Linear programming based finite blocklength converses for some network-like problems

The linear programming (LP) based approach we introduced in [1] for finding finite blocklength converses for joint source-channel coding is extended to some network-like settings. Finite blocklength channel coding of compound and averaged channels under the maximum probability error criterion is considered. Through the LP approach new converses are obtained which imply a weak converse for both channels and a strong converse for the compound channel. The LP approach is also extended to the networked setting and a new finite blocklength converse for Slepian-Wolf coding which improves on the converse in Han [2, Lemma 7.2.2] is derived.

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