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

Author

Dumer, Ilya

Author_Institution

Coll. of Eng., Univ. of California, Riverside, CA

Volume

52

Issue

3

fYear

2006

fDate

3/1/2006 12:00:00 AM

Firstpage

954

Lastpage

963

Abstract

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 nlnn and corrects most error patterns of the Euclidean weight of order radicn/lnn, instead of the decoding threshold radicd/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

Keywords

Reed-Muller codes; channel coding; decoding; memoryless systems; recursive estimation; Euclidean weight; RM code; Reed-Muller code; bounded distance decoding; error pattern; memoryless channel; recursive decoding algorithm; soft-decision decoding; Algorithm design and analysis; Codes; Communication system control; Decoding; Error correction; Euclidean distance; Extraterrestrial measurements; Hamming distance; Memoryless systems; Decoding threshold; Plotkin construction; Reed–Muller (RM) codes; memoryless channel; recursive decoding;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2005.864425

Filename

1603764