IEEE Transactions on Information Theory
Multitrial decoding of concatenated codes using fixed thresholds
Problems of Information Transmission
Asymptotic single-trial strategies for GMD decoding with arbitrary error-erasure tradeoff
Problems of Information Transmission
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Consider a code C with Hamming distance d. Assume we have a decoder Φ that corrects Ɛ errors and θ erasures if λƐ + θ ≤ d - 1, where a real number 1 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 ơ {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 ρF ≈ d/2 (1-l-m/2). For the adaptive erasing strategy, ρA ≈ 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 (logld+1). This means that 2 or 3 trials are sufficient to reach ρA = d/2 in many practical cases if l 1.