Almost disjunctive list-decoding codes

Almost disjunctive list-decoding codes We say that an s-subset of codewords of a binary code X is s L -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 L -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 L -LD code) if it does not contain s L -bad subsets of codewords. We consider a probabilistic generalization of s L -LD codes; namely, we say that a code X is an almost disjunctive s L -LD code if the fraction of s L -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 L -LD codes. For this ensemble, the obtained lower bounds are tight and show that the capacity of almost disjunctive s L -LD codes is greater than the zero-error capacity of disjunctive s L -LD codes. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

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Publisher
Springer Journals
Copyright
Copyright © 2015 by Pleiades Publishing, Inc.
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S0032946015020039
Publisher site
See Article on Publisher Site

Abstract

We say that an s-subset of codewords of a binary code X is s L -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 L -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 L -LD code) if it does not contain s L -bad subsets of codewords. We consider a probabilistic generalization of s L -LD codes; namely, we say that a code X is an almost disjunctive s L -LD code if the fraction of s L -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 L -LD codes. For this ensemble, the obtained lower bounds are tight and show that the capacity of almost disjunctive s L -LD codes is greater than the zero-error capacity of disjunctive s L -LD codes.

Journal

Problems of Information TransmissionSpringer Journals

Published: Jul 7, 2015

References

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