A density evolution based framework for dirty paper code design using TCQ and multilevel LDPC codes

We propose a density evolution based dirty-paper code design framework that combines trellis coded quantization with multi-level low-density parity-check (LDPC) codes. Unlike existing design techniques based on Gaussian approximation and EXIT charts, the proposed framework tracks the empirically collected log-likelihood ratio (LLR) distributions at each iteration, and employs density evolution and differential evolution algorithms to design each LDPC component code. In order for the approximated LLR distributions obtained using density evolution to better match the true LLR distributions, a novel decorrelator is added to the decoder to make channel LLRs and check node LLRs almost independent of each other. Simulation results show that at 1 bit per sample transmission rate, the dirty-paper codes designed using the proposed method operate within 0.53 dB of the theoretical limit, reducing the best known result (with a 0.58 dB gap to the limit) by 0.05 dB at the same complexity and block length, while this improvement can be as large as 0.21 dB (corresponding to a 0.37 dB gap to the limit) when we use higher complexity encoder/decoder with longer block length.