Practical Dirty Paper Coding with Nested Binary LDGM-LDPC Codes

The superior shaping performance of low-density generation matrix (LDGM) codes makes them important in the design of capacity-approaching dirty paper coding (DPC) schemes. One possible LDGM-based DPC scheme is the nested LDGM-LDPC code proposed by Wainwright and Martinian, which has been shown to be capacity-achieving under optimal encoding and decoding. In this paper, considering the Gaussian DPC problem limited to a binary alphabet, we propose practical encoding and decoding algorithms for the nested LDGM-LDPC code utilizing ideas from the fast LDPC encoding algorithm to satisfy the parity constraints, and optimize the degree distributions of the code through density evolution. Simulation results show that the proposed scheme can indeed closely approach the alphabet-constrained DPC capacity.