Wyner-Ziv coding based on TCQ and LDPC codes

This paper considers trellis coded quantization (TCQ) and low-density parity-check (LDPC) codes for the quadratic Gaussian Wyner-Ziv coding problem. After TCQ of the source X, LDPC codes are used to implement Slepian-Wolf coding of the quantized source Q(X) with side information Y at the decoder. Assuming 256-state TCQ and ideal Slepian-Wolf coding in the sense of achieving the theoretical limit H(Q(X)|Y ), we experimentally show that Slepian-Wolf coded TCQ performs 0.2 dB away from the Wyner-Ziv distortion-rate function D_WZ(R) at high rate. This result mirrors that of entropy-constrained TCQ in classic source coding of Gaussian sources. Furthermore, using 8,192-state TCQ and assuming ideal Slepian-Wolf coding, our simulations show that Slepian-Wolf coded TCQ performs only 0.1 dB away from D_WZ(R) at high rate. These results establish the practical performance limit of Slepian-Wolf coded TCQ for quadratic Gaussian Wyner-Ziv coding. Practical designs give performance very close to the theoretical limit. For example, with 8,192-state TCQ, irregular LDPC codes for Slepian-Wolf coding and optimal non-linear estimation at the decoder, our performance gap to D_WZ(R) is 0.20 dB, 0.22 dB, 0.30 dB, and 0.93 dB at 3.83 bit per sample (b/s), 1.83 b/s, 1.53 b/s, and 1.05 b/s, respectively. When 256-state 4-D trellis-coded vector quantization instead of TCQ is employed, the performance gap to D_WZ(R) is 0.51 dB, 0.51 dB, 0.54 dB, and 0.80 dB at 2.04 b/s, 1.38 b/s, 1.0 b/s, and 0.5 b/s, respectively.

I. Introduction

Wyner-Ziv coding [29] deals with the problem of rate-distortion with side information at the decoder. It asks the question of how many bits are needed to encode an input source under a distortion constraint , assuming that some correlated side information is available at the decoder but not at the encoder. This problem generalizes the setup of near-lossless source coding with decoder side information considered by Slepian and Wolf [21]. Driven by a host of emerging applications (e.g., wireless video and distributed sensor networks), distributed source coding (e.g., Slepian-Wolf coding and Wyner-Ziv coding) has recently become a very active research area – more than 30 years after Slepian and Wolf laid its theoretical foundation.