Abstract: The invention relates to the transmission and reception of non-binary error correcting code words. The transmission method includes a first modulation (56) which implements a set of q sequences comprising q-1 sequences of q-1 chips, each sequence being obtained by circular shifting of a basic pseudo-random sequence, and a partially invariant sequence, invariant to a predetermined subset of circular shifts. The first modulation (56) further implements an association between each code word symbol and a sequence of the set of sequences wherein said finite field GFq has a non-zero primitive element, the symbol zero being associated with said partially invariant sequence and a symbol equal to a power j of the primitive element, j being an integer comprised between 0 and q-2, being associated with a pseudo-random sequence determined by j circular shifts of the basic pseudo-random sequence.

Abstract: A method for decoding a Low Density Parity Check code. At each decoding iteration, as long as the syndrome of the estimated word indicates an error, a set ({tilde over (F)}) of the least reliable bits of the word is determined as those where the value of a local energy function ({tilde over (E)}n) is less than a threshold value. The local energy value of a bit includes a first component proportional to the correlation between this bit and a sample corresponding to the observed signal, a second component representing the number of non-satisfied constraints wherein the bit acts, and a third component decreasing with the number (n) of iterations made since the last flipping of this bit. The bits of the estimated word belonging to this set are flipped, where applicable with a predetermined probability, to provide a new estimated word at the following iteration.

Abstract: A method for correcting a color code over a quantum erasure channel. First, a forest spanning the erased qubits over the lattice defining the color code is determined and syndrome qubits are calculated for each face of the tiling. If none of the faces of the tiling is touched by more than one tree, the erased qubits of each tree are sequentially decoded according to a trimming process. If a face of the tiling is touched by different trees, pseudo-erasures can be first inserted in order to connect these trees and the extended forest is subjected to the trimming process. Where a face of the tiling touched by a leaf is also touched by another vertex of the forest, the vertex belonging to this face and to the forest can be inactivated, and when the trimming process is terminated, a linear system with variables associated by the inactivated vertices of the forest is solved.

Abstract: A method for decoding a Low Density Parity Check code. At each decoding iteration, as long as the syndrome of the estimated word indicates an error, a set ({tilde over (F)}) of the least reliable bits of the word is determined as those where the value of a local energy function ({tilde over (E)}n) is less than a threshold value. The local energy value of a bit includes a first component proportional to the correlation between this bit and a sample corresponding to the observed signal, a second component representing the number of non-satisfied constraints wherein the bit acts, and a third component decreasing with the number (n) of iterations made since the last flipping of this bit. The bits of the estimated word belonging to this set are flipped, where applicable with a predetermined probability, to provide a new estimated word at the following iteration.

Abstract: A polar code decoding method in which a first decoding attempt by successive cancellation is performed and in the case where the decoded frame is erroneous, an ordered list of bit positions to be tested in the frame is generated, the order relation being given by a metric of first error, the value of this metric depending on the reliability of the decision about the bit as well as on the reliability of the decisions about the bits preceding it in the frame. For each of the positions of the list, an inversion of the bit and a decoding of the subsequent bits are undertaken, doing so as long as the list has not been exhausted or the frame has not been decoded without error. In case of failure, a new decoding attempt based on a double-inversion of bits can be envisaged.

Abstract: An in-between layer partial syndrome stopping (IBL-PS) criterion for a layered LDPC decoder. The IBL-PS syndrome is obtained by applying the parity checks (Hr,r+1) of a couple of a first layer (r) and a second layer (r+1) on the variables after the first layer has been processed and before the second layer is processed by the decoder, the decoding being stopped if said in-between layer syndrome (sr,r+1) is satisfied for at least a couple of consecutive layers.

Abstract: A polar code decoding method in which a first decoding attempt by successive cancellation is performed and in the case where the decoded frame is erroneous, an ordered list of bit positions to be tested in the frame is generated, the order relation being given by a metric of first error, the value of this metric depending on the reliability of the decision about the bit as well as on the reliability of the decisions about the bits preceding it in the frame. For each of the positions of the list, an inversion of the bit and a decoding of the subsequent bits are undertaken, doing so as long as the list has not been exhausted or the frame has not been decoded without error. In case of failure, a new decoding attempt based on a double-inversion of bits can be envisaged.

Abstract: An in-between layer partial syndrome stopping (IBL-PS) criterion for a layered LDPC decoder. The IBL-PS syndrome is obtained by applying the parity checks (Hr,r+1) of a couple of a first layer (r) and a second layer (r+1) on the variables after the first layer has been processed and before the second layer is processed by the decoder, the decoding being stopped if said in-between layer syndrome (sr,r+1) is satisfied for at least a couple of consecutive layers.

Abstract: A method associates terminals with cells in a network including at least one macro-cell and a plurality of small cells. According to this association method, each terminal performs, for each possible association, a power measurement on the radio link and deduces a quality indicator of that link therefrom. The subset of associations is next selected making it possible to respect the usage constraints of the different users. For each possible association of this subset, a metric characteristic of the overall capacity of the network is computed and an optimal association is determined maximizing this metric.

