the variable cmb_loc_nouv. This step 970 corresponds to the end of this algorithm.

FIG. 10 depicts an algorithm for solving a linear system based on the Gauss-Jordan algorithm to determine a new local combination from a global combination, corresponding to step 715 of FIG. 7 and to FIG. step 915 of FIG. 9. The key point of this figure is the memorization, at each iteration of the algorithm, of the operations in the steps 1025, 1030, 1045 and of the temporary matrices in the step 1075. This memorization will thus make it possible to repeat the calculations at selected iterations and not restart fully the recovery to a new loss of a useful packet in the current superframe. The input parameter is the linear system to be solved: A (3 = g, with: - 13 the unknown column vector [(31, .., 13s], S the total number of packets received and to be received during the superframe - g = [gl, .., gM] the column vector representing the global combination cmb_glob_pred; - A the dimension matrix (M, S) of which each coefficient aii is equal to r'i ,.

In step 1005, a matrix A "= [A g] of dimension (M, S + 1) is constructed, that is to say that A" consists of A with an additional column located in the last position constituted of the vector g. Block 1010 initializes the variable k to 1, where k represents the current iteration of the resolution algorithm.

Step 1015 searches for a line i of A-) such that i is greater than k and an element a.k (k-) is different from zero. If the test (step 1020) is negative, proceed to step 1060 if not to step 1025. In step 1060, all the matrices of A (k) are initialized to A (mm (Ms to matrix A (kl) and keep all these matrices in memory Another storage alternative is to indicate the iteration (here k) from which the matrices are all equal to A (kl) Then end of the algorithm (step 1080 At step 1025, the lines li and lk are switched, this operation is stored, and then step 1030 is performed.

In step 1030, the following operation is then performed for each element of the line k of the matrix denoted by A (k): lk (k) = (1 / akk (k-1)) lk (k-1) • The operation is memorized. Then, in step 1035, the variable i is initialized to 1. Then, in step 1040, it is checked whether i is different from k. If yes, proceed to step 1045, otherwise step 1050. In step 1045, the lines i of A (k) are updated in the following manner: li (k) = li (k- 1) -aik (k-1) .lk (k).

The operation is stored. Then we go to step 1050 in which the variable i is then incremented. Then we go to step 1055. In the test step 1055, we check if i is strictly greater than m, that is to say if all the rows of the matrix were tested. If yes, go to step 1075, otherwise go back to step 1040.

In step 1075, the temporary matrix A (k) is stored. Then we go to step 1070. In step 1070, we check if k is equal to M or S, where S is the number of packets received and to receive in the superframe. If yes, the algorithm is finished (step 1080), otherwise we go to step 1065 in which we increment k (that is to say change to the next iteration) and then return to step 1015. FIG. 11 describes an algorithm for recovery of the reconstitution of a local combination (of a relay node affected by a loss of link), corresponding to step 570 of FIG. 5. This algorithm is practically identical to the algorithm launch of reconstitution of a local combination of a relay node affected by a loss of link (Figure 6). The different key step is step 1115 which, instead of relaunching the resolution of the linear system, resumes the resolution of the linear system. The input parameters are as follows:> The global combination of the received packet p, denoted cmb_glob_rec; - The temporary relay matrix R 'containing updated at step 525. At step 1105, it is checked whether each source packet of cmb_glob_pred is at least in a packet received or to receive (necessary condition to hope to reconstruct the combination global cmb_glob_pred with received packets). For that, one checks that no column of the matrix R 'corresponding to a source package of cmb_glob_pred is null (all its null coefficients). If the test (step 1110) is positive, proceed to step 1115 if not to step 1145. Step 1115 allows the reconstitution of a local combination cmb_loc_nouv. Step 1115 is the resumption of the resolution algorithm of the linear system. This algorithm is described in FIG. 12. If the attempt (step 1120) is successful, the reconstitution is local and is transparent for the other nodes of the network, and one goes to step 1125. Otherwise one proceeds to step 1145 At step 1125, the new local combination cmb_loc_nouv is stored, the packets are momentarily updated, and then step 1140 is carried out. At step 1140, the momentarily useful packets received are concatenated to form a part the resulting package. If we arrive at step 1145, this means that even with the packets to be received we will not be able to determine a new local combination cmb_loc_nouv associated with the global combination cmb_glob_pred. The final recovery algorithm explained in Figure 8 is then launched to find a local combination cmb_loc_nouv associated with a global combination close to cmb_glob_pred. The sooner this one is executed, the better it is because being based on exhaustive tests, it is very expensive in computing time. FIG. 12 describes an algorithm for resuming the resolution of the linear system linked to the resumption algorithm of the reconstitution of a local combination, corresponding to step 1115 of FIG. 11.

