Applications of correlation inequalities to low density graphical codes
Laboratoire de Théorie des Communications, École Polytechnique Fédérale de Lausanne, Station 14 - LTHC -EPFL, 1015 Lausanne, Switzerland
Corresponding author: a email@example.com
Revised: 6 December 2005
Published online: 12 April 2006
This contribution is based on the contents of a talk delivered at the Next-SigmaPhi conference held in Crete in August 2005. It is adressed to an audience of physicists with diverse horizons and does not assume any background in communications theory. Capacity approaching error correcting codes for channel communication known as Low Density Parity Check (LDPC) codes have attracted considerable attention from coding theorists in the last decade. Surprisingly strong connections with the theory of diluted spin glasses have been discovered. In this work we elucidate one new connection, namely that a class of correlation inequalities valid for Gaussian spin glasses can be applied to the theoretical analysis of LDPC codes. This allows for a rigorous comparison between the so called (optimal) maximum a posteriori and the computationaly efficient belief propagation decoders. The main ideas of the proofs are explained and we refer to recent works for the more lengthy technical details.
PACS: 05.20.-y – Classical statistical mechanics / 89.70.+c – Information theory and communication theory / 02.90.+p – Other topics in mathematical methods in physics
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2006