Approaching 1.53-dB Shaping Gain with LDGM Quantization Codes

Approaching the 1.53-dB shaping gain limit in mean-squared error (MSE) quantization of Rⁿ is important in a number of problems, notably dirty-paper coding. Unlike the traditional method of trellis-coded quantization (TCQ), in this paper we propose quantization codebooks constructed from binary low-density generation-matrix (LDGM) codes and from two such codes combined with Gray mapping. The quantization algorithm is based on belief propagation, and it uses a novel adaptive decimation procedure to do the guessing necessary for convergence. Simulation results show that the proposed code can achieve a shaping gain of 1.477 dB, or 0.056 dB from the limit, which is significantly better than the 1.40 dB previously achieved with TCQ.