This algorithm corresponds to a reconsideration of previously marked temporarily useful packets, when launching the recovery algorithm (step 565) or during a previous recovery of this recovery algorithm (step 570). The received p packet, marked momentarily useful by step 565 or 570, and not yet received at the execution of the recovery algorithm does not contain the expected combination, i.e. the predetermined one when constructing the network coding scheme at initialization (Figure 4). But the algorithm of modification was based on this hypothesis so its results are questioned. But instead of reactivating the algorithm of step 565, the results thereof are used to resume it at a selected iteration, which allows for fewer operations. The input parameters are:> The temporary relay matrix R ', updated notably with the global combination of the received packet p noted cmb_glob rec; - The linear system built in step 710 when launching the intermediate recovery algorithm; - The operations and the temporary matrices memorized during each iteration, during the algorithm of resolution of this system (figure 10). In step 1205, the positions in the superframe are retrieved from the relay nodes that sent unexpected packets (ie, packets that are unavailable or containing unexpected source packets) p1, .., pK between the present date and the last call of the recovery algorithm (started at step 565 or resumed at step 570) during the current superframe. Let T denote this period between two successive calls of the recovery algorithm and t1, ... tK the positions of these relay nodes (notation based on a chronological classification). These positions also represent the positions of the lines corresponding to these unexpected packets in the matrix R 'but above all indicate the positions of the columns associated with these packets in the matrix A of the linear system created in step 715. Let us note cl, .. ck the columns associated with the positions t1, ... tK which represent the global combinations of the received packets. Note: Recovering only the position of the p packet may not be sufficient because there may be unexpected redundant packets received during this period. However, if we do not restart the recovery algorithms with these redundant packets not expected, to limit the number of operations, the new combination of these packages must be taken into account. But the most likely situation is that during T, all the redundant packets are those expected and in this case tl is the unique position and corresponds to the position of p. Then, in step 1210, the columns ci, .. cK of the matrix A (uu stored during the system solving algorithm are modified.The Gauss-Jordan algorithm is repeated at the ithth iteration because all the operations performed on the previous packets, that is to say all the columns positioned before t1, remain valid, the modification has no impact on these columns.To modify these columns, we start from the global combinations cmb_glob_rec of each packet. global package p can be represented by a column vector v (i) = [vi (i), ... vM (i)] We apply to this column vector the successive list of linear operations of (t1-1) first stored iterations (see Figure 10), note v '(i) this new vector, and then we replace the associated column c, of A (uu by v' (i), then go to step 1215. step 1215, then, in step t1, the Gauss-Jordan algorithm described in FIG. in step 1220, it is verified that the system is compatible or not (that is, admits a solution or not) (see paragraph 2.2.3 above). If yes, we go to step 1230, otherwise step 1225 (failure and end of the algorithm). In step 1230, the values of [(31, .., 13s] given by the Gauss-Jordan algorithm are then assigned to the following: If the system admits an infinity of solutions, the value of the coefficients 13i which are secondary unknowns is assigned to zero Then success and end of the algorithm (step 1235) Figure 13 depicts an algorithm for assigning a confidence index to a local linear combination, corresponding to step 930 of FIG.

The confidence index measures the impact of the new local combination to send over the network. At the initialization of the system, the network coding scheme has been calculated in such a way that all the source packets sent in the network can be decoded by all the destination nodes (it is considered that the topology of the network is not a constraint; it is even oversized, in the case of a wireless network, which creates redundant incoming packets). So, if the number of source nodes (hence source packets) is equal to m and the number of destination nodes is N, the number of source packets decoded in the network is equal to m X N. This variable (number of packets sources decoded by the network) is the confidence index of the new local combination. To measure it, each relay node needs all the matrices of destination D; of all network destination nodes.

The other input parameter is of course the tested local linear combination, called cmb_loc_test, but more specifically the associated global linear combination, denoted cmb_glob_test, which is different from cmb_glob_pred. The output parameter is the cmb_loc_test confidence index and therefore whether cmb_glob_test has an impact on the network or not.

In step 1305, the coefficients of the destination matrices that are impacted by the combination cmb_glob_test are modified, that is to say, the elements of each destination matrix involving the new coefficients of cmb_glob_test are modified (modification of the corresponding line). to the resulting package that the relay node must send).

At step 1310, the confidence index of cmb_glob_test is calculated, that is to say the number of source packets decodable by all the destination nodes. The number of source packets decodable by a destination node D i, denoted by Nb_src_pkt_dec (Di), is determined by the algorithm described in FIG. 19. The confidence index of cmb_loc_test, denoted ind_conf (cmb_loc_test), is then equal to: Ind_conf (cmb_glob_test) = ENb_src_pkt_dec (Di), i = 1..N It is stored in step 1315. In step 1320, it is checked whether the confidence index of cmb_loc_test is equal to m X N. If yes , cmb_loc_test has no impact on the network (output of the algorithm by step 1325) otherwise it has an impact (output of the algorithm by step 1330) (at least one destination node can not decode at least one source package). FIG. 14 describes an algorithm for selecting the overall linear combination that has the least impact on the network, corresponding to step 965 of FIG. 9. The input parameters are: The predetermined global combination cmb_glob pred; The set Scand of the local and global combinations tested during the algorithm of FIG. 9 and rejected by the test of step 930.

The output parameter is the local linear combination associated with the global combination that has the least impact on the network. Since this algorithm is applied when no global combination having no impact on the network has been found in the algorithm of Figure 9, the combination necessarily has an impact.

In step 1405, we first look for a local combination cmb_loc_candl associated with a global combination cmb_glob_candl closest to cmb_glob_pred. By closer, we mean containing the most associated source packages of cmb_glob_pred by banning source packages not contained in cmb_glob_pred. This algorithm is described in Figure 15.

In step 1410, the confidence index of cmb_glob_candl is determined using the algorithm described in FIG. 13. At step 1415, one selects from the set Scand constructed during the algorithm of FIG. step 950), the global combination cmb_glob_cand2 which has the highest confidence index (a conventional sort is performed).

