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• W2892598878 abstract "Recently, two extensions of Wyner's common informationtextemdash exact and Renyi common informationstextemdash were introduced respectively by Kumar, Li, and El Gamal (KLE), and the present authors. The class of common information problems involves determining the minimum rate of the common input to two independent processors needed to exactly or approximately generate a target joint distribution. For the exact common information problem, exact generation of the target distribution is required, while for Wyner's and $alpha$-Renyi common informations, the relative entropy and Renyi divergence with order $alpha$ were respectively used to quantify the discrepancy between the synthesized and target distributions. The exact common information is larger than or equal to Wyner's common information. However, it was hitherto unknown whether the former is strictly larger than the latter for some joint distributions. In this paper, we first establish the equivalence between the exact and $infty$-Renyi common informations, and then provide single-letter upper and lower bounds for these two quantities. For doubly symmetric binary sources, we show that the upper and lower bounds coincide, which implies that for such sources, the exact and $infty$-Renyi common informations are completely characterized. Interestingly, we observe that for such sources, these two common informations are strictly larger than Wyner's. This answers an open problem posed by KLE. Furthermore, we extend Wyner's, $infty$-Renyi, and exact common informations to sources with countably infinite or continuous alphabets, including Gaussian sources." @default.
• W2892598878 created "2018-10-05" @default.
• W2892598878 creator A5057874208 @default.
• W2892598878 creator A5058345431 @default.
• W2892598878 date "2018-09-30" @default.
• W2892598878 modified "2023-09-27" @default.
• W2892598878 title "On Exact and $infty$-R'enyi Common Informations" @default.
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