LDGM-Based Multiple Description Coding for Finite Alphabet Sources

This work presents an LDGM-based practical successive coding scheme for the multiple description (MD) problem for finite alphabet sources. The scheme, which targets the Zhang-Berger (ZB) rate-distortion region, is shown to be asymptotically optimal with joint typicality encoding, while as a practical encoding solution a message passing algorithm is adopted. We further discuss in more detail the application of the coding scheme in three cases of the MD problem with the Hamming distortion measure: 1) no excess sum-rate for binary sources, 2) successive refinement, and 3) no excess marginal rate for the uniform binary source. In the no excess sum-rate case some progress is made in the characterization of fundamental limits by deriving the analytical expression of the distortion region for general binary sources, and of the auxiliary variables needed to achieve its boundary. The exact expression of the Zhang-Berger upper bound to the central distortion is also provided for the case of no excess marginal rate for the uniform binary source. The proposed LDGM-based coding scheme is tested in practice for all three aforementioned cases. The experimental results show very good performance, demonstrating its ability to approach the theoretical rate-distortion limits or the available upper bounds.