Commissariat &#xc0; L'&#xc9;nergie Atomique Et Aux &#xc9;nergies Alternatives

Commissariat a L'energie Atomique

Cy Cergy Paris Universite

Université De Bretagne Sud

Ecole Nationale Superieure De L'elecronique Et De Ses Applications (ensea)

Politechnica University of Timisoara

Ecole Nationale Superieure De L'electronique Et Applications(ensea)

Eutelsat S a

Université De Cergy Pontoise

Ensea - Ecole Nationale Supérieure De L'electronique Et De Ses Applications

Valentin Savin

David Declercq

Emmanuel Boutillon

Mathieu Bouvier Des Noes

Dimitri Ktenas

Lam Pham Sy

Sangjun Lee

Oana Boncalo

Ludovic Chandesris

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.

Method for decoding colour codes over a quantum erasure channel

The invention relates to the transmission and reception of non-binary error correcting code words. The transmission method includes a first modulation () 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 () further implements an association between each code word symbol and a sequence of the set of sequences wherein said finite field GFhas 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.

Methods and devices for transmitting and receiving non-binary error correcting code words

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)}) 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 () 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.

Method for decoding inertia-effect bit-flip LDPC codes

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.

Method for decoding a polar code with inversion of unreliable bits

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 (H) 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 (s) is satisfied for at least a couple of consecutive layers.

Stopping criterion for decoding Quasi-Cyclic LDPC codes

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 (), a multiplication step for the sequence of samples obtained with the first M-sequence () and an iterative decoding step for the decoded values () 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 (), the receiver is synchronized with this satellite at said given time ().

Method of acquiring a GPS signal by iterative decoding

The invention relates to a coding method with incremental redundancy in which it is determined () 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 () 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.

LDPC coding process with incremental redundancy

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 (&#x3b1;) as a message by said variable node to said control node relative to that transmitted (&#x3b1;) at the previous iteration, and in the event of a sign change, said extrinsic information is subjected to an amplitude reduction operation (F) before it is transmitted to the control node.

Message-passing and forced convergence decoding method

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.

Method for transmitting non-binary codes and decoding the same

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. The method includes at least the following steps: setting up at least one message of a variable node, according to the values, by an information representative of the ratio between the probability of having the most likely symbol at a position corresponding to the variable node and the probability of having the current symbol at the position; determining at least one message, relating to a determined symbol, of a control node to a determined variable node, as the selected minimal value, among the symbol sequences corresponding to the control node equation using the determined symbol at the determined variable node, by the maximal value of the messages received at the control node from variable nodes different from the determined variable node and each relating to the symbol associated with the different variable node in the sequence corresponding to the equation; and determining the messages of a variable node to a control node that relate to the whole set of symbols so that the minimal value of said messages is equal to zero.

Method and device for decoding LDPC codes and communication apparatus including such device

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: The invention also relates to a computer program designed to implement said decoding method.

Growing community of inventors

Grenoble, France

Valentin Savin