Soft-decision decoding of Reed-Muller codes: A simplified algorithm

被引：25

作者：

Dumer, I ^{[1
]}

机构：

[1] Univ Calif Riverside, Coll Engn, Riverside, CA 92521 USA

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2006年 / 52卷 / 03期

基金：

美国国家科学基金会;

关键词：

decoding threshold; memoryless channel; Plotkin construction; recursive decoding; Reed-Muller (RM) codes;

D O I：

10.1109/TIT.2005.864425

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Soft-decision decoding is considered for general Reed-Muller (RM) codes of length n and distance d used over a memoryless channel. A recursive decoding algorithm is designed and its decoding threshold is derived for long RM codes. The algorithm has complexity of order n In n and corrects most error patterns of the Euclidean weight of order root n/ln n, instead of the decoding threshold root d/2 of the bounded distance decoding. Also, for long RM codes of fixed rate R, the new algorithm increases 4/pi times the decoding threshold of its hard-decision counterpart.

引用

页码：954 / 963

页数：10

共 14 条

[1] Simple MAP decoding of first-order Reed-Muller and hamming codes
Ashikhmin, A
Litsyn, S
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2004, 50 (08) : 1812 - 1818
[2] Recursive error correction for general Reed-Muller codes
Dumer, I
Shabunov, K
[J]. DISCRETE APPLIED MATHEMATICS, 2006, 154 (02) : 253 - 269
[3] Recursive decoding and its performance for low-rate Reed-Muller codes
Dumer, I
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2004, 50 (05) : 811 - 823
[4] Soft-decision majority decoding of Reed-Muller codes
Dumer, I
Krichevskiy, R
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2000, 46 (01) : 258 - 264
[5] Feller W., 1991, An Introduction to Probability Theory and Its Applications, VII
[6] CLOSEST COSET DECODING OF (U)(U + V) CODES
HEMMATI, F
[J]. IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, 1989, 7 (06) : 982 - 988
[7] PROBABILITY-INEQUALITIES FOR SUMS OF BOUNDED RANDOM-VARIABLES
HOEFFDING, W
[J]. JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 1963, 58 (301) : 13 - +
[8] KABATYANSKII GA, 1990, P 2 INT WORKSH ALG C, P87
[9] KRICHEVSKIY RE, 1970, DOKL SOVIET ACAD SCI, V191, P541
[10] Litsyn S., 1988, PROC 9 UNION C CODIN, P202

← 1 2 →