Non-linear programming approaches to decoding low-density parity-check codes

Abstract

We consider the decoding problem for low-density parity-check codes, and apply nonlinear programming methods. Firstly, a multistage LP decoder based on the branch-andbound method is proposed. This decoder makes use of the ML-certificate property of the LP decoder to refine the results when an error is reported. Secondly, we transform the original LP decoding formulation into a box-constrained quadratic programming form. Efficient linear-time parallel and serial decoding algorithms are proposed and their convergence properties are investigated. Extensive simulation studies are performed to assess the performance of the proposed decoders. It is seen the proposed multistage LP decoder outperforms the conventional sum-product (SP) decoder considerably for LDPC code with short to medium block length. The proposed box-constrained quadratic programming decoder has similar complexity to the SP decoder and yields much better performance for LDPC code with regular structure.