Decoding LDPC Codes by Using Negative Proximal Regularization

Abstract

The low-density parity-check (LDPC) decoding problem can be expressed as an integer linear programming (ILP) problem. One efficient method to solve the ILP problem is to relax the integer constraints and add penalty terms to the objective function, and the revised problem can be solved via the alternating direction method of multipliers (ADMM) algorithm. These penalty terms can punish the non-integral solutions and improve the decoding performance of the decoder. However, ADMM decoders are easily trapped in a local solution, which limits the frame error rate (FER) performance of the decoders at low signal-to-noise ratios (SNR). In this paper, we propose a restartable ADMM-based decoder using a negative proximal regularization. The negative proximal term will be updated whenever the decoder finds a new local solution. Therefore, the decoder can be restarted several times and the candidate solution which satisfies the parity-check equations and has the lowest objective function value can be selected as the decoder’s output. Some properties, together with several choices of penalty terms are discussed. We also investigate the convergence of our proposed decoder, and prove that the possibility of decoding errors is independent of the codeword that is transmitted. Simulation results show that our proposed decoder outperforms other ADMM-based decoders in most cases, while the decoding complexity maintains the same.