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List decoding
About: List decoding is a research topic. Over the lifetime, 7251 publications have been published within this topic receiving 151182 citations.
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TL;DR: In this paper, the authors review factor graphs, which can be used to describe codes and the joint probability distributions that must be dealt with in decoding, and show how this algorithm leads to iterative decoding algorithms for codes defined on graphs.
Abstract: Low-density parity-check codes, turbo codes, and indeed most practically decodable capacity-approaching error correcting codes can all be understood as codes defined on graphs. Graphs not only describe the codes, but, more important, they structure the operation of the sum-product decoding algorithm (or one of many possible variations), which can be used for iterative decoding. Such coding schemes have the potential to approach channel capacity, while maintaining reasonable decoding complexity. In this tutorial article we review factor graphs, which can be used to describe codes and the joint probability distributions that must be dealt with in decoding. We also review the sum-product algorithm, and show how this algorithm leads to iterative decoding algorithms for codes defined on graphs.
71 citations
TL;DR: A generalized Euclidean algorithm, which is based on a generalized polynomial division algorithm, is presented and it is shown that the algorithm can be applied to the decoding of many cyclic codes for which multiple syndrome sequences are available.
Abstract: The problem of finding a linear-feedback shift register of shortest length capable of generating prescribed multiple sequences is considered. A generalized Euclidean algorithm, which is based on a generalized polynomial division algorithm, is presented. A necessary and sufficient condition for the uniqueness of the solution is given. When the solution is not unique, the set of all possible solutions is also derived. It is shown that the algorithm can be applied to the decoding of many cyclic codes for which multiple syndrome sequences are available. When it is applied to the case of a single sequence, the algorithm reduces to that introduced by Y. Sugiyama et al. (Inf. Control, vol.27, p.87-9, Feb. 1975) in the decoding of BCH codes. >
71 citations
24 Jun 2001
TL;DR: The paper describes inner and outer code doping to enable iterative decoding of serially concatenated codes (SCC) which use inner rate one recursive convolutional codes of memory greater than one.
Abstract: The paper describes inner and outer code doping to enable iterative decoding of serially concatenated codes (SCC) which use inner rate one recursive convolutional codes of memory greater than one.
71 citations
TL;DR: This work introduces exceptionally simple decoding algorithms for the two extended Golay codes based on recent methods of Conway and Curtis of finding the unique blocks containing five points in either the (5,8,24) Steiner system or the ( 5,6,12) Steiners system.
Abstract: We introduce exceptionally simple decoding algorithms for the two extended Golay codes The algorithms are based on recent methods of Conway and Curtis of finding the unique blocks containing five points in either the (5,8,24) Steiner system or the (5,6,12) Steiner system These decoding methods are simple enough to enable decoding extended Golay codes by hand Both of the methods involve relations between the extended Golay codes and other self-dual codes Proofs are given explaining these relationships and why the decoding methods work The decoding algorithms are explained and illustrated with many examples [3 , chap 12] has facts about the Mathieu group and some details about decoding the Golay codes
71 citations
Patent•
14 Nov 2006TL;DR: In this paper, a method, medium, and apparatus encoding and decoding an image in order to increase the decoding efficiency by performing binary-arithmetic coding/decoding on a binary value of a syntax element using a probability model having the same syntax element probability value for respective context index information of each of at least two image components.
Abstract: A method, medium, and apparatus encoding and/or decoding an image in order to increase encoding and decoding efficiency by performing binary-arithmetic coding/decoding on a binary value of a syntax element using a probability model having the same syntax element probability value for respective context index information of each of at least two image components.
71 citations