In step 1420, the two confidence indices of cmb_glob_candl and cmb_glob_cand2 are compared. If the confidence index of global cmb_glob_cand2 is greater than that of cmb_glob_candl, then step 1430 is proceeded to if not at step 1425. At step 1425, the local linear combination cmb_loc_candl is selected. At step 1430, the local combination associated with cmb_glob_cand2, a local combination that was stored in Scand, is selected. FIG. 15 depicts an algorithm for reconstituting a local combination associated with a closest overall combination of another global combination, corresponding to step 820 of FIG. 8. Closest means to contain the most source packages associated with cmb_glob_pred by banning source packages not contained in cmb_glob_pred. The input parameters are: - the predetermined global combination cmb_glob pred. It consists of P associated source packets (which corresponds to p non-zero coefficients among the M coefficients associated with the source packets); The temporary relay matrix R ', containing global combinations of the packets received before access to the medium of this relay node.

The output parameter is a local combination cmb_loc_cand and a global combination associated cmb_glob_cand, the global combination closest to cmb_glob_pred.

In step 1510, the variable nb_src_pkt_to_del corresponding to the number of associated source packets to be removed from cmb_glob_pred is initialized to 1.

In step 1515, the number of different global combinations is determined by deleting nb_src_pkt_to_del source packets. This value nb_test is equal to the combination in the mathematical sense:

C (P, nb_src_pkt_to_del) = P! / (Nb_src_pkt_to_del)! (P - nb_src_pkt_to_del)! with! corresponding to the factorial operation.

In step 1520, the variable iter is initialized to 1, a counter that tests at each iteration a new set of associated source packets to delete S_pkt (iter).

Let cmb_glob_cand be the global combination equal to cmb_glob_pred except for source packages of S_pkt (iter) where the coefficients are set to zero. Let g '= [g'l, .., g'M] be the column vector representing this global combination cmb_glob_cand. The goal now is to determine a local combination cmb_loc_cand associated with cmb_glob_cand.

At step 1525, a linear system is then constructed from the temporary relay matrix R 'in order to determine the coefficients to be assigned to cmb_loc_cand. Note 131 these coefficients, with S the number of packets received. For each source packet X ;, the coefficient g '; associated with this one in cmb_glob_cand is found in the sum of the packets received from cmb_loc_cand, that is to say we must have the R relation = g 'for each source package. We thus have a linear system: A (3 = gi = 1 with 13 the vector column of the unknowns [(31, .., (31], g '= [g'l, .., g'M] the column vector of cmb_glob_cand and A matrix of dimension (M, 1) of which each coefficient aii is equal to r'j ;.

In step 1530, the linear system created in step 1525 is solved by the Gauss-Jordan method.

Then in the test step 1535, the compatibility of the system (i.e., whether or not the system admits a solution) is verified. If yes, proceed to step 1540, otherwise step 1550. In step 1550, it is checked whether the variable iter is equal to Nb test, that is, if all the global combinations have been tested with a number of associated source packets deleted equal to nb_src_pkt. If not, proceed to step 1565, in which the variable iter is incremented and a new set of associated source packets is selected to delete S_pkt (iter), then return to step 1525. If yes, we proceed to step 1555.

In step 1555, it is checked whether the variable nb_src_pkt_to_del is equal to p, the number of associated source packages in cmb_glob_pred. If yes, we go to step 1570, this corresponds to the fact that there are no more source packages available to delete. At step 1570, then returns the local and global null combinations. If the test of step 1555 is negative, then the variable nb_src_pkt_to_del is incremented (step 1560) and we return to step 1515. At step 1540, the values of [(31, .., ( 3,] given by the Gauss-Jordan algorithm If the system admits an infinite number of solutions, the value of the coefficients 13i associated with the secondary unknowns is set to zero.

At step 1545, the local combination cmb_loc_cand associated with the column vector [(31, .., (31] and the global combination cmb_cand_glob associated with the column vector g'M] is memorized. a received packet, implemented by a destination node in a particular embodiment of a network coding method according to the invention The input parameters are as follows:> An expected packet p, to be received; destination D, containing predetermined global combinations of the packets to be received during the superframe.This algorithm is therefore launched cyclically at each expected reception of a packet (step 1605).

