This paper considers noisy Wyner-Ziv coding (WZC), in which a remote noisy source is compressed with side information at the decoder only. The decoder side information is not limited to being Gaussian, thus this noisy WZC problem cannot be transformed into the conventional one tailored for noiseless sources. A new coding structure, named the residual-quantization (RQ) based noisy WZC, is proposed to solve the problem. This scheme explicitly constructs the theoretical auxiliary random variable to facilitate optimal reconstruction of the noisy source. In this two-stage encoder, the noisy source is quantized twice and the quantization error (residue) of the first stage is the input of the second stage. By sending only the quantization index of the second stage to the decoder, the corresponding code rate can theoretically approach the noisy WZC bound. Moreover, the RQ-based noisy WZC is implemented using graph-based codes. The main challenge is that it is necessary to design a codebook that is simultaneously good for source and channel coding for the first stage quantization, since this quantization code also acts as a channel code at the decoder. This problem is solved by constructing a low-density parity check (LDPC) code with edge degrees optimized for channel coding, and enhancing its performance for source coding by using a modified reinforced belief-propagation quantization algorithm. Simulation results show that the noisy Wyner-Ziv bounds can be practically approached by our implementation. In addition, the proposed implementation offers more flexibility in the code rates compared with the existing practical designs, making it more suitable for emerging applications such as fronthaul compression.

Wyner-Ziv coding (WZC) is a compression technique which uses decoder side-information to help reconstruction. We present a new coding structure using two-stage successive quantization with two codebooks to solve the Wyner-Ziv problem in the quadratic Gaussian case. The optimal Wyner-Ziv bound is proved to be achievable by random coding analysis. Compared to the existing nested-lattice based design approaches, the two component codes in our construction can be designed independently, which simplifies the code design significantly. Moreover, besides the original noiseless setting where the source is directly observed by the encoder, our coding also suits for the noisy WZC problem where the source is observed via a noisy memoryless channel.