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On Asymptotic Strategies for GMD Decoding with Arbitrary Error-Erasure Tradeoff

Abstract : Consider a block code C of length n with Hamming distance d. Assume we have a decoder Φ, which corrects e errors and t erasures, as soon as λe + t ≤ d − 1, where the real number 1 < λ ≤ 2 is the error-erasure tradeoff of the decoder Φ. In the classical case of bounded minimum distance decoder we have λ = 2, while smaller values of λ arise in decoding, e.g., interleaved or folded Reed–Solomon codes, as well as in algebraic decoding algorithms like Sudan or Guruswami–Sudan. Given a word r with reliabilities of symbols, the goal of generalized minimum distance (GMD) decoding is to find a nearest codeword c ∈ C in generalized Hamming metric, defined by these reliabilities. We use multi-trial GMD Forney's decoder, which at every trial applies Φ to decode r, where some low reliable symbols are erased. We investigate different erasing strategies based on either erasing a fraction of the received symbols or erasing all symbols whose reliability values are below a certain threshold. The erasing strategy may be either static or adaptive, where adaptive means that the erasing parameters are a function of the reliabilities. For every strategy we propose an optimal set of parameters and evaluate the error-correction radius of m-trial GMD decoder defined by each strategy. We use an asymptotic approach, i.e., large n, which drastically simplifies the analysis and presentation of the results over existing literature.
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https://hal.inria.fr/hal-01276219
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Joschi Brauchle, Vladimir Sidorenko. On Asymptotic Strategies for GMD Decoding with Arbitrary Error-Erasure Tradeoff. WCC2015 - 9th International Workshop on Coding and Cryptography 2015, Anne Canteaut, Gaëtan Leurent, Maria Naya-Plasencia, Apr 2015, Paris, France. ⟨hal-01276219⟩

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