TY - GEN

T1 - Decoding Reed - Solomon codes beyond half the minimum distance using shift-register synthesis

AU - Schmidt, Georg

AU - Sidorenko, Vladimir

AU - Bossert, Martin

PY - 2006

Y1 - 2006

N2 - It is known, that Interleaved Reed-Solomon codes can be decoded algebraically beyond half the minimum distance using collaborative decoding strategies. Based on the same principles, we suggest a new effective algebraic decoding method, which is able to decode a single low rate Reed-Solomon code beyond half the minimum distance. This new algorithm is based on multi-sequence shift-register synthesis, and is able to correct errors within a correcting radius similar to the Sudan algorithm. In contrast to the Sudan algorithm, which may obtain a list of codewords, our algorithm yields a decoding failure if there does not exist a unique solution. However, the probability of such a failure is very small.

AB - It is known, that Interleaved Reed-Solomon codes can be decoded algebraically beyond half the minimum distance using collaborative decoding strategies. Based on the same principles, we suggest a new effective algebraic decoding method, which is able to decode a single low rate Reed-Solomon code beyond half the minimum distance. This new algorithm is based on multi-sequence shift-register synthesis, and is able to correct errors within a correcting radius similar to the Sudan algorithm. In contrast to the Sudan algorithm, which may obtain a list of codewords, our algorithm yields a decoding failure if there does not exist a unique solution. However, the probability of such a failure is very small.

UR - http://www.scopus.com/inward/record.url?scp=39049123289&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2006.261711

DO - 10.1109/ISIT.2006.261711

M3 - Conference contribution

AN - SCOPUS:39049123289

SN - 1424405041

SN - 9781424405046

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 459

EP - 463

BT - Proceedings - 2006 IEEE International Symposium on Information Theory, ISIT 2006

T2 - 2006 IEEE International Symposium on Information Theory, ISIT 2006

Y2 - 9 July 2006 through 14 July 2006

ER -