Improved linear programming decoding using frustrated cycles

Abstract

We consider transmission over a binary-input additive white Gaussian noise channel using low-density parity-check codes. One of the most popular techniques for decoding lowdensity parity-check codes is the linear programming decoder. In general, the linear programming decoder is suboptimal. I.e., the word error rate is higher than the optimal, maximum a posteriori decoder.In this paper we present a systematic approach to enhance the linear program decoder. More precisely, in the cases where the linear program outputs a fractional solution, we give a simple algorithm to identify frustrated cycles which cause the output of the linear program to be fractional. Then adding these cycles, adaptively to the basic linear program, we show improved word error rate performance.

Graphical Models and Belief Propagation Hierarchy for Physics-Constrained Network Flows

“…Once the loopy structure is identified one may want to modify GM, or equivalently introduce some additional constraint between beliefs associated with the loops and not linked before in the bare LP-BP. This scheme was developed in [34,35] based on the notion of frustrated cycles and an associated Constrained Satisfaction Problem (CSP) stated in terms of beliefs optimal for the original LP-BP. Similar but different heuristic approaches were also discussed in [61,62,60] for a aGM of a general position.…”

Belief Propagation for Linear Programming

“…This line of work established a solid theoretical link between message passing algorithms and optimization theory. It provides a practical certificate of exactness/integrality for MAP inference when using BP and has also suggested strategies for improving upon BP's results, by adding constraints that reduce the BPLP integrality gap [14], [15], [16].…”