On the Heegard-Berger problem 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 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 the point-topoint (Wyner-Ziv) problem. In this paper, this result is extended to the Heegard-Berger (HB) problem and to its variant with cooperating decoders. Specifically, for the HB problem, the ratedistortion function is derived under the assumption that the side information sequences at the two decoders are stochastically degraded. The rate-distortion function is also calculated explicitly for the special case of binary source and erased side information with Hamming distortion metric. The rate-distortion function is then characterized also for the HB problem with cooperating decoders and physically degraded side information.

Source Coding Problems With Conditionally Less Noisy Side Information

“…Generalisations of the problem include the Wyner-Ziv successive-refinement work of [13]- [15] and the joint source-channel coding setup of [16]- [18]. Other variations of the problem have been investigate with causal side information [19], [20] and common reconstructions [21]. The converse methods presented in this paper may be applicable to these and other problems, particularly to those with existing results on physically degraded side information.…”

Constrained Source-Coding With Side Information

“…Timo, Grant, and Kramer [4], [5] and Ahmadi, Tandon, Simeone, and Poor [6], [7] derived the rate-distortions function under a common-reconstruction constraint for two special cases of the Heegard-Berger/Kaspi problem (the Wyner-Ziv problem with two decoders): [6], [7] for physically degraded side informations, and [4], [5] for complementary side informations. Ahmadi, Tandon, Simeone, and Poor [6], [7] also presented the rates-distortions function under a common-reconstruction constraint for a cascade source-coding problem when the side informations are physically degraded. Finally, already in [2], Steinberg studied the implications of the commonreconstruction constraint on the simultaneous transmission of data and state and on joint source-channel coding for the degraded broadcast channel.…”

“…Kittichokechai, Oechtering, and Skoglund [3] determined the ratedistortion function under a common-reconstruction constraint for a modified Wyner-Ziv setup where the encoder can influence the decoder's side information via an action-generator. Timo, Grant, and Kramer [4], [5] and Ahmadi, Tandon, Simeone, and Poor [6], [7] derived the rate-distortions function under a common-reconstruction constraint for two special cases of the Heegard-Berger/Kaspi problem (the Wyner-Ziv problem with two decoders): [6], [7] for physically degraded side informations, and [4], [5] for complementary side informations. Ahmadi, Tandon, Simeone, and Poor [6], [7] also presented the rates-distortions function under a common-reconstruction constraint for a cascade source-coding problem when the side informations are physically degraded.…”

Source Coding Problems with Conditionally Less Noisy Side Information

“…Generalisations of the problem include the Wyner-Ziv successive-refinement work of [13]- [15] and the joint source-channel coding setup of [16]- [18]. Other variations of the problem have been investigate with causal side information [19], [20] and common reconstructions [21]. The converse methods presented in this paper may be applicable 1 Matsuta and Uyematsu [4] recently presented matching achievability and converse bounds for Heegard and Berger's RD function using an information-spectrum approach; these bounds, however, are not computable.…”