LDPC code optimization with joint source-channel decoding of quantized Gauss-Markov signals

This paper proposes an extrinsic information transfer (EXIT)-chart based optimization technique of LDPC codes for the transmission of quantized Gauss-Markov (GM) source samples over additive white Gaussian (AWGN) noise channels. A joint source and channel (JSC) decoding technique of the proposed code is also devised. In the proposed scheme, no interleaving is performed between the source and the JSC encoder so that the decoder can well exploit the relatively low entropy of the source with memory compared to memory-less sources. At the transmitter, the quantized samples are converted to bit sequences with an injective mapping and the bit sequences are encoded using a systematic binary LDPC code. The proposed JSC decoder is a concatenation of a multi-state BCJR Markov decoder and a sum-product (SP) LDPC decoder. Decoding thresholds of the optimized codes at certain code rates are investigated for both uniform and Lloyd-Max quantizations in different numbers of bits. The decoding thresholds are close to the Gaussian code book Shannon limits for code rate R_c ≤ 0.5, although the gap to the Shannon limit notably increases at the higher rates. Finally, the simulation results confirm the significant improvement of coding gain on the bit error rate (BER) performances of the optimized LDPC codes with both the quantization schemes.