TY - GEN

T1 - On extended fomey-kovalev GMD decoding

AU - Sidorenko, Vladimir R.

AU - Chaaban, Anas

AU - Senger, Christian

AU - Bossert, Martin

PY - 2009

Y1 - 2009

N2 - Consider a code C with Hamming distance d. Assume we have a decoder Φ that corrects ε errors and θ erasures if λε+θ ≤ d - 1, where a real number 1 < λ ≤ 2 is the tradeoff rate between errors and erasures for this decoder. This holds e.g, for l-punctured Reed-Solomon codes, i.e., codes over the field Fql of length n < q with locators taken from the subfield Fq, where l ε {1, 2, ⋯} and λ = 1+1/l. We propose an m-trial generalized minimum distance (GMD) decoder based on Φ. Our approach extends results of Forney and Kovalev (obtained for λ = 2) to the whole given range of λ. We consider both fixed erasing and adaptive erasing GMD strategies. For l > 1 the following approximations hold. For the fixed erasing strategy the error correcting radius is PF ≈ d/2(1 - l-m/2). For the adaptive erasing strategy, PA ≈ d/2(1 - l-2m) quickly approaches d/2 if l or m grows. The minimum number of decoding trials required to reach an error correcting radius d/2 is mA = 1/2 (logl d + 1). This means that 2 or 3 trials are sufficient to reach PA = d/2 in many practical cases if l > J.

AB - Consider a code C with Hamming distance d. Assume we have a decoder Φ that corrects ε errors and θ erasures if λε+θ ≤ d - 1, where a real number 1 < λ ≤ 2 is the tradeoff rate between errors and erasures for this decoder. This holds e.g, for l-punctured Reed-Solomon codes, i.e., codes over the field Fql of length n < q with locators taken from the subfield Fq, where l ε {1, 2, ⋯} and λ = 1+1/l. We propose an m-trial generalized minimum distance (GMD) decoder based on Φ. Our approach extends results of Forney and Kovalev (obtained for λ = 2) to the whole given range of λ. We consider both fixed erasing and adaptive erasing GMD strategies. For l > 1 the following approximations hold. For the fixed erasing strategy the error correcting radius is PF ≈ d/2(1 - l-m/2). For the adaptive erasing strategy, PA ≈ d/2(1 - l-2m) quickly approaches d/2 if l or m grows. The minimum number of decoding trials required to reach an error correcting radius d/2 is mA = 1/2 (logl d + 1). This means that 2 or 3 trials are sufficient to reach PA = d/2 in many practical cases if l > J.

UR - http://www.scopus.com/inward/record.url?scp=70449504844&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2009.5205900

DO - 10.1109/ISIT.2009.5205900

M3 - Conference contribution

AN - SCOPUS:70449504844

SN - 9781424443130

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 1393

EP - 1397

BT - 2009 IEEE International Symposium on Information Theory, ISIT 2009

T2 - 2009 IEEE International Symposium on Information Theory, ISIT 2009

Y2 - 28 June 2009 through 3 July 2009

ER -