Heegard–Berger and Cascade Source Coding Problems With Common Reconstruction Constraints

Abstract

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,

On the Heegard-Berger problem with common reconstruction constraints

“…In the remaining case, namely D 2 ≤ D 1 ≤ 1/2, the rate-distortion function does not follow from the point-to-point result (14) as for the regimes discussed thus far. The analysis of this case can be found in [4,Appendix D]. Similar arguments apply also for the erasure distortion metric.…”

“…The proof of the converse can be found in [4]. Achievability follows as a special case of Theorem 3 of [1] and can be easily shown using standard arguments.…”

“…II-C. The case of Gaussian sources under quadratic distortion is tackled in [4]. The proofs of the results presented in the paper are omitted due to space limitations and can be found in [4].…”

Lossy broadcasting with common transmitter-receiver reconstructions

“…It was noticed that while the imposition of this constraint restricted the use of receiver side-information, it also allows to have explicit control over the receiver reconstructions. Since Steinberg's work, various extensions and applications of common reconstruction constraints have been studied [8]- [11]. In our recent work [10], the capacity regions the noiseless broadcast problem (Heegard-Berger problem) with two versions of the common reconstructions constraints were derived.…”

“…where ( * ) follows because the source realization and the source codeword selected are jointly ε-strongly typical when the event 8 ∩ k=1 E c k occurs. Note that the above results are averages for an ensemble of random codebooks.…”