Exponential Strong Converse for Successive Refinement with Causal Decoder Side Information
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We revisit the successive refinement problem with causal decoder side information considered by Maor and Merhav (2008) and strengthen their result by deriving an exponential strong converse theorem. To be specific, we show that for any rate-distortion tuple outside the rate-distortion region of the successive refinement problem with causal decoder side information, the 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.
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