Abstract
A multi-terminal network, in which an encoder is assisted by a side-information-aided helper, describes a memoryless identically distributed source to a receiver, is considered. The encoder provides a non-causal one-shot description of the source to both the helper and the receiver. The helper, which has access to causal side-information, describes the source to the receiver sequentially by sending a sequence of causal descriptions depending on the message conveyed by the encoder and the side-information subsequence it has observed so far. The receiver reconstructs the source causally by producing on each time unit an estimate of the current source symbol based on what it has received so far. Given a reconstruction fidelity measure and a maximal allowed distortion, we derive the rates-distortion region for this setting and express it in terms of an auxiliary random variable. When the source and side-information are drawn from an independent identically distributed Gaussian law and the fidelity measure is the squared-error distortion we show that for the evaluation of the rates-distortion region it suffices to choose the auxiliary random variable to be jointly Gaussian with the source and side-information pair.
Highlights
In the classical source coding with decoder side information problem, the source and side information are generated by independent drawings ( Xk, Yk ) of the pair ( X, Y ) ∼ PXY
The encoder forms a description of the source sequence X n = ( X1, . . . , Xn ) using a map f (n) : X n → {1, . . . , b2nR c}, while the decoder forms its reconstruction Xn depending on both the side-information sequence Y n and the index T ∈ {1, . . . , b2nR c} conveyed by the encoder
Wyner–Ziv source coding with non-causal decoder side-information involves binning the implementation of which is complex
Summary
In the classical source coding with decoder side information problem, the source and side information are generated by independent drawings ( Xk , Yk ) of the pair ( X, Y ) ∼ PXY. A successive refinement for the Wyner–Ziv problem with side-information (Y, Z ) is a variant of the Wyner–Ziv model, in which the encoder provides a two-layer description of the source sequence. K =1 in a causal manner, per channel use k, uses the descriptions it had received so far and the source subsequence Z k to form its reconstruction Xk for the source symbol Xk. Given a fidelity measure and a maximal allowed distortion, the goal is to determine the set of all rate pairs ( R, Rh ) that satisfy the distortion constraint. With the aim of reducing encoder/decoder complexity, a two layer description model with successive refinement has been considered in [5], under the setting that the side information is available causally at each of the decoders. The extension of the model [5] with a causal helper has recently been studied in [6]
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