منابع مشابه
Almost disjunctive list-decoding codes
Abstract. A binary code is said to be a disjunctive list-decoding sL-code, s ≥ 1, L ≥ 1, (briefly, LD sL-code) if the code is identified by the incidence matrix of a family of finite sets in which the union of any s sets can cover not more than L− 1 other sets of the family. In this paper, we introduce a natural probabilistic generalization of LD sL-code when the code is said to be an almost di...
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We study the list-decodability of multiplicity codes. These codes, which are based on evaluations of high-degree polynomials and their derivatives, have rate approaching 1 while simultaneously allowing for sublinear-time error-correction. In this paper, we show that multiplicity codes also admit powerful list-decoding and local list-decoding algorithms correcting a large fraction of errors. Sta...
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We briefly survey some recent progress on list decoding algorithms for binary codes. The results discussed include: – Algorithms to list decode binary Reed-Muller codes of any order up to the minimum distance, generalizing the classical GoldreichLevin algorithm for RM codes of order 1 (Hadamard codes). These algorithms are “local” and run in time polynomial in the message length. – Construction...
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Codes constructed as subsets of the projective geometry of a vector space over a finite field have recently been shown to have applications as unconditionally secure authentication codes and random network error correcting codes. If the dimension of each codeword is restricted to a fixed integer, the code forms a subset of a finite-field Grassmannian, or equivalently, a subset of the vertices o...
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List decoding of turbo codes is analyzed under the assumption of a maximum-likelihood (ML) list decoder. It is shown that large asymptotic gains can be achieved on both the additive white Gaussian noise (AWGN) and fully interleaved flat Rayleigh-fading channels. It is also shown that the relative asymptotic gains for turbo codes are larger than those for convolutional codes. Finally, a practica...
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ژورنال
عنوان ژورنال: Designs, Codes and Cryptography
سال: 2016
ISSN: 0925-1022,1573-7586
DOI: 10.1007/s10623-016-0278-4