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Almost disjunctive list-decoding codes.

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Bibliographic Details
Title: Almost disjunctive list-decoding codes.
Authors: D'yachkov, A., Vorob'ev, I., Polyansky, N., Shchukin, V.
Source: Problems of Information Transmission; Apr2015, Vol. 51 Issue 2, p110-131, 22p
Subject Terms: CODING theory, MATHEMATICAL bounds, SET theory, EXISTENCE theorems, COMBINATORIAL probabilities
Abstract: We say that an s-subset of codewords of a binary code X is s-bad in X if there exists an L-subset of other codewords in X whose disjunctive sum is covered by the disjunctive sum of the given s codewords. Otherwise, this s-subset of codewords is said to be s-good in X. A binary code X is said to be a list-decoding disjunctive code of strength s and list size L (an s-LD code) if it does not contain s-bad subsets of codewords. We consider a probabilistic generalization of s-LD codes; namely, we say that a code X is an almost disjunctive s- LD code if the fraction of s-good subsets of codewords in X is close to 1. Using the random coding method on the ensemble of binary constant-weight codes, we establish lower bounds on the capacity and error exponent of almost disjunctive s-LD codes. For this ensemble, the obtained lower bounds are tight and show that the capacity of almost disjunctive s-LD codes is greater than the zero-error capacity of disjunctive s-LD codes. [ABSTRACT FROM AUTHOR]
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Abstract:We say that an s-subset of codewords of a binary code X is s-bad in X if there exists an L-subset of other codewords in X whose disjunctive sum is covered by the disjunctive sum of the given s codewords. Otherwise, this s-subset of codewords is said to be s-good in X. A binary code X is said to be a list-decoding disjunctive code of strength s and list size L (an s-LD code) if it does not contain s-bad subsets of codewords. We consider a probabilistic generalization of s-LD codes; namely, we say that a code X is an almost disjunctive s- LD code if the fraction of s-good subsets of codewords in X is close to 1. Using the random coding method on the ensemble of binary constant-weight codes, we establish lower bounds on the capacity and error exponent of almost disjunctive s-LD codes. For this ensemble, the obtained lower bounds are tight and show that the capacity of almost disjunctive s-LD codes is greater than the zero-error capacity of disjunctive s-LD codes. [ABSTRACT FROM AUTHOR]
ISSN:00329460
DOI:10.1134/S0032946015020039