Lossy source encoding via message-passing and decimation over generalized codewords of LDGM codes

M.J. Wainwright, E. Maneva
2005 Proceedings. International Symposium on Information Theory, 2005. ISIT 2005.  
We describe message-passing and decimation approaches for lossy source coding using low-density generator matrix (LDGM) codes. In particular, this paper addresses the problem of encoding a Bernoulli( ¡ ) source: for randomly generated LDGM codes with suitably irregular degree distributions, our methods yield performance very close to the rate distortion limit over a range of rates. Our approach is inspired by the survey propagation (SP) algorithm, originally developed by Mézard et al. [1] for
more » ... lving random satisfiability problems. Previous work by Maneva et al. [2] shows how SP can be understood as belief propagation (BP) for an alternative representation of satisfiability problems. In analogy to this connection, our approach is to define a family of Markov random fields over generalized codewords, from which local message-passing rules can be derived in the standard way. The overall source encoding method is based on message-passing, setting a subset of bits to their preferred values (decimation), and reducing the code.
doi:10.1109/isit.2005.1523592 dblp:conf/isit/WainwrightM05 fatcat:yzitym25xvharl3pvhdheziws4