Heegard-Berger and Cascade Source Coding Problems with Common Reconstruction Constraints

In lossy source coding with side information at the decoder (i.e., the Wyner-Ziv problem), the estimate of the source obtained at the decoder cannot be generally reproduced at the encoder, due to its dependence on the side information. In some applications this may be undesirable, and a Common Reconstruction (CR) requirement, whereby one imposes that the encoder and decoder be able to agree on the decoder’s estimate, may be instead in order. The rate-distortion function under the CR constraint has been recently derived for a point-to-point (Wyner-Ziv) problem. In this paper, this result is extended to three multiterminal settings with three nodes, namely the Heegard-Berger (HB) problem, its variant with cooperating decoders and the cascade source coding problem. The HB problem consists of an encoder broadcasting to two decoders with respective side information. The cascade source coding problem is characterized by a two-hop system with side information available at the intermediate and final nodes. For the HB problem with the CR constraint, the rate-distortion function is derived under the assumption that the side information sequences are (stochastically) degraded. The rate-distortion function is also calculated explicitly for three examples, namely Gaussian source and side information with quadratic distortion metric, and binary source and side information with erasure and Hamming distortion B. Ahmadi and O. Simeone are with the CWCSPR, New Jersey Institute of Technology, Newark, NJ 07102 USA (e-mail: {behzad.ahmadi,osvaldo.simeone}@njit.edu). R. Tandon was with Princeton University, Princeton, NJ 08544 USA. He is now with Virginia Tech, Blacksburg, VA, 24061 (e-mail: [email protected], [email protected]). H. V. Poor is with Princeton University, Princeton, NJ 08544 USA (e-mail: [email protected]). The material in this paper was presented in part at the IEEE International Symposium on Information Theory, Cambridge, MA, USA, July 1-6, 2012. October 26, 2012 DRAFT