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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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
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Posted Content
A Goppa-like bound on the trellis state complexity of algebraic geometric codes
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TL;DR: In this paper, the trellis state complexity of a linear code of length n and dimension k was shown to be upper bounded by w(k,n-k), where k is the genus of the underlying curve.
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The weighted coordinates bound and trellis complexity of block codes and periodic packings
I. Reuven,Yair Be'ery +1 more
TL;DR: It is shown that any bounds on the trellis structure of block codes, and in particular, the bound presented in this work, are applicable to periodic packings, and that the new bound is limited to a given coordinate system.
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TL;DR: In this paper, a class of linear codes with good parameters is constructed in this correspondence, and it turns out that linear codes of this class are subcodes of the subfield sub codes of Goppa's geometry codes.
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.