In step 1610, it is checked whether the packet p is available. This means is based for example on radio information, such as the signal-to-noise ratio (SNR) or the power of the received signal (RSSI). If these variables exceed a predefined threshold, the packet is considered available and proceed to step 1615, otherwise the packet is considered unavailable and proceed to step 1620. At step 1615, it is checked whether the received packet is well constituted of the predetermined linear combination of the source packets. For this, it detects whether the packet includes a notification or not. If yes, proceed to step 1620 or step 1625. In step 1620, the new combination of the received packet is stored. For this, we use a temporary destination matrix D '= (d', i), valid only for the execution of this algorithm in the current superframe. If this is the first modification detection of a packet during the superframe, the matrix D 'is created otherwise it is updated. The creation is characterized by the following steps: - Initialization of the value of the coefficients of, i of the temporary destination matrix to the value of the coefficients d, i of the predetermined destination matrix; If the received packet is unavailable (test of step 1610), the line corresponding to this packet becomes a null line (all the coefficients of the line are set to zero); If the packet received does not consist of the predetermined linear combination (test of step 1615), the line corresponding to this packet is modified and takes into account the modifications of the notification: an element of, i modified means the package associated with this line has been modified. Package i was received with a notification. Column j corresponds to the identifier (315) of the source packet indicated in the notification. The new value of d ', i corresponds to the coefficient indicated in the notification (320). Then, in step 1625, it is checked whether p is a packet considered useful. If yes, proceed to step 1630 otherwise the algorithm is complete (step 1665). In step 1630, check again if p has a notification. If yes, proceed to step 1645, otherwise step 1635. In step 1635, the packet is introduced into the run-on decoding algorithm described in section 2.2.2. -above. It is clear that as soon as the decoding algorithm has received all the useful packets (to decode all or some of the source packets) of the current superframe and thus the source packets are decoded, these are sent directly to the user. application (module 230, FIG. 2). In step 1640, it is checked whether the final decoding has already been started or not during the current superframe. If yes, we go to step 1645, in which this algorithm is started again because a new useful packet has been modified. The final algorithm is described in FIG. 19. Otherwise, we go to the test step 1650.

In the test step 1650, it is checked whether the modification algorithm of the decoding matrix is in progress during the current superframe. The algorithm is running when it has been started and the last momentarily useful packet needed has not yet been received. If yes, proceed to step 1660, otherwise step 1655. In step 1655, the algorithm for modifying the decoding matrix is started.

This algorithm is described in FIG. 17. In step 1660, the algorithm for modifying the decoding matrix is updated. This algorithm is described in FIG. 18. FIG. 17 describes an algorithm for modifying the decoding matrix, corresponding to step 1655 of FIG. 16. The input parameters are: The received packet p, not constituted of the predetermined global combination cmb_glob_pred but of the combination cmb_glob_rec; The destination matrix of the destination node D, containing global combinations of the packets received and to be received. In step 1705, a triangulation of the matrix D 'is carried out by the Gauss-Jordan method, which is called over the water. This method is almost identical to that described in Figure 10. Step 1005 is not used because it does not solve a linear system. At the end of each iteration, each temporary matrix is stored. We denote by A (k) the temporary matrix at the end of the kth iteration. The major differentiation (which justifies the name in the course of the water) is in the temporary matrices. At initialization, A (°) is reduced to the first line of D '. At the end of the first iteration, a new matrix (in this case, a new line) A (1) is determined and stored.

At the next iteration (between steps 1070 and 1015, FIG. 10), the second line of D 'is introduced in A (1) at the last position. The operation is repeated at each iteration: at the end of the kth iteration, the matrix A (k) is stored and the line (k + 1) of D 'is added to Au at the last position. Let T be the final matrix obtained at the end of step 1705. Then, in step 1710, it is checked whether T has M non-zero lines. If yes, proceed to step 1720, otherwise step 1715. Step 1715 is initiated to failure of the test of step 1710. This means that even with the packets to receive, no will not happen to have a matrix that decodes the set of M source packages. The final decoding explained in FIG. 19 is then launched. This determines the number of decodable source packets, the associated decoding matrix and the momentarily useful associated packets. The sooner this one is executed, the better it is because being based on exhaustive tests, it is very expensive in computing time. Then, in step 1725, the set of momentarily useful packets already received are introduced into the run-on decoding algorithm. The transition to step 1720 indicates that the M source packets are decodable with the packets received and to be received. A temporary decoding matrix C-'prou is constructed. This temporary decoding matrix, valid only during the period of the current superframe, is constructed from T. The packets associated with the temporary decoding matrix are momentarily marked useful. Then, in step 1725, the set of momentarily useful packets already received are introduced into the run-on decoding algorithm. FIG. 18 describes an algorithm for taking up the modification of the decoding matrix, corresponding to step 1660 of FIG. 16.

This algorithm corresponds to a reconsideration of the previously marked temporarily useful packets, when launching the modification algorithm of the decoding matrix (step 1655) or during a previous recovery of this recovery algorithm (step 1660). The received p packet received momentarily useful in step 1655 or 1660, and which was not yet received at the execution of the modification algorithm, does not contain the expected combination, i.e. predetermined during the construction of the network coding scheme at initialization (Figure 4). But the algorithm of modification was based on this hypothesis so its results are questioned. But instead of reactivating the algorithm of step 1655, the results thereof are used to resume it at a selected iteration. This allows for fewer operations. The input parameters are: - the destination matrix of the destination node D '(see FIG. 17); - The temporary matrices A (k) stored during the first execution of the Gauss-Jordan algorithm. At step 1805, the recovery iteration is determined, that is to say at what iteration will be taken over the Gauss-Jordan algorithm. For this, the algorithm retrieves the positions, in the superframe, of the relay nodes that sent unexpected packets (that is, packets that are unavailable or contain unexpected source packets) p1, .., pK between the present date and the last call of the algorithm for modifying the decoding matrix (launching at step 1655 or resuming at step 1660) during the current superframe. Let T denote this period between two successive calls of a recovery algorithm and t1, ... tK the positions of these relay nodes (notation based on a chronological classification). The recovery iteration is tl. Note: The recovery of only the position of the packet p may not be sufficient because it may be that unexpected redundant packets have been received during this period. However, if we do not restart the modification algorithms with these redundant packets not expected to limit the number of operations, the new combination of these packages must be taken into account. But the most likely situation is that during T, all the redundant packets are those expected and in this case tl is the unique position and corresponds to the position of p. In step 1810, the matrix A (t-1 temporary matrix stored at the end of (t1-1) 1th iteration of the Gauss-Jordan method is retrieved, to this matrix, the new t-th added line is not the predetermined global combination of the packet pl but the new global received combination of pl contained in the line theme of D. Indeed, all the operations performed before the iteration remain valid, so there is no use of restart the entire modification process described in Figure 17. This reduction in the number of operations allows the decoder to reconstruct a resulting package as soon as possible.

