Hybrid Decoding of LDPC Codes Based on Interior Point Method

In this paper, a hybrid decoding algorithm for finite-geometry low-density parity-check (FG-LDPC) codes is proposed. The algorithm is based on the interior point method with barrier function introduced by Wadayama [6]. First, an efficient implementation of Wadayama's algorithm is presented. The main idea behind the modification is to approximate the barrier function for the fundamental polytope defining the code so that it contains only one linear constraint for each of the parity-check constraints. A two-stage hybrid decoding which combines the interior point decoding (IPD) and a low-complexity decoding algorithm for FG-LDPC codes is then proposed. In the first stage, the interior point decoding is used to generate a search point. If the first stage decoding fails, the decoding is continued by the low-complexity algorithm that is initialized by the result of the IPD. Compared with a conventional iterative message-passing (IMP) decoder, the proposed hybrid algorithm achieves better bit-error rate (BER) and frame-error rate (FER) for small block lengths at medium to high signal-to-noise ratio (SNR).