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- W2898973357 abstract "Recently, two extensions of Wyner’s common information—exact and Renyi common informations—were introduced respectively by Kumar, Li, and El Gamal (KLE), and the present authors. The class of common information problems refers to determining the minimum rate of the common input to two independent processors needed to generate an exact or approximate joint distribution. For the exact common information problem, an exact generation of the target distribution is required, while for Wyner’s and α-Renyi common informations, the relative entropy and Renyi divergence with order α 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. In this paper, we first establish the equivalence between the exact and ∞-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 ∞-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." @default.
- W2898973357 created "2018-11-09" @default.
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- W2898973357 date "2019-07-01" @default.
- W2898973357 modified "2023-09-23" @default.
- W2898973357 title "On Exact and ∞-Rényi Common Informations" @default.
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- W2898973357 doi "https://doi.org/10.1109/isit.2019.8849586" @default.
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