On ML redundancy of codes
Junsheng Han
Siegel, P.H.
Qualcomm Inc., San Diego, CA;
This paper appears in: Information Theory, 2008. ISIT 2008. IEEE International Symposium on
Publication Date: 6-11 July 2008
On page(s): 280-284
Location: Toronto, ON,
ISBN: 978-1-4244-2256-2
INSPEC Accession Number: 10156276
Digital Object Identifier: 10.1109/ISIT.2008.4594992
Current Version Published: 2008-08-08
Abstract
The ML redundancy of a code is defined as the smallest number of rows in its parity-check matrix such that a message-passing decoder working in the corresponding Tanner graph achieves maximum-likelihood (ML) performance on an erasure channel. General upper bounds on ML redundancy are obtained. In particular, it is shown that the ML redundancy of a q-ary code is at most the number of minimal codewords in its dual code, divided by q-1. Special upper bounds are derived for codes whose dual code contains a covering design. For example, the ML redundancy of a Simplex code of length n is shown to be no greater than (n2 - 4n + 9)/6.
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