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• W2227692978 abstract "The basic two-terminal common randomness (CR) and key generation models are considered, where the communication between the terminals may be limited, and in particular may not be enough to achieve the maximum CR/key rate. We introduce general notions of $XY$-absolutely continuity and $XY$-concave function, and characterize the first order CR/key-communication tradeoff in terms of the evaluation of the $XY$-concave envelope of a functional defined on a set of distributions, which is simpler than the multi-letter characterization. Two extreme cases are given special attention. First, in the regime of very small communication rates, the CR bits per interaction bit (CRBIB) and key bits per interaction bit (KBIB) are expressed with a new symmetrical strong data processing constant, defined as the minimum of a parameter such that a certain information-theoretic functional touches its $XY$-concave envelope at a given source distribution. We also provide a computationally friendly strong converse bound for CRBIB and a similar (but not necessarily strong) one for KBIB in terms of the supremum of the maximal correlation coefficient over a set of distributions. The proof uses hypercontractivity and properties of the R'enyi divergence. A criterion the tightness of the bound is given with applications to binary symmetric sources. Second, a new characterization of the minimum interaction rate needed for achieving the maximum key rate (MIMK) is given, and we resolve a conjecture by Tyagi and Narayan cite{tyagi2013common} regarding the MIMK for binary sources. We also propose a new conjecture for binary symmetric sources." @default.
• W2227692978 created "2016-06-24" @default.
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• W2227692978 date "2016-01-05" @default.
• W2227692978 modified "2023-10-18" @default.
• W2227692978 title "Common Randomness and Key Generation with Limited Interaction." @default.
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• W2227692978 hasPublicationYear "2016" @default.
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