3 research outputs found
Exponential Strong Converse for Successive Refinement with Causal Decoder Side Information
We consider the -user successive refinement problem with causal decoder
side information and derive an exponential strong converse theorem. The
rate-distortion region for the problem can be derived as a straightforward
extension of the two-user case by Maor and Merhav (2008). We show that for any
rate-distortion tuple outside the rate-distortion region of the -user
successive refinement problem with causal decoder side information, the joint
excess-distortion probability approaches one exponentially fast. Our proof
follows by judiciously adapting the recently proposed strong converse technique
by Oohama using the information spectrum method, the variational form of the
rate-distortion region and H\"older's inequality. The lossy source coding
problem with causal decoder side information considered by El Gamal and
Weissman is a special case () of the current problem. Therefore, the
exponential strong converse theorem for the El Gamal and Weissman problem
follows as a corollary of our result
Exponential Strong Converse for Source Coding with Side Information at the Decoder
We consider the rate distortion problem with side information at the decoder posed and investigated by Wyner and Ziv. Using side information and encoded original data, the decoder must reconstruct the original data with an arbitrary prescribed distortion level. The rate distortion region indicating the trade-off between a data compression rate R and a prescribed distortion level Δ was determined by Wyner and Ziv. In this paper, we study the error probability of decoding for pairs of ( R , Δ ) outside the rate distortion region. We evaluate the probability of decoding such that the estimation of source outputs by the decoder has a distortion not exceeding a prescribed distortion level Δ . We prove that, when ( R , Δ ) is outside the rate distortion region, this probability goes to zero exponentially and derive an explicit lower bound of this exponent function. On the Wyner–Ziv source coding problem the strong converse coding theorem has not been established yet. We prove this as a simple corollary of our result