On complexity of trellis structure of linear block codes
Tadao Kasami,T. Takata,Toru Fujiwara,Shu Lin +3 more
- Vol. 39, Iss: 3, pp 1057-1064
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TLDR
An upper bound on the number of states of a minimal trellis diagram for a linear block code is derived and a cyclic code or its extended code is shown to be the worst in terms of Trellis state complexity among the linear codes of the same length and dimension.Abstract:
An upper bound on the number of states of a minimal trellis diagram for a linear block code is derived. Using this derivation a cyclic (or shortened cyclic) code or its extended code is shown to be the worst in terms of trellis state complexity among the linear codes of the same length and dimension. The complexity of the minimal trellis diagrams for linear block codes of length 2/sup m/, including the Reed-Muller codes, is analyzed. The construction of minimal trellis diagrams for some extended and permuted primitive BCH codes is presented. It is shown that these codes have considerably simpler trellis structure than the original codes in cyclic form without bit-position permutation. >read more
Citations
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Journal ArticleDOI
Maximum-likelihood soft decision decoding of BCH codes
Alexander Vardy,Yair Be'ery +1 more
TL;DR: The authors show that the same kind of direct-sum structure exists in all the primitive B CH codes, as well as in the BCH codes of composite block length, and introduce a related structure termed the "concurring-sum", and establish its existence in the primitive binary BCH code.
Journal ArticleDOI
On iterative soft-decision decoding of linear binary block codes and product codes
R. Lucas,M. Bossert,M. Breitbach +2 more
TL;DR: A decoding algorithm which only uses parity check vectors of minimum weight is proposed, which gives results close to soft decision maximum likelihood (SDML) decoding for many code classes like BCH codes.
Journal ArticleDOI
Space-time codes and concatenated channel codes for wireless communications
T.H. Liew,Lajos Hanzo +1 more
TL;DR: It is concluded that over the nondispersive or narrow-band fading channels, the best performance versus complexity tradeoff is constituted by Alamouti's twin-antenna block space-time code concatenated with turbo convolutional codes.
Journal ArticleDOI
New class of nonlinear systematic error detecting codes
TL;DR: A class of optimal nonlinear q-ary systematic robust codes (robust codes) minimizing over all (n, q/sup k/)-codes the maximum of Q(e) for nonzero e.
Journal ArticleDOI
Simple MAP decoding of first-order Reed-Muller and Hamming codes
Alexei Ashikhmin,Simon Litsyn +1 more
TL;DR: New MAP decoding algorithms for binary and nonbinary RM-1 and Hamming codes are presented, which have complexities proportional to q/sup 2/n log/sub q/n, where q is the alphabet size.
References
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Book
The Theory of Error-Correcting Codes
TL;DR: This book presents an introduction to BCH Codes and Finite Fields, and methods for Combining Codes, and discusses self-dual Codes and Invariant Theory, as well as nonlinear Codes, Hadamard Matrices, Designs and the Golay Code.
Book
Error control coding : fundamentals and applications
Shu Lin,Daniel J. Costello +1 more
TL;DR: This book explains coding for Reliable Digital Transmission and Storage using Trellis-Based Soft-Decision Decoding Algorithms for Linear Block Codes and Convolutional Codes, and some of the techniques used in this work.
Journal ArticleDOI
Efficient Modulation for Band-Limited Channels
TL;DR: This paper attempts to present a comprehensive tutorial survey of the development of efficient modulation techniques for bandlimited channels, such as telephone channels, with principal emphasis on coded modulation techniques, in which there is an explosion of current interest.
Journal ArticleDOI
Generalized Hamming weights for linear codes
TL;DR: By viewing the minimum Hamming weight as a certain minimum property of one-dimensional subcodes, a generalized notion of higher-dimensional Hamming weights is obtained, which characterize the code performance on the wire-tap channel of type II.