Fast Decoding Algorithms for First Order Reed-Muller and Related Codes

Authors:
Alexey E. Ashikhmin;Simon N. Litsyn
Affiliations:
Institute for Problems of Information Transmission, Ermolovoy 19, Moscow, Russia;Department of Electrical Engineering-Systems, Tel Aviv University, Ramat Aviv 69978 Israel
Venue:
Designs, Codes and Cryptography
Year:
1996

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Abstract

Fast decoding algorithms for short codes based on modifications of maximum likelihood decoding algorithms of first order Reed-Muller codes are described. Only additions-subtractions, comparisons and absolute value calculations are used in the algorithms. Soft and hard decisions maximum likelihood decoding algorithms for first order Reed-Muller and the Nordstrom-Robinson codes with low complexity are proposed.