At step 1815, the first iteration of the Gauss-Jordan algorithm described in FIG. 17 is restarted. At the end of the Gauss-Jordan algorithm, the test of step 1820 checks whether T has M lines. not zero. If yes, we go to step 1830, otherwise step 1825. Step 1825 is started to fail the test of step 1820. This means that even with packets to receive, we will not arrive. not to have a matrix that decodes the set of M source packages. The final decoding explained in FIG. 19 is then launched. This determines the maximum number of decodable source packets, the associated decoding matrix, and associated useful packets (marked momentarily useful). Then, we go to step 1835, in which the set of useful notified packets already received are introduced in the run-on decoding algorithm. The transition to step 1830 indicates that the M source packets are decodable with the packets received and to be received. The packets used in the decoding are momentarily marked useful. A new temporary decoding matrix C-'prou is constructed. This temporary decoding matrix, only valid during the period of the current superframe, is built from T. Then, we go to step 1835, in which all the momentarily useful packets already received are introduced into the algorithm. decoding over water. FIG. 19 describes an algorithm for determining the number of decodable source packets, and consequently for determining the associated decoding matrix, corresponding to step 1715 of FIG. 17 and step 1645 of FIG. 16. This algorithm is called:> either at a relay node R; (see step 1310, FIG. 13), to determine the impact on the destination nodes of the sending of a new global combination by the relay node; - And of course at a destination node D; (See steps 1645, 1715 and 1825, in FIGS. 16, 17 and 18 respectively), when the latter must modify its decoding matrix. It should therefore be noted that the step 1960 is not implemented in the relay nodes. The output parameter is therefore, at the relay nodes, the number of decodable packets, nb_src_pkt_to_del, and at the destination nodes, the temporary decoding matrix C-'prou. To determine the maximum number of decodable source packets, the algorithm tests whether the M source packets are decodable. If yes, the algorithm is finished, otherwise we test if (M-1) source packages are decodable, and so on. In step 1910, the number of source packets to be deleted, nb_src_pkt_to_del, is initialized to zero. In the test step 1915, it is checked whether this number is strictly lower than M. If yes, we go to step 1920, otherwise to step 1935. In the latter case, this means that no source packet is decodable, the variable nb_src_pkt_dec is initialized to zero and of course there is no decoding matrix (step 1980, end of the algorithm).

At step 1920, the number of sets of source packets to be deleted is determined. This value nb_test is equal to the combination in the mathematical sense: C (M, nb_src_pkt_to_del) = M! / (nb_src_pkt_to_del)! (M - nb_src_pkt_to_del)! with! corresponding to the factorial operation. In step 1920, the variable iter is also initialized to 1, a counter that tests at each iteration a new set of nb_src_pkt_to_delete associated source packets to be deleted. In step 1925, a set of nb_src_pkt_to_del source packages to be deleted, set different for each iteration iterated. In step 1930, a temporary destination matrix D ', sub-matrix of the destination matrix D; is determined. The resulting packets containing the source packets to be deleted, determined in step 1920, are not taken into account. So D '; corresponds to the destination matrix D; minus the columns corresponding to the source packets to be deleted, and minus the rows which had a non-zero coefficient at the level of the columns corresponding to the source packets to be deleted.

Then, in step 1940, it is checked whether there remain source packets, that is to say if the matrix D '; still has lines. If yes, we go to step 1945, if not to step 1965. In step 1945, we search for the rank of the matrix D ', noted rand Di. For this, the Gauss-Jordan method is still used by triangulating the matrix D '. Let T be the triangulated matrix. The rank is the number of non-zero lines of T. Store in memory the matrix T '(consisting only of the non-zero lines of T) and the resulting packets associated with the lines of T'.

At step 1950, it is checked whether the value of rank Di is equal to (M-nb_src_pkt_to_ del). If yes, all the source packages present in the matrix D '; are decodable, we go to step 1955. Otherwise the matrix T 'is deleted and we go to step 1965.

At step 1955, nb_src_pkt_dec (D;) is updated to rand Di. Then if the node is a relay node, the algorithm is complete (step 1980). On the other hand, if the node is a destination node, it goes to step 1960 and then to step 1985 before the end of the algorithm (step 1980). At step 1960, the matrix T 'is recovered, an inversion thereof is performed (T' is a square matrix of dimension (M-nb_src_pkt_to_del, M-nb_src_pkt_to_del)) and the inverse matrix C-'prou is stored. of T ', where C-'prou is the temporary decoding matrix (valid for the current superframe). In addition, packets stored in step 1945 are marked as momentarily useful packets. In step 1985, the set of momentarily useful packets already received are introduced into the run-on decoding algorithm. In step 1965, it is checked whether all the sets of nb_src_pkt_to_del have been tested, that is to say if the variable iter is equal to Nb test. If yes, we go to step 1975, if not to step 1970. In step 1970, the variable iter is incremented and a new set of nb_src_pkt_to_del source packages to be deleted is determined. Then, we return to step 1930. In step 1975, we increment the number of source packets to delete nb_src_pkt_to_del, then we return to the test step 1915.

