A Fast Approximate Check Polytope Projection Algorithm for ADMM Decoding of LDPC Codes

Abstract

Simplifying the Euclidean projection onto check polytope is an efficient way to reduce the computational complexity of alternating direction method of multipliers (ADMM) decoding algorithm for low-density parity-check (LDPC) codes. Existing algorithms for check polytope projection require sorting operation or iterative operation, which happens to be the most complex part of the projection. In this letter, a novel and fast projection algorithm is proposed without sorting and iterative operations. In the proposed algorithm, line segment projection replaces check polytope projection to approach approximate Euclidean projection at low computational complexity. Simulation results show that the proposed algorithm can substantially reduce the projection time while maintaining the frame error rate (FER) performance. In particular, the proposed algorithm can save the average projection time by 43% compared with cut search algorithm (CSA) when the dimension of the input vector is 20.