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Sequential decoding
About: Sequential decoding is a research topic. Over the lifetime, 8667 publications have been published within this topic receiving 204271 citations.
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TL;DR: The last part of a three-part series on threshold decoding new convolutional codes concludes the list with new rate 1/2 codes and suggests the concatenation of such codes based upon the uncorrectable error statistics of the decoder.
Abstract: This paper is the last part of a three-part series on threshold decoding new convolutional codes. The first part of this paper concludes the list with new rate 1/2 codes. For these codes a characteristic equation, in terms of the number of correctable errors and code constraint length, is derived by least square approximations. The second part of the paper is concerned with the usefulness of the codes derived including those in Parts I and II. Based upon the uncorrectable error statistics of the decoder, the concatenation of such codes is suggested. The characteristic of this class of codes with the property of not producing additional and bursty errors at the output of the decoder when the capability of the decoder is exceeded, is not shared by most powerful decoders such as Reed-Solomon, BCH, and Viterbi.
54 citations
TL;DR: The design of a communications system consisting of a sequential encoder-decoder, working in conjunction with a modulation-detection system is considered from the point of view of high-information transmission efficiency and emphasis is placed on M orthogonal signal modulation and a scheme known as list-of- l quantization.
Abstract: The design of a communications system consisting of a sequential encoder-decoder, working in conjunction with a modulation-detection system is considered from the point of view of high-information transmission efficiency. Emphasis is placed on M orthogonal signal modulation and a scheme known as list-of- l quantization. The results of a computer study of the computational behavior of the sequential decoder are described and used to predict buffer memory overflow probability. The described design procedure allows prediction of system performance to within a fraction of a decibel. A practical sequential decoder and a list-of- l modulation-detection system of reasonable complexity, can achieve performance on a white Gaussian channel to within 4.5 dB of the Shannon limit with coherent reception and to within 7 dB with incoherent reception.
54 citations
TL;DR: A recursive decoding algorithm is designed and its decoding threshold is derived for long RM codes and it corrects most error patterns of the Euclidean weight of order radicn/lnn, instead of the decoding threshold radicd/2 of the bounded distance decoding.
Abstract: Soft-decision decoding is considered for general Reed-Muller (RM) codes of length n and distance d used over a memoryless channel. A recursive decoding algorithm is designed and its decoding threshold is derived for long RM codes. The algorithm has complexity of order nlnn and corrects most error patterns of the Euclidean weight of order radicn/lnn, instead of the decoding threshold radicd/2 of the bounded distance decoding. Also, for long RM codes of fixed rate R, the new algorithm increases 4/pi times the decoding threshold of its hard-decision counterpart
54 citations
07 Jul 2013
TL;DR: In this article, the theory of rank metric and Gabidulin codes is transposed to the case of fields of characteristic zero and the Frobenius automorphism is replaced by any element of the Galois group.
Abstract: We transpose the theory of rank metric and Gabidulin codes to the case of fields of characteristic zero. The Frobenius automorphism is then replaced by any element of the Galois group. We derive some conditions on the automorphism to be able to easily transpose the results obtained by Gabidulin as well and a classical polynomial-time decoding algorithm. We also provide various definitions for the rank-metric.
54 citations
03 Oct 2011
TL;DR: This work considers the decoding of spatially coupled codes through a windowed decoder that aims to retain many of the attractive features of belief propagation, while trying to reduce complexity further, by defining thresholds on channel erasure rates that guarantee a target erasure rate.
Abstract: We study windowed decoding of spatially coupled codes when the transmission occurs over the binary erasure channel. We characterize the performance of this scheme by defining thresholds on channel erasure rates that guarantee a target bit erasure rate. We give analytical lower bounds on these thresholds and show that the performance approaches that of belief propagation exponentially fast in the window size. We give numerical results including the thresholds computed using density evolution and the erasure rate curves for finite-length spatially coupled codes.
54 citations