Large Scale LP Decoding with Low Complexity

Linear program (LP) decoding has become increasingly popular for error-correcting codes due to its simplicity and promising performance. Low-complexity and efficient iterative algorithms for LP decoding are of great importance for practical applications. In this paper we focus on solving the binary LP decoding problem by using the alternating direction method of multipliers (ADMM). Our main contribution is that we propose a linear-complexity algorithm for the projection onto a parity polytope (having a computational complexity of small O(d), where small d is the check-node degree), as compared to recent work , which has a computational complexity of small O(d log d). In particular, we show that the projection onto the parity polytope can be transformed to a projection onto a simplex.