Tight Exponential Strong Converse for Source Coding Problem with Encoded Side Information

09/21/2022

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by   Daisuke Takeuchi, et al.

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The source coding problem with encoded side information is considered. A lower bound on the strong converse exponent has been derived by Oohama, but its tightness has not been clarified. In this paper, we derive a tight strong converse exponent. The achievability part is derived by a careful analysis of the type argument. The converse part is proved by a judicious use of the change-of-measure argument, which was introduced by Gu-Effros and further developed by Tyagi-Watanabe. Interestingly, the soft Markov constraint, which was introduced by Oohama as a proof technique, is naturally incorporated into the characterization of the exponent.