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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Dissertation
Compound codes based on irregular graphs and their iterative decoding.
TL;DR: A new class of codes called Generalized Irregular Low-Density (GILD) parity-check codes are introduced, which are adapted from the previously known class of Generalized Low- Density (GLD) codes, which have a significant advantage over GLD codes in terms of encoding and decoding complexity.
Dissertation
Decoding complexity and trellis structure of lattices
TL;DR: The Kannan's algorithm, which is currently known as the fastest method for the decoding of a general lattice, is analyzed, and it is shown that it is a special case of a wider category of algorithms, called recursive cube search (RCS) algorithms, and tight upper and lower bounds are established on the decoding complexity of lattices.
Proceedings ArticleDOI
The state complexity of trellis diagrams for a class of generalized concatenated codes
TL;DR: This work constructs several decomposable codes for which a multistage decoding up to the minimum distance can be employed and discusses the state complexity of trellis diagrams for a class of generalized concatenated codes.
Patent
Method and apparatus for MAP decoding of first-order reed muller codes and related error correction codes
TL;DR: In this article, a MAP decoding algorithm for Reed-Muller error correction codes is presented. But the complexity of the algorithm is proportional to n log q n for the decoding of the Reed-muller codes, which is exponential for general code sets.
Proceedings 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 first order Reed-Muller and Hamming codes are presented and complexities are proportional to n/spl times/log/sub 2/(n), where n is the code length.
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.