Claims (22)

REVENDICATIONS1. A network encoding method in a mesh network comprising at least one relay node which, in accordance with a predetermined network coding scheme, expects to receive a plurality of data packets as input and is to output a predetermined resulting packet obtained in a combination predetermined linear pattern of a portion of said plurality of data packets expected at input, the data packets belonging to said portion being said useful packets and the data packets not belonging to said part being said to be redundant packet, each of the packets of input data expected having an expected source packet composition, in accordance with said predetermined network coding scheme, said method being implemented by at least one relay node and being characterized by including steps consisting of: I) detecting (510 to 530) an altered useful packet, defined as a useful packet that is not received or received correctly but does not have a source packet composition (s) expected; II) if an altered useful packet is detected, determining (555, 565, 570), before the end of receiving said plurality of data packets, a new linear combination of expected input packets to construct a resulting packet reconstituted using, in accordance with a modified network coding scheme, all or part of the redundant packets, the packets associated with said new linear combination being said momentarily useful packets; III) with the new linear combination of expected incoming packets, constructing (645, 840, 830, 1140), before the end of receiving said plurality of expected data packets at the input, at least a portion of said reconstructed resulting packet, using the momentarily useful packets already correctly received. 2. Method according to claim 1, characterized in that said step II) comprises a step IL1) (620, 625, 630, 640, 1115, 1120, 1125) of determining, if it exists, a new linear combination of packets. expected as input to construct a resultant reconstructed package identical to the predetermined resulting packet. 3. Method according to claim 2, characterized in that said step IL1) comprises a step (620) of testing whether said corrupted user packet can be replaced by a redundant packet received or to be received by said given relay node. 4. Method according to claim 2, characterized in that said step IL1) comprises an execution of a complete recovery mechanism, comprising the steps of (625, 710 to 735): determining a predetermined linear combination of source packets, associated with said predetermined linear combination of expected incoming packets, and providing said predetermined resultant packet; constructing a linear system A (3 = g, where 13 is a column vector of the coefficients of said new linear combination of expected input packets to be determined, where g is a column vector of the coefficients of said predetermined linear combination of source packets, and where A is a matrix of dimension (M, S), with M the number of source packets and S the number of packets expected at input by said given relay node, the matrix A being defined as follows: * each line of the matrix A is associated with a source packet, * each column of matrix A is associated with an expected packet as input, * each element aii of matrix A represents: - either the coefficient of source packet i in a packet composition (s) ) the actual source (s) of the expected packet j, if the expected packet ja has already been received, - or the coefficient of the source packet i in a source packet composition (s) expected from the expected packet j, if the expected packet has not yet been received; - resolving said linear system by a predetermined resolution method, storing, at each iteration k of said predetermined resolution method, operations and a temporary matrix A (k); if the linear system admits a solution, determining said new linear combination of packets expected at the input, as a function of the column vector 13 of said solution. 15 20 25 5. The method as claimed in claim 4, characterized in that, at each reception of one of said momentarily useful packets, it comprises the steps of (FIG. 12): detecting (510 to 530) a momentarily useful altered packet, defined as a momentarily useful packet that is not correctly received or received correctly but does not have a source packet composition (s) expected; - if a corrupted momentarily useful packet is detected, perform a partial recovery mechanism, comprising the steps of (1205-1235): * determine the expected packet (s), including said momentarily useful packet corrupted, received since a last execution of the partial recovery mechanism or since an execution of the full recovery mechanism, an altered expected packet being defined as an expected packet that is not correctly received or is correctly received but does not have a composition in source packet (s) expected; in the temporary matrix A (11-1) stored at a (t1 1 st) iteration of said predetermined resolution method, modifying the altered column (s) corresponding to the expected packet (s) altered, where t1 is the rank of the first of the expected packet (s) altered in a predetermined sequence defining the order in which said plurality of expected data packets are expected, as well as that the order in which the columns of said matrix A are classified, the altered column (s) being modified by the stored operations during the (tl ù 1) first iterations of said predetermined resolution method; resuming resolution of said linear system at the iteration of said predetermined resolution method, storing, at each iteration k of said predetermined resolution method, operations and a temporary matrix A); if the linear system admits a solution, determining said second linear combination of expected packets as input, according to the column vector 13 of said solution. 30 6. Method according to any one of claims 2 to 5, characterized in that, in the event of failure of said step IL1), said step II) comprises a step IL2) (555, 615, 2015). 30805-835, 1145), comprising determining a new linear combination of expected input packets for constructing a closest reconstructed result packet, according to at least one determined criterion, of the predetermined resultant packet (Fig. 8). 7. Method according to claim 6, characterized in that, at each reception of one of said momentarily useful packets, it comprises the steps of: detecting (510 to 530) a momentarily useful altered packet, defined as a momentarily useful packet that is not correctly received or is correctly received but does not have a source packet composition (s) expected; if a momentarily useful, corrupted packet is detected, repeat steps IL2) and III). The method according to any one of claims 6 and 7, characterized in that said step IL2) comprises steps consisting of (910 to 975): a) determining a new linear combination of expected packets as input to construct a packet resulting reconstituted containing source packets not contained in the predetermined resulting packet; b) obtaining relative information, for at least one other node participating in the predetermined network coding scheme, to a modified network coding scheme that would result from sending the reconstituted resulting packet mentioned in step a); c) based on the information obtained in step b), selecting the new linear combination determined in step a) or repeating