From BP to MAP via Spatially Coupling

Friday, November 09, 2012

It is well-known that belief-propagation (BP) decoding of low-density parity-check (LDPC) codes is suboptimal and that the noise threshold of maximum-a-posteriori (MAP) decoding can be larger than the BP threshold.  Recently, Kudekar et al. proved that regular LDPC ensembles can be spatially coupled (SC) so that the BP noise threshold saturates to the MAP noise threshold of the original ensemble.  These SC ensembles are instances of LDPC convolutional (LDPCC) codes and the new proof explains an earlier observation by Lentmaier et al. that terminated LDPCC codes allow reliable communication at rates very close to capacity.The main benefit of SC codes is that code optimization is not required for near-optimal performance.  For a variety of problems, this allows SC codes to approach capacity universally (e.g., like random codes with MAP decoding).  This talk will give an overview of these recent results and describe a simple proof technique that allows one prove threshold saturation for a broad class of spatially-coupled systems.


Henry D. Pfister received his Ph.D. in electrical engineering from UCSD in 2003 and he joined the faculty of the School of Engineering at Texas A&M University in 2006.  Prior to that he spent two years in R&D at Qualcomm, Inc. and one year as a post-doc at EPFL.He received the NSF Career Award in 2008 and was a coauthor of the 2007 IEEE COMSOC best paper in Signal Processing and Coding for Data Storage.His current research interests include information theory, channel coding, and iterative decoding with applications in wireless communications and data storage.