Abstract: The invention relates to a method of acquiring a GPS signal, spread by a Gold sequence obtained as the sum of a first M-sequence and a second M-sequence, this second M-sequence being characteristic of a satellite among a plurality of satellites in the GPS system. The acquisition method comprises a sampling step starting from a given time (410), a multiplication step for the sequence of samples obtained with the first M-sequence (420) and an iterative decoding step for the decoded values (430) making it possible to estimate the content of the second shift register of the second M-sequence at said given time. If the content thus estimated is identical to the initial content of the second register for an identified satellite (443), the receiver is synchronized with this satellite at said given time (490).

Abstract: The invention relates to a method of acquiring a GPS signal, spread by a Gold sequence obtained as the sum of a first M-sequence and a second M-sequence, this second M-sequence being characteristic of a satellite among a plurality of satellites in the GPS system. The acquisition method comprises a sampling step starting from a given time (410), a multiplication step for the sequence of samples obtained with the first M-sequence (420) and an iterative decoding step for the decoded values (430) making it possible to estimate the content of the second shift register of the second M-sequence at said given time. If the content thus estimated is identical to the initial content of the second register for an identified satellite (443), the receiver is synchronised with this satellite at said given time (490).

Abstract: The present invention relates to a method of error correction coding for a channel with quasi-periodic fade, such as the RSC (railroad satellite channel). According to an embodiment, it uses a block code (N, K) in which the parity check matrix comprises a sub-matrix obtained by horizontal concatenation of a plurality of identity matrices. The coding applies preferably to the level of the link layer, on data packets of the physical layer, without prior interleaving of said packets.

Abstract: The invention relates to a coding method with incremental redundancy in which it is determined (620) whether to carry out the coding of a sequence of information symbols using a first code (C), of the LDPC type, defined by a first check matrix, H, or rather using a second code ({tilde over (C)}), of lesser efficiency than that of the first code, the second code being defined by a second check matrix, {tilde over (H)}, obtained by fractionation (630) of the rows of the first check matrix. The invention finds application to, among others, a link adaptation method, a turbo-coding method, a distributed coding method within a cooperative network, a packet transmission method using an IR-HARQ protocol.

Abstract: The invention relates to an iterative decoding method of the message-passing type for decoding an error correcting code susceptible of representation by a bipartite graph including a plurality of variable nodes and a plurality of control nodes, said messages being expressed in terms of a log likelihood ratio. At each iteration of a plurality of decoding iterations, for each pair consisting of a variable node and a control node, a change is detected in the sign of the extrinsic information intended to be transmitted (?mntemp) as a message by said variable node to said control node relative to that transmitted (?mn) at the previous iteration, and in the event of a sign change, said extrinsic information is subjected to an amplitude reduction operation (Fred) before it is transmitted to the control node.

Abstract: The invention relates to a decoding method for non-binary codes, in particular non-binary LDPC codes, amenable to representation by a bipartite graph representing N variables and M constraints. The invention also relate to a transmission method for transmitting non-binary codes, in particular non-binary LDPC codes, and to a reception to receive the same. The invention can be applied in particular to an IR-HARQ or a cooperative network using a non-binary code, in particular a non-binary LDPC code.

Abstract: A device and method for the iterative decoding of a received word represented by signal values according to a parity control matrix code of the type for passing messages between variable nodes and control nodes of a two-part graph related to the matrix.

Abstract: The invention relates to an iterative method by message passing for decoding of an error correction code that can be displayed in a bipartite graph comprising a plurality of variable nodes and a plurality of check nodes. For each iteration in a plurality of decoding iterations of said method: variable nodes or check nodes are classified (720) as a function of the corresponding degrees of reliability of decoding information available in the neighborhoods (Vn(d),Vm(d)) of these nodes, a node with a high degree of reliability being classified before a node with a low degree of reliability; each node thus classified (725) passes at least one message (?mn,?mn) to an adjacent node, in the order defined by said classification. The invention also relates to a computer program designed to implement said decoding method.

Abstract: The invention relates to a coding method with incremental redundancy in which it is determined (620) whether to carry out the coding of a sequence of information symbols using a first code (C), of the LDPC type, defined by a first check matrix, H, or rather using a second code ({tilde over (C)}), of lesser efficiency than that of the first code, the second code being defined by a second check matrix, {tilde over (H)}, obtained by fractionation (630) of the rows of the first check matrix. The invention finds application to, among others, a link adaptation method, a turbo-coding method, a distributed coding method within a cooperative network, a packet transmission method using an IR-HARQ protocol.

Abstract: The invention relates to a decoding method for non-binary codes, in particular non-binary LDPC codes, amenable to representation by a bipartite graph representing N variables and M constraints. The invention also relate to a transmission method for transmitting non-binary codes, in particular non-binary LDPC codes, and to a reception to receive the same. The invention can be applied in particular to an IR-HARQ or a cooperative network using a non-binary code, in particular a non-binary LDPC code.

Abstract: A device and method for the iterative decoding of a received word represented by signal values according to a parity control matrix code of the type for passing messages between variable nodes and control nodes of a two-part graph related to the matrix.