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Nonasymptotic Upper Bounds for Deletion Correcting Codes

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Title Nonasymptotic Upper Bounds for Deletion Correcting Codes
 
Creator KULKARNI, AA
KIYAVASH, N
 
Subject Deletion channel
hypergraphs
integer linear programming
linear programming relaxation
multiple-deletion correcting codes
nonasymptotic bounds
single-deletion correcting codes
Varshamov-Tenengolts codes
SYNCHRONIZATION ERRORS
EFFICIENT RECONSTRUCTION
SEQUENCES
CHANNELS
SUBSEQUENCES
HYPERGRAPHS
 
Description Explicit nonasymptotic upper bounds on the sizes of multiple-deletion correcting codes are presented. In particular, the largest single-deletion correcting code for q-ary alphabet and string length n is shown to be of size at most q(n)-q/(q-1)(n-1). An improved bound on the asymptotic rate function is obtained as a corollary. Upper bounds are also derived on sizes of codes for a constrained source that does not necessarily comprise of all strings of a particular length, and this idea is demonstrated by application to sets of run-length limited strings. The problem of finding the largest deletion correcting code is modeled as a matching problem on a hypergraph. This problem is formulated as an integer linear program. The upper bound is obtained by the construction of a feasible point for the dual of the linear programming relaxation of this integer linear program. The nonasymptotic bounds derived imply the known asymptotic bounds of Levenshtein and Tenengolts and improve on known nonasymptotic bounds. Numerical results support the conjecture that in the binary case, the Varshamov-Tenengolts codes are the largest single-deletion correcting codes.
 
Publisher IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
 
Date 2014-10-16T05:58:38Z
2014-10-16T05:58:38Z
2013
 
Type Article
 
Identifier IEEE TRANSACTIONS ON INFORMATION THEORY, 59(8)5115-5130
http://dx.doi.org/10.1109/TIT.2013.2257917
http://dspace.library.iitb.ac.in/jspui/handle/100/15397
 
Language en