On low-complexity linear-programming decoding of LDPC codes

We consider linear-programming (LP) decoding of low-density parity-check (LDPC) codes. While one can use any general-purpose LP solver to solve the LP that appears in the decoding problem, we argue in this paper that the LP at hand is equipped with a lot of structure that can be exploited. Towards this goal, we study the dual LP and show how coordinate-ascent methods lead to very simple update rules that are tightly connected to the min-sum algorithm. Moreover, replacing minima in the formula of the dual LP with soft-minima one obtains update rules that are tightly connected to the sum-product algorithm. This shows that LP solvers with complexity similar to the min-sum algorithm and the sum-product algorithm are feasible. Copyright (C) 2007 John Wiley & Sons, Ltd.