Lossy source coding with Gaussian or erased side-information

Abstract

In this paper we find properties that are shared between two seemingly unrelated lossy source coding setups with side-information. The first setup is when the source and sideinformation are jointly Gaussian and the distortion measure is quadratic. The second setup is when the side-information is an erased version of the source. We begin with the observation that in both these cases the Wyner-Ziv and conditional ratedistortion functions are equal. We further find that there is a continuum of optimal strategies for the conditional rate distortion problem in both these setups. Next, we consider the case when there are two decoders with access to different side-information sources. For the case when the encoder has access to the sideinformation we establish bounds on the rate-distortion function and a sufficient condition for tightness. Under this condition, we find a characterization of the rate-distortion function for physically degraded side-information. This characterization holds for both the Gaussian and erasure setups.

Cascade source coding with erased side information

“…Furthermore, it was also shown in [5] and [6] that for such source-side-information pair and Hamming distortion, we do not have a rate-loss, i.e., the conditional rate distortion function, R X|Y (D) equals the Wyner-Ziv rate distortion function. The Heegard-Berger rate distortion function is given as follows:…”

“…It is well known that for setup (a), the Wyner-Ziv rate distortion function equals the conditional rate-distortion function. It was shown in [5] and [6] that the same property holds for setup (b). In light of this observation, it is not surprising that we can establish the solution of the cascade source coding problems for uniform source and erasure side information.…”

“…We therefore first state these rate distortion functions for the pair of sources described in (6)-(7) subject to the Hamming distortion constraints (8). The Wyner-Ziv rate distortion function is given as follows [5], [6]:…”

“…Case-3 (D 1 , D 2 ) ∈ L 3 : In this case, we have a Wyner-Ziv problem with respect to decoder 2. Therefore, we select U = W = φ, and V = X ⊕Z, with Z ∼ Ber(D 2 /p) and proceed as in [5] to achieve the distortion D 2 at the optimal rates R 1 = R 2 = p(1−h(D 2 /p)).…”

Is rateless paradigm fitted for lossless compression of erasure-impaired sources?

“…Despite the complexity and versatility of real sources, we reasoned that a simple but useful model, namely binary erasure source, would be easier to analyze, and also more general, so that our conclusions could be instructive even for studies of source coding in multiple terminal networks. In [11] the authors propose that the binaryerasure setting is a promising tool to analyze problems in source coding with side-information as all the results obtained for the Gaussian case hold in an analogous way for the binaryerasure case. The results in [11] suggest that there may be more connections between the Gaussian and erasure setups, and that such connections may provide insights into previously unresolved questions, which is also illustrated by our example of the BEQ applicability at the end of Subsection II-A.…”