Improved Penalty Functions of ADMM Penalized Decoder for LDPC Codes

By making the pseudocodewords more costly than codewords, the alternating direction method of multipliers (ADMM) penalized decoder can improve the error rate performances significantly for low-density parity-check (LDPC) codes at low signal-to-noise ratios. In this letter, we design two improved piecewise penalty functions for ADMM penalized decoder by increasing the slope of the penalty function at the points near x = 0 and x = 1. The improved penalty functions can punish pseudocodewords more quickly and thus increase the decoding speed. Simulation results over two LDPC codes show that the proposed method improves the error rate performances and reduces the decoding time considerably.