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

TL;DR

This paper derives the rate-distortion functions and regions for Heegard-Berger and cascade source coding problems with common reconstruction constraints, focusing on degraded side information scenarios and providing explicit solutions for Gaussian and binary sources.

Contribution

It provides the first explicit rate-distortion functions for these problems with CR constraints under degraded side information, including new bounds and special case solutions.

Findings

Explicit rate-distortion functions for Gaussian sources with quadratic distortion.

Rate-distortion regions characterized for binary sources with erasure and Hamming metrics.

Bounds shown to coincide in key example cases.

Abstract

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 metrics. The rate-distortion function is then characterized for the HB problem with cooperating decoders and (physically) degraded side information. For the cascade problem with the CR constraint, the rate-distortion region is obtained under the assumption that side information at the final node is physically degraded with respect to that at the intermediate node. For the latter two cases, it is worth emphasizing that the corresponding problem without the CR constraint is still open. Outer and inner bounds on the rate-distortion region are also obtained for the cascade problem under the assumption that the side information at the intermediate node is physically degraded with respect to that at the final node. For the three examples mentioned above, the bounds are shown to coincide. Finally, for the HB problem, the rate-distortion function is obtained under the more general requirement of constrained reconstruction, whereby the decoder's estimate must be recovered at the encoder only within some distortion.