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Title: Erasure List-Decodable Codes From Random and Algebraic Geometry Codes
Authors: Ding, Yang
Jin, Lingfei
Xing, Chaoping
Keywords: Erasure codes; list decoding; algebraic geometry codes; generalized Hamming weights
Issue Date: 2014
Source: Ding, Y., Jin, L., & Xing, C. (2014). Erasure List-Decodable Codes From Random and Algebraic Geometry Codes. IEEE Transactions on Information Theory, 60(7), 3889-3894.
Series/Report no.: IEEE Transactions on Information Theory
Abstract: Erasure list decoding was introduced to correct a larger number of erasures by outputting a list of possible candidates. In this paper, we consider both random linear codes and algebraic geometry codes for list decoding from erasures. The contributions of this paper are twofold. First, for arbitrary 0 < R < 1 and ϵ > 0 (R and ϵ are independent), we show that with high probability a q-ary random linear code of rate R is an erasure list-decodable code with constant list size qO(1/ϵ) that can correct a fraction 1 - R - ϵ of erasures, i.e., a random linear code achieves the information-theoretic optimal tradeoff between information rate and fraction of erasures. Second, we show that algebraic geometry codes are good erasure list-decodable codes. Precisely speaking, a q-ary algebraic geometry code of rate R from the Garcia-Stichtenoth tower can correct 1 - R - (1/√q - 1) + (1/q) - ϵ fraction of erasures with list size O(1/ϵ). This improves the Johnson bound for erasures applied to algebraic geometry codes. Furthermore, list decoding of these algebraic geometry codes can be implemented in polynomial time. Note that the code alphabet size q in this paper is constant and independent of ϵ.
ISSN: 0018-9448
DOI: 10.1109/TIT.2014.2314468
Rights: © 2014 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The published version is available at: [].
Fulltext Permission: open
Fulltext Availability: With Fulltext
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