Sequential decoding

About: Sequential decoding is a research topic. Over the lifetime, 8667 publications have been published within this topic receiving 204271 citations.

Minimal permutation sets for decoding the binary Golay codes (Corresp.)

Abstract: For permutation decoding of an e error-correcting linear code, a set of permutations which move all error vectors of weight \leq e out of the information places is needed. A method of finding minimal decoding sets is given, along with minimal sets obtained with this method for the binary Golay codes.

Algebraic-geometric codes and multidimensional cyclic codes: a unified theory and algorithms for decoding using Grobner bases

Abstract: It is proved that any algebraic-geometric (AG) code can be expressed as a cross section of an extended multidimensional cyclic code. Both AG codes and multidimensional cyclic codes are described by a unified theory of linear block codes defined over point sets: AG codes are defined over the points of an algebraic curve, and an m-dimensional cyclic code is defined over the points in m-dimensional space. The power of the unified theory is in its description of decoding techniques using Grobner bases. In order to fit an AG code into this theory, a change of coordinates must be applied to the curve over which the code is defined so that the curve is in special position. For curves in special position, all computations can be performed with polynomials and this also makes it possible to use the theory of Grobner bases. Next, a transform is defined for AG codes which generalizes the discrete Fourier transform. The transform is also related to a Grobner basis, and is useful in setting up the decoding problem. In the decoding problem, a key step is finding a Grobner basis for an error locator ideal. For AG codes, multidimensional cyclic codes, and indeed, any cross section of an extended multidimensional cyclic code, Sakata's algorithm can be used to find linear recursion relations which hold on the syndrome array. In this general context, the authors give a self-contained and simplified presentation of Sakata's algorithm, and present a general framework for decoding algorithms for this family of codes, in which the use of Sakata's algorithm is supplemented by a procedure for extending the syndrome array.

Iterative decoding of multi-dimensional concatenated single parity check codes

Abstract: This paper is concerned with the decoding technique and performance of multi-dimensional concatenated single-parity-check (SPC) code. A very efficient sub-optimal soft-in-soft-out decoding rule is presented for the SPC code, costing only 3 addition-equivalent-operations per information bit. Multi-dimensional concatenated coding and decoding principles are investigated. Simulation results of rate 5/6 and 4/5 3-dimensional concatenated SPC codes are provided. Performance of BER=10/sup -4/-10/sup -5/ can be achieved by the MAP and max-log-MAP decoders, respectively, with E/sub b//N/sub 0/ only 1 and 1.5 dB away from the theoretical limits.

On the fly gaussian elimination for LT codes

Abstract: We propose an improved algorithm for decoding LT codes using Gaussian elimination. Our algorithm performs useful processing at each coded packet arrival thus distributing the decoding work during all packets reception, obtaining a shorter actual decoding time. Furthermore, using a swap heuristic the decoding matrix is kept sparse, decreasing the cost of both triangularization and back-substitution steps.

The Cryptographic Security of the Syndrome Decoding Problem for Rank Distance Codes

Abstract: We present an algorithm that achieves general syndrome decoding of a (n, k, r) linear rank distance code over GF(q m ) in O(nr + m)3q(m−r)(r−1)) elementary operations. As a consequence, the cryptographical schemes [Che94, Che96] which rely on this problem are not secure with the proposed parameters. We also derive from our algorithm a bound on the minimal rank distance of a linear code which shows that the parameters from [Che94] are inconsistent.