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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An upper bound on the effective error coefficient of two-stage decoding, and good two-level decompositions of some Reed-Muller codes
TL;DR: An upper bound on the effective error coefficient of a two-level code with two-stage decoding is presented and this bound provides a guideline for constructing two- level codes to achieve a good trade-off between the error performance and decoding complexity.
Journal ArticleDOI
The Extraction and Complexity Limits of Graphical Models for Linear Codes
Thomas R. Halford,Keith M. Chugg +1 more
TL;DR: In this paper, a generalization of the square root bound for tree-biting trellises to graphical models with arbitrary cyclic topologies is proposed. But the work is focused on extractive graphical model problems and aims to lay out some of the foundations of such problems for linear codes.
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Higher Hamming weights for locally recoverable codes on algebraic curves
Edoardo Ballico,Chiara Marcolla +1 more
TL;DR: In this paper, a new family of algebraic geometric LRC codes from the Norm-Trace curve is proposed, which is based on the Hermitian LRC code, and a bound on the generalized Hamming weight of these codes is given.
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Generalized Bezout's theorem and its applications in coding theory
TL;DR: A new approach to determine a lower bound on the minimum distance for algebraic-geometric codes defined from a class of plane curves is introduced, based on the generalized Bezout theorem.
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On bit-error probability of a concatenated coding scheme
TL;DR: In this paper, the bit-error probability of a concatenated coding system for BPSK transmission over the AWGN channel was evaluated by a combination of simulation and analysis.
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.