On Asymptotic Strategies for GMD Decoding with Arbitrary Error-Erasure Tradeoff
Résumé
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.
Domaines
Théorie de l'information [cs.IT]
Origine : Fichiers produits par l'(les) auteur(s)
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