step a) to determine another new linear combination. The method according to claim 8, characterized in that step a) comprises the steps of: i) determining a predetermined linear combination of source packets, to obtain said reconstituted resulting packet containing source packets not contained in the predetermined resulting package; ii) constructing a linear system A (3 = g, where 13 is a column vector of the coefficients of said new linear combination of expected input packets to be determined, where g is a column vector of the coefficients of said predetermined linear combination of source packets, and where A is a matrix of dimension (M, S), with M the number of source packets and S the number of packets expected to be input by said given relay node, the matrix A being defined as follows: * each line of the matrix A is associated with a source packet, * each column of matrix A is associated with an expected packet as input, * each element aii of matrix A represents: - either the coefficient of source packet i in a packet composition (s) ) actual source (s) of the expected packet j, if the expected packet ja has already been received, - or the coefficient of the source packet i in a composition in source packet (s) expected from the expected packet j, if the packet waits it has not yet been received, iii) resolving said linear system by a predetermined resolution method; iv) if the linear system admits a solution, determining said new linear combination of expected packets as input according to the column vector 13 of said solution, otherwise repeating step i) with another predetermined linear combination of source packets. The method according to any one of claims 8 and 9, characterized in that, in step b), said information relating to the modified network coding scheme, which would result from the sending of the resulting reconstituted packet mentioned in FIG. step a), is the sum of the number of source packets decodable by the set of destination nodes of the network if the reconstituted resulting packet mentioned in step a) is assumed to be sent, and in that in step c) the new linear combination determined in step a) is selected if said information relating to the modified network coding scheme is equal to the number of source nodes in the network multiplied by the number of destination nodes in the network. 11. Method according to any one of claims 8 to 10, characterized in that, in case of failure of steps a), b) and c), said step IL2) further comprises steps of (1405 to 1430 Determining a first new linear combination of packets expected as input, making it possible to construct a first reconstituted resulting packet different from the predetermined resulting packet but containing only source packets included in the predetermined resulting packet; obtaining a first relative information, for at least one other node participating in the predetermined network coding scheme, to a modified network coding scheme that would result from sending the first reconstructed resultant packet, the first new linear combination being associated with said first information on the modified network coding scheme; among the new linear combination (s) not selected in step c), selecting a second new linear combination of packets expected at the input, according to said information, obtained at step b) for each new linear combination not selected in step c), on the modified network coding scheme, the second new linear combination being associated with a second piece of information relating to the modified network coding scheme; selecting between the first and second new linear combinations, according to the first and second information relating to the modified network coding scheme. The method according to any one of claims 6 and 7, characterized in that said step IL2) comprises a step of: - determining a new linear combination of expected packets as input to construct a reconstituted resulting packet different from the resulting packet predetermined but containing only source packets included in the predetermined resulting packet. 13. A network coding method in a mesh network comprising at least one destination node which, according to a predetermined network coding scheme, expects to receive a plurality of data packets as input and must output at least one source packet. a predetermined predetermined linear combination of a portion of said plurality of input data packets, the data packets belonging to said portion being said useful packets and the data packets not belonging to said party being said packet redundant, each of the expected input data packets having an expected source packet composition, in accordance with said predetermined network coding scheme, said method being implemented by at least one destination node and being characterized in that it comprises the steps of: I) detecting (1605-1630) an altered useful packet, defined as me a useful package that is not correctly received or is correctly received but does not have a composition in source package (s) expected; II) if an altered useful packet is detected, determining (1645, 1655, 1660), before the end of the reception of said plurality of data packets, at least one new linear combination of expected input packets allowing to build at least one source packet reconstituted using, in accordance with a modified network coding scheme, all or part of the redundant packets, the packets associated with said at least one new linear combination being said momentarily useful packets; III) with said at least one new linear combination of packets expected to input, construct (1725, 1835, 1985), before the end of receiving said plurality of data packets expected at input, at least a portion of said at least one reconstituted source package, using momentarily useful packets already correctly received. The method according to claim 13, characterized in that said step II) comprises a step IL1) (1705, 1710, 1720) of determining, if it exists, a new decoding matrix identical to a predetermined decoding matrix, allowing constructing a set of reconstituted source packets identical to a set of all the predetermined source packets, each line of said new decoding matrix defining a new linear combination of expected input packets for constructing a reconstituted source packet identical to one of predetermined source packets. 