A Recursive Maximum Likelihood Decoding Algorithm for Some Transitive Invariant Binary Block Codes
Summary :
Recently, a trellis-based recursive maximum likelihood decoding (RMLD) algorithm has been proposed for decoding binary linear block codes. This RMLD algorithm is computationally more efficient than the Viterbi decoding algorithm. However, the computational complexity of the RMLD algorithm depends on the sectionalization of a code trellis. In general, minimization of the computational complexity results in non-uniform sectionalization of a code trellis. From implementation point of view, uniform sectionalization of a code trellis and regularity among the trellis sections are desirable. In this paper, we apply the RMLD algorithm to a class of codes which are transitive invariant. This class includes Reed-Muller (RM) codes, the extended and permuted BCH (EBCH) codes and their subcodes. For this class of codes, the binary uniform sectionalization of a code trellis results in the following regular structure. At each step of decoding recursion, the metric table construction procedure is applied uniformly to all the sections and the size and structure of each metric table are the same. This simplifies the implementation of the RMLD algorithm. Furthermore, for all RM codes of lengths 64 and 128 and EBCH codes of lengths 64 and 128 with relatively low rate, the computational complexity of the RMLD algorithm based on the binary uniform sectionalization of a code trellis is almost the same as that based on an optimum sectionalization of a code trellis.
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- IEICE TRANSACTIONS on Fundamentals Vol.E81-A No.9 pp.1916-1924
- Publication Date
- 1998/09/25
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- Information Theory and Coding Theory
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Tadao KASAMI, Hitoshi TOKUSHIGE, Toru FUJIWARA, Hiroshi YAMAMOTO, Shu LIN, "A Recursive Maximum Likelihood Decoding Algorithm for Some Transitive Invariant Binary Block Codes" in IEICE TRANSACTIONS on Fundamentals,
vol. E81-A, no. 9, pp. 1916-1924, September 1998, doi: .
Abstract: Recently, a trellis-based recursive maximum likelihood decoding (RMLD) algorithm has been proposed for decoding binary linear block codes. This RMLD algorithm is computationally more efficient than the Viterbi decoding algorithm. However, the computational complexity of the RMLD algorithm depends on the sectionalization of a code trellis. In general, minimization of the computational complexity results in non-uniform sectionalization of a code trellis. From implementation point of view, uniform sectionalization of a code trellis and regularity among the trellis sections are desirable. In this paper, we apply the RMLD algorithm to a class of codes which are transitive invariant. This class includes Reed-Muller (RM) codes, the extended and permuted BCH (EBCH) codes and their subcodes. For this class of codes, the binary uniform sectionalization of a code trellis results in the following regular structure. At each step of decoding recursion, the metric table construction procedure is applied uniformly to all the sections and the size and structure of each metric table are the same. This simplifies the implementation of the RMLD algorithm. Furthermore, for all RM codes of lengths 64 and 128 and EBCH codes of lengths 64 and 128 with relatively low rate, the computational complexity of the RMLD algorithm based on the binary uniform sectionalization of a code trellis is almost the same as that based on an optimum sectionalization of a code trellis.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e81-a_9_1916/_p
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@ARTICLE{e81-a_9_1916,
author={Tadao KASAMI, Hitoshi TOKUSHIGE, Toru FUJIWARA, Hiroshi YAMAMOTO, Shu LIN, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Recursive Maximum Likelihood Decoding Algorithm for Some Transitive Invariant Binary Block Codes},
year={1998},
volume={E81-A},
number={9},
pages={1916-1924},
abstract={Recently, a trellis-based recursive maximum likelihood decoding (RMLD) algorithm has been proposed for decoding binary linear block codes. This RMLD algorithm is computationally more efficient than the Viterbi decoding algorithm. However, the computational complexity of the RMLD algorithm depends on the sectionalization of a code trellis. In general, minimization of the computational complexity results in non-uniform sectionalization of a code trellis. From implementation point of view, uniform sectionalization of a code trellis and regularity among the trellis sections are desirable. In this paper, we apply the RMLD algorithm to a class of codes which are transitive invariant. This class includes Reed-Muller (RM) codes, the extended and permuted BCH (EBCH) codes and their subcodes. For this class of codes, the binary uniform sectionalization of a code trellis results in the following regular structure. At each step of decoding recursion, the metric table construction procedure is applied uniformly to all the sections and the size and structure of each metric table are the same. This simplifies the implementation of the RMLD algorithm. Furthermore, for all RM codes of lengths 64 and 128 and EBCH codes of lengths 64 and 128 with relatively low rate, the computational complexity of the RMLD algorithm based on the binary uniform sectionalization of a code trellis is almost the same as that based on an optimum sectionalization of a code trellis.},
keywords={},
doi={},
ISSN={},
month={September},}
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TY - JOUR
TI - A Recursive Maximum Likelihood Decoding Algorithm for Some Transitive Invariant Binary Block Codes
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1916
EP - 1924
AU - Tadao KASAMI
AU - Hitoshi TOKUSHIGE
AU - Toru FUJIWARA
AU - Hiroshi YAMAMOTO
AU - Shu LIN
PY - 1998
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E81-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 1998
AB - Recently, a trellis-based recursive maximum likelihood decoding (RMLD) algorithm has been proposed for decoding binary linear block codes. This RMLD algorithm is computationally more efficient than the Viterbi decoding algorithm. However, the computational complexity of the RMLD algorithm depends on the sectionalization of a code trellis. In general, minimization of the computational complexity results in non-uniform sectionalization of a code trellis. From implementation point of view, uniform sectionalization of a code trellis and regularity among the trellis sections are desirable. In this paper, we apply the RMLD algorithm to a class of codes which are transitive invariant. This class includes Reed-Muller (RM) codes, the extended and permuted BCH (EBCH) codes and their subcodes. For this class of codes, the binary uniform sectionalization of a code trellis results in the following regular structure. At each step of decoding recursion, the metric table construction procedure is applied uniformly to all the sections and the size and structure of each metric table are the same. This simplifies the implementation of the RMLD algorithm. Furthermore, for all RM codes of lengths 64 and 128 and EBCH codes of lengths 64 and 128 with relatively low rate, the computational complexity of the RMLD algorithm based on the binary uniform sectionalization of a code trellis is almost the same as that based on an optimum sectionalization of a code trellis.
ER -
English
