Efficient iterative LP decoding of LDPC codes with alternating direction method of multipliers

In this paper, we propose an efficient message-passing algorithm to solve the LP decoding problem. This algorithm is based on the alternating direction method of multipliers (ADMM), a classic technique in convex optimization theory that is designed for parallel implementation. The computational complexity of ADMM-based LP decoding is largely determined by the method used to project a vector of real values to the parity polytope of a given parity check. The key contribution of this paper is a novel, efficient projection algorithm that can substantially improve the decoding speed of the ADMM-based LP decoder.