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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Proceedings ArticleDOI
Adaptive nested trellis decoding for block codes
TL;DR: A new adaptive trellis decoding technique for block codes is proposed, based on an encoding technique which allows the design of almost all known linear codes together with their minimal trellises.
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Parity Check Codes for Second Order Diversity.
TL;DR: A diversity preserving hard decision decoding scheme for parity check codes (PCC) over Rayleigh fading channels and the proposed flip decoding scheme has linear complexity in the block length is proposed.
Dissertation
Improved error control techniques for data transmission
TL;DR: The work presented in this Thesis is intended to provide practical decoding algorithms which can be implemented in real systems and an algorithm by which near-optimum performance may be achieved with a complexity lower than the Viterbi algorithm.
Dissertation
Trellis decoding of Reed Solomon and related linear block codes
TL;DR: The aim is to construct a trellis from the generator matrix of a Reed-Solomon code and to show that apart from the historical Berlekamp Massey frequency domain techniques, other techniques usually reserved for convolutional code decoding can be successfully applied in the decoding process.
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Trellis Decoding For Qudit Stabilizer Codes And Its Application To Qubit Topological Codes
TL;DR: In this article, the authors further develop the theoretical framework for the quantum trellis decoder proposed by Ollivier and Tillich in 2006, and demonstrate the effectiveness of this approach numerically by natively decoding the rotated surface code and the 4.8/6.6 color code families on qubits for moderate distances without any concept of homology.
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.