Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Bounds on the rate of disjunctive codes

Bounds on the rate of disjunctive codes A binary code is said to be a disjunctive (s, ℓ) cover-free code if it is an incidence matrix of a family of sets where the intersection of any ℓ sets is not covered by the union of any other s sets of this family. A binary code is said to be a list-decoding disjunctive of strength s with list size L if it is an incidence matrix of a family of sets where the union of any s sets can cover no more that L − 1 other sets of this family. For L = ℓ = 1, both definitions coincide, and the corresponding binary code is called a disjunctive s-code. This paper is aimed at improving previously known and obtaining new bounds on the rate of these codes. The most interesting of the new results is a lower bound on the rate of disjunctive (s, ℓ) cover-free codes obtained by random coding over the ensemble of binary constant-weight codes; its ratio to the best known upper bound converges as s → ∞, with an arbitrary fixed ℓ ≥ 1, to the limit 2e −2 = 0.271 ... In the classical case of ℓ = 1, this means that the upper bound on the rate of disjunctive s-codes constructed in 1982 by D’yachkov and Rykov is asymptotically attained up to a constant factor a, 2e −2 ≤ a ≤ 1. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

Loading next page...
1
 
/lp/springer_journal/bounds-on-the-rate-of-disjunctive-codes-7a4t1fhTtK

References (42)

Publisher
Springer Journals
Copyright
Copyright © 2014 by Pleiades Publishing, Inc.
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
DOI
10.1134/S0032946014010037
Publisher site
See Article on Publisher Site

Abstract

A binary code is said to be a disjunctive (s, ℓ) cover-free code if it is an incidence matrix of a family of sets where the intersection of any ℓ sets is not covered by the union of any other s sets of this family. A binary code is said to be a list-decoding disjunctive of strength s with list size L if it is an incidence matrix of a family of sets where the union of any s sets can cover no more that L − 1 other sets of this family. For L = ℓ = 1, both definitions coincide, and the corresponding binary code is called a disjunctive s-code. This paper is aimed at improving previously known and obtaining new bounds on the rate of these codes. The most interesting of the new results is a lower bound on the rate of disjunctive (s, ℓ) cover-free codes obtained by random coding over the ensemble of binary constant-weight codes; its ratio to the best known upper bound converges as s → ∞, with an arbitrary fixed ℓ ≥ 1, to the limit 2e −2 = 0.271 ... In the classical case of ℓ = 1, this means that the upper bound on the rate of disjunctive s-codes constructed in 1982 by D’yachkov and Rykov is asymptotically attained up to a constant factor a, 2e −2 ≤ a ≤ 1.

Journal

Problems of Information TransmissionSpringer Journals

Published: Apr 15, 2014

There are no references for this article.