Rate distortion when side information may be absent

Abstract

The problem is considered of encoding a discrete memoryless source when correlated side information may or may not be available to the decoder. It is assumed that the side information is not available to the encoder. The rate-distortion function R(D,, D2) is determined where D, is the distortion achieved with side information and D, is the distortion achieved without it. A generalization is made to the case of m decoders, each of which is privy to its own side information. An appropriately defined D-admissible rate for this general case is shown to equal R(D) when the side information sources satisfy a specified degradedness condition. Explicit results are obtained in the quadratic Gaussian case and in the binary Hamming case.

Source coding with conditionally less noisy side information

“…The best achievability result (upper bound to R * ) can be distilled from [1], [2], [7] and is summarised next.…”

“…Suppose that Receiver 1 requires lossless copies of X and Z; Receiver 2 requires lossless copies of Y and Z; and Receiver 3 requires a lossless copy of Z. A code (f, g 1 , g 2 , g 3 ) for this setup is defined analogously to (1). Let (X,Ẑ 1 ), (Ŷ ,Ẑ 2 ) andẐ 3 denote the reconstructions at receivers 1, 2 and 3 respectively.…”

“…The described problem is a special case of the rate-distortion functions in [1], [2]. Single-letter expressions for R * are known in the following three special cases: (i) equal source components X = Y [8]; (ii) complementary side information U = Y and V = X [3]; and (iii) degraded side information (X, Y ) − −U − −V [1].…”

“…Single-letter expressions for R * are known in the following three special cases: (i) equal source components X = Y [8]; (ii) complementary side information U = Y and V = X [3]; and (iii) degraded side information (X, Y ) − −U − −V [1]. In this paper, we determine R * for the case where H(Y |U ) ≤ H(Y |V ) and the side information U at Receiver 1 is conditionally less noisy than the side information V at Receiver 2 given Y .…”

Cascade and Triangular Source Coding With Side Information at the First Two Nodes

“…Of special interest in lossy source coding is the Gaussian case with quadratic distortion, which in many source coding problems is amenable to an analytical solution such as in the Wyner--Ziv problem [12] where side information is available to the decoder, the Heegard--Berger problem [13] where side information at the decoder may be absent, Kaspi's problem [14], [15] where side information is known to the encoder and may or may not be known to the decoder, the multiple description problem [16], [17], the two-way source coding problem [18], the multiterminal problem [19], [20], the CEO problem [21]- [23], rate distortion with a helper [24], [25], and successive refinement [26] and its extension to successive refinement for the Wyner--Ziv problem [27].…”