The Capacity Region of a Product Gaussian Broadcast Channel with Degraded Message Sets
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abstract
A product Gaussian broadcast channel with three receivers and degraded message sets is considered. A single-letter characterization of the capacity region was obtained in a recent work of Nair and El Gamal based on superposition coding and indirect decoding. Through Lagrangian theory and an extremal entropy inequality, the single-letter expression of Nair and El Gamal is evaluated for the specific product Gaussian model, which leads to an explicit characterization of the capacity region.