Binary Wyner–Ziv code design based on compound LDGM–LDPC structures

In this study, a practical coding scheme is designed for the binary Wyner–Ziv (WZ) problem by using nested low-density generator-matrix (LDGM) and low-density parity-check (LDPC) codes. This scheme contains two steps in the encoding procedure. The first step involves applying the binary quantisation by employing LDGM codes and the second one is using the syndrome-coding technique by utilising LDPC codes. The decoding algorithm of the proposed scheme is based on the sum-product algorithm with the help of a side information available at the decoder side. It is theoretically shown that the compound structure has the capability of achieving the WZ bound. The proposed method approaches this bound by utilising the iterative message-passing algorithms in both encoding and decoding, although theoretical results show that it is asymptotically achievable.