15. Method according to claim 14, characterized in that said step IL1) comprises an execution of a complete recovery mechanism, comprising the steps of (1705, 1710, 1720): constructing a matrix D 'of dimension (S , M), with S the number of packets expected at input by said given destination node and M the number of source packets, the matrix D 'being defined as follows: * each row of matrix D' is associated with a packet expected at input, * each column of matrix D 'is associated with a source packet, * each element d, i of matrix D' represents: - either the coefficient of source packet j in a source packet composition (s) ( s) of the expected packet i, if the expected packet has already been received, - is the coefficient of the source packet j in a composition in source packet (s) expected from the expected packet i, if the expected packet i n ' has not yet been received, - construction of a resulting matrix T from the matrix D ', by a predetermined triangulation method taking into account the rows one after the other, by memorizing, at each iteration k of said predetermined triangulation method, operations and a temporary matrix A (k); if the resulting matrix T has M non-zero lines, constructing said new decoding matrix from the resulting matrix T. 16. The method of claim 15, characterized in that, at each reception of one of said momentarily useful packets, it comprises the steps of: detecting (1605 to 1630) a momentarily useful altered packet, defined as a momentarily useful packet that is not correctly received or is correctly received but does not have a source packet composition (s) expected; - if a corrupted momentarily useful packet is detected, execute a partial recovery mechanism, comprising steps of (1805, 1810, 1815, 1820, 1830): * determine the expected packet (s) altered (s), including said corrupted momentarily useful packet, received since a last run of the partial recovery mechanism or since an execution of the full recovery mechanism, an altered expected packet being defined as an expected package that is not correctly received or correctly received but does not have a source packet composition (s) expected; * in the temporary matrix A (tl - u stored at one (tl û 1) th iteration of said predetermined resolution method, modify the altered column (s) corresponding to the (x) expected packet (s) altered (s), where t1 is the rank of the first of the expected packet (s) altered in a predetermined sequence defining the order in which said plurality of expected data packets are expected, as well as the order in which the rows of said matrix D 'are classified, the altered line (s) being modified by the operations stored during the (tl-1) first iterations of said predetermined triangulation method; constructing the resulting matrix T at the tth iteration of said predetermined triangulation method, storing, at each iteration k of said predetermined triangulation method, operations and a temporary matrix Au; * if the matrix resets subsequent T a M nonzero lines, construction of said new decoding matrix from the resulting matrix T. 17. A method according to any one of claims 14 to 16, characterized in that, in the event of failure of said step IL1), said step II) comprises a step IL2) (1825) of determining a new matrix of decoding different from a predetermined decoding matrix, but making it possible to construct a maximum number of reconstituted source packets identical to predetermined source packets, each line of said new decoding matrix defining a new linear combination of packets expected as input to construct a reconstituted source package identical to one of the predetermined source packages. 18. A method according to claim 17, characterized in that, at each reception of one of said momentarily useful packets, it comprises the steps of: detecting (1605 to 1630) a momentarily useful altered packet, defined as a momentarily useful packet which is not correctly received or received but does not have a source packet composition (s) expected; If a momentarily corrupted packet is detected, repeat steps IL2) and III). 19. Computer program product downloadable from a communication network and / or recorded on a computer readable medium and / or executable by a processor, characterized in that it comprises program code instructions for the implementation of the method according to at least one of claims 1 to 12 and / or the method according to at least one of claims 13 to 18, when said program is run on a computer. 20. A computer readable storage medium, possibly totally or partially removable, storing a computer program comprising a set of instructions executable by a computer to implement the method according to at least one of claims 1 to 12 and / or the process according to at least one of claims 13 to 18. A relay node included in a mesh network and participating in a network coding method in said mesh network, said relay node, according to a predetermined network coding scheme, expecting to receive as input a plurality of data packets and to generate at the output a predetermined resulting packet obtained according to a predetermined linear combination of a part of said plurality of data packets expected at input, the data packets belonging to said part being said useful packets and the data packets not belonging to said part being said to be redundant packet, each of the expected data packets input having a composition in source packet (s) expected, in accordance with said predetermined network coding scheme, said given relay node being characterized in that it comprises: - detection means, for detecting an altered useful packet, defined as a useful packet that is not t not correctly received or received but does not have a source packet composition (s) expected; determination means, activated if an altered useful packet is detected, making it possible to determine, before the end of the reception of said plurality of data packets, a new linear combination of expected input packets making it possible to construct a resulting packet reconstituted using, in accordance with a modified network coding scheme, all or part of the redundant packets, the packets associated with said new linear combination being said momentarily useful packets; means for constructing, with the new linear combination of expected input packets, and before the end of receiving said plurality of expected data packets, at least a portion of said reconstituted resulting packet, using momentarily useful packets already correctly received. 22. A destination node included in a mesh network and participating in a network coding method in said mesh network, said destination node, according to a predetermined network coding scheme, expecting to receive as input a plurality of data packets and to generate in output at least one predetermined source packet obtained according to a predetermined linear combination of a part of said plurality of data packets expected at input, the data packets belonging to said part being said useful packets and the data packets not belonging said part being said redundant packet, each of the expected data packets having an expected source packet composition (s), according to said predetermined network coding scheme, said given destination node being characterized in that it comprises detection means for detecting an altered useful packet, defined as a p a useful aquet that is not correctly received or is correctly received but does not have a source packet composition (s) expected; determination means, activated if an altered useful packet is detected, determining, to determine, before the end of the reception of said plurality of data packets, at least one new linear combination of packets expected at the input allowing constructing at least one reconstituted source packet using, in accordance with a modified network coding scheme, all or part of the redundant packets, the packets associated with said at least one new linear combination being said momentarily useful packets; means of construction, making it possible to construct, with said at least one new linear combination of packets expected as input, and before the end of the reception of said plurality of data packets expected at input, at least a portion of said at least one a reconstituted source packet, using the momentarily useful packets already correctly received.