On extended fomey-kovalev GMD decoding

Vladimir R. Sidorenko, Anas Chaaban, Christian Senger, Martin Bossert

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

7 Citations (Scopus)

Abstract

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.

Original languageEnglish
Title of host publication2009 IEEE International Symposium on Information Theory, ISIT 2009
Pages1393-1397
Number of pages5
DOIs
Publication statusPublished - 2009
Externally publishedYes
Event2009 IEEE International Symposium on Information Theory, ISIT 2009 - Seoul, Korea, Republic of
Duration: 28 Jun 20093 Jul 2009

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8102

Conference

Conference2009 IEEE International Symposium on Information Theory, ISIT 2009
Country/TerritoryKorea, Republic of
CitySeoul
Period28/06/093/07/09

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