Nonasymptotic Upper Bounds for Deletion Correcting Codes
DSpace at IIT Bombay
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Title |
Nonasymptotic Upper Bounds for Deletion Correcting Codes
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Creator |
KULKARNI, AA
KIYAVASH, N |
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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 |
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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.
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Publisher |
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
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Date |
2014-10-16T05:58:38Z
2014-10-16T05:58:38Z 2013 |
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Type |
Article
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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 |
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Language |
en
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