Smooth compression, Gallager bound and nonlinear sparse-graph codes
Montanari, A.
Mossel, E.
EE & Stat. Depts., Stanford Univ., Stanford, CA;
This paper appears in: Information Theory, 2008. ISIT 2008. IEEE International Symposium on
Publication Date: 6-11 July 2008
On page(s): 2474-2478
Location: Toronto, ON,
ISBN: 978-1-4244-2256-2
INSPEC Accession Number: 10156457
Digital Object Identifier: 10.1109/ISIT.2008.4595436
Current Version Published: 2008-08-08
Abstract
A data compression scheme is defined to be smooth if its image (the codeword) depends gracefully on the source (the data). Smoothness is a desirable property in many practical contexts, and widely used source coding schemes lack of it. We introduce a family of smooth source codes based on sparse graph constructions, and prove them to achieve the (information theoretic) optimal compression rate for a dense set of iid sources. As a byproduct, we show how Gallager bound on sparsity can be overcome using non-linear function nodes.
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