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 sa...

Full description

Saved in:
Bibliographic Details
Published in:Problems of information transmission Vol. 51; no. 2; pp. 110 - 131
Main Authors: D’yachkov, A. G., Vorob’ev, I. V., Polyansky, N. A., Shchukin, V. Yu
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.04.2015
Subjects:
Coding Theory
Communications Engineering
Control
Electrical Engineering
Engineering
Information Storage and Retrieval
Networks
Systems Theory
Information Transmission
Broadcasting Channel
Multiple Access Channel
Random Code
Error Probability
ISSN:0032-9460, 1608-3253
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0032-9460
1608-3253
DOI:10.1134/S0032946015020039