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Abstract
We consider the k-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 k-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 Hölder’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.
Highlights
We consider the k-user successive refinement problem with causal decoder side information shown in Figure 1, which we refer to as the k-user causal successive refinement problem
We strengthen the result in [1] by providing an exponential strong converse theorem for the full k-user causal successive refinement problem, which states that the joint excess-distortion probability approaches one exponentially fast if the rate-distortion tuple falls outside the rate-distortion region
In this paper, we prove an exponential strong converse theorem for the k-user causal successive refinement problem, which significantly strengthens the weak converse as it implies that the joint excess-distortion probability tends to one exponentially fast with respect to the blocklength if the rate-distortion tuple falls outside the rate-distortion region
Summary
We consider the k-user successive refinement problem with causal decoder side information shown in Figure 1, which we refer to as the k-user causal successive refinement problem. The decoders aim to recover the source sequence based on the encoded symbols and causally available private side information sequences. K}, the j-th user aims to recover the i-th source symbol using the codewords from encoders The causal successive refinement problem was first considered by Maor and Merhav in [1] who fully characterized the rate-distortion region for the two-user version. For the k-user successive refinement problem, the loss of performance due to causal decoder side information can be derived using Theorem 1 of the present paper and the results in [2,3] for the k-user case, under certain conditions on the degradedness of the side information in [2,3]. We strengthen the result in [1] by providing an exponential strong converse theorem for the full k-user causal successive refinement problem, which states that the joint excess-distortion probability approaches one exponentially fast if the rate-distortion tuple falls outside the rate-distortion region
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