Physical Sciences and Mathematics Commons^™

Characterizations Of Pseudo-Codewords Of Ldpc Codes, Ralf Koetter, Wen-Cheng W. Li, Pascal O. Vontobel, Judy L. Walker

Department of Mathematics: Faculty Publications

An important property of high-performance, low complexity codes is the existence of highly efficient algorithms for their decoding. Many of the most efficient, recent graph-based algorithms, e.g. message passing algorithms and decoding based on linear programming, crucially depend on the efficient representation of a code in a graphical model. In order to understand the performance of these algorithms, we argue for the characterization of codes in terms of a so called fundamental cone in Euclidean space which is a function of a given parity check matrix of a code, rather than of the code itself. We give a number of …