Topic
Sequential decoding
About: Sequential decoding is a research topic. Over the lifetime, 8667 publications have been published within this topic receiving 204271 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: An erasures-and-errors decoding algorithm for Goppa codes is presented, where a modified key equation is solved using Euclid's algorithm to determine the error locator polynomial and the errata evaluatorPolynomial.
Abstract: An erasures-and-errors decoding algorithm for Goppa codes is presented. Given the Goppa polynomial and the modified syndrome polynomial, a modified key equation is solved using Euclid's algorithm to determine the error locator polynomial and the errata evaluator polynomial.
51 citations
TL;DR: It will be shown that the proposed incremental Gaussian elimination decoding significantly improves on the decoding time over the usual Gaussian Elimination decoding while maintaining the same decoding performance.
Abstract: In this letter, we investigate an efficient Gaussian elimination decoding scheme of Raptor codes used over the binary erasure channel. It will be shown that the proposed incremental Gaussian elimination decoding significantly improves on the decoding time over the usual Gaussian elimination decoding while maintaining the same decoding performance.
51 citations
TL;DR: The implementation of such complete reconstruction for convolutional codes of any rate is presented, for both noiseless and noisy communications, and yields a new characterization of convolutionAL codes along with some properties.
Abstract: Assuming we only have the coded sequence produced by a convolutional encoder at one's disposal, is it possible to recover all the parameters defining this encoder ? The implementation of such complete reconstruction for convolutional codes of any rate is presented in this paper, for both noiseless and noisy communications. Each time, several different solutions, i.e. alleged reconstructed encoders, are obtained, contrary to the awaited unicity. Their study yields a new characterization of convolutional codes along with some properties.
51 citations
TL;DR: In this article, the minimum distance of matrix-product codes was computed and a decoding algorithm for non-singular by columns matrix was proposed. But the decoding algorithm only decodes up to half of the required minimum distance.
Abstract: We consider matrix-product codes $${[C_1\cdots C_s] \cdot A}$$, where $${C_1, \ldots , C_s}$$are nested linear codes and matrix A has full rank. We compute their minimum distance and provide a decoding algorithm when A is a non-singular by columns matrix. The decoding algorithm decodes up to half of the minimum distance.
51 citations
TL;DR: Using the close relationship between guessing and sequential decoding, a tight lower bound is given to the complexity of sequential decoding in joint source-channel coding systems, complementing earlier works by Koshelev and Hellman.
Abstract: We extend our earlier work on guessing subject to distortion to the joint source-channel coding context. We consider a system in which there is a source connected to a destination via a channel and the goal is to reconstruct the source output at the destination within a prescribed distortion level with respect to (w.r.t.) some distortion measure. The decoder is a guessing decoder in the sense that it is allowed to generate successive estimates of the source output until the distortion criterion is met. The problem is to design the encoder and the decoder so as to minimize the average number of estimates until successful reconstruction. We derive estimates on nonnegative moments of the number of guesses, which are asymptotically tight as the length of the source block goes to infinity. Using the close relationship between guessing and sequential decoding, we give a tight lower bound to the complexity of sequential decoding in joint source-channel coding systems, complementing earlier works by Koshelev (1973) and Hellman (1975). Another topic explored here is the probability of error for list decoders with exponential list sizes for joint source-channel coding systems, for which we obtain tight bounds as well. It is noteworthy that optimal performance w.r.t. the performance measures considered here can be achieved in a manner that separates source coding and channel coding.
51 citations