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Title: "ON ALGEBRAIC DECODING OF Q-ARY REED-MULLER AND PRODUCT REED-SOLOMON CODES"

Abstract

We consider a list decoding algorithm recently proposed by Pellikaan-Wu for q-ary Reed-Muller codes RM{sub q}({ell}, m, n) of length n {le} q{sup m} when {ell} {le} q. A simple and easily accessible correctness proof is given which shows that this algorithm achieves a relative error-correction radius of {tau} {le} (1-{radical}{ell}q{sup m-1}/n). This is an improvement over the proof using one-point Algebraic-Geometric decoding method given in. The described algorithm can be adapted to decode product Reed-Solomon codes. We then propose a new low complexity recursive aJgebraic decoding algorithm for product Reed-Solomon codes and Reed-Muller codes. This algorithm achieves a relative error correction radius of {tau} {le} {Pi}{sub i=1}{sup m} (1 - {radical}k{sub i}/q). This algorithm is then proved to outperform the Pellikaan-Wu algorithm in both complexity and error correction radius over a wide range of code rates.

Authors:
 [1]
  1. Los Alamos National Laboratory
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
OSTI Identifier:
984531
Report Number(s):
LA-UR-07-0469
TRN: US201016%%1377
DOE Contract Number:
AC52-06NA25396
Resource Type:
Conference
Resource Relation:
Conference: ISIT 2007 ; 200706 ; NICE
Country of Publication:
United States
Language:
English
Subject:
99; ALGORITHMS; ALGEBRA; LANL; COMPUTERS

Citation Formats

SANTHI, NANDAKISHORE. "ON ALGEBRAIC DECODING OF Q-ARY REED-MULLER AND PRODUCT REED-SOLOMON CODES". United States: N. p., 2007. Web.
SANTHI, NANDAKISHORE. "ON ALGEBRAIC DECODING OF Q-ARY REED-MULLER AND PRODUCT REED-SOLOMON CODES". United States.
SANTHI, NANDAKISHORE. Mon . ""ON ALGEBRAIC DECODING OF Q-ARY REED-MULLER AND PRODUCT REED-SOLOMON CODES"". United States. doi:. https://www.osti.gov/servlets/purl/984531.
@article{osti_984531,
title = {"ON ALGEBRAIC DECODING OF Q-ARY REED-MULLER AND PRODUCT REED-SOLOMON CODES"},
author = {SANTHI, NANDAKISHORE},
abstractNote = {We consider a list decoding algorithm recently proposed by Pellikaan-Wu for q-ary Reed-Muller codes RM{sub q}({ell}, m, n) of length n {le} q{sup m} when {ell} {le} q. A simple and easily accessible correctness proof is given which shows that this algorithm achieves a relative error-correction radius of {tau} {le} (1-{radical}{ell}q{sup m-1}/n). This is an improvement over the proof using one-point Algebraic-Geometric decoding method given in. The described algorithm can be adapted to decode product Reed-Solomon codes. We then propose a new low complexity recursive aJgebraic decoding algorithm for product Reed-Solomon codes and Reed-Muller codes. This algorithm achieves a relative error correction radius of {tau} {le} {Pi}{sub i=1}{sup m} (1 - {radical}k{sub i}/q). This algorithm is then proved to outperform the Pellikaan-Wu algorithm in both complexity and error correction radius over a wide range of code rates.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Mon Jan 22 00:00:00 EST 2007},
month = {Mon Jan 22 00:00:00 EST 2007}
}

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