Capacity Analysis for Continuous Alphabet Channels with Side Information, Part I: A General Framework

Capacity analysis for channels with side information at the receiver has been an active area of interest. This problem is well investigated for the case of finite alphabet channels. However, the results are not easily generalizable to the case of continuous alphabet channels due to analytic difficulties inherent with continuous alphabets. In the first part of this two-part paper, we address an analytical framework for capacity analysis of continuous alphabet channels with side information at the receiver. For this purpose, we establish novel necessary and sufficient conditions for weak* continuity and strict concavity of the mutual information. These conditions are used in investigating the existence and uniqueness of the capacity-achieving measures. Furthermore, we derive necessary and sufficient conditions that characterize the capacity value and the capacity-achieving measure for continuous alphabet channels with side information at the receiver.Comment: Submitted to IEEE Trans. Inform. Theor

On regret of parametric mismatch in minimum mean square error estimation

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On capacity analysis for continuous alphabet channels

In this paper, we address an analytical framework for capacity analysis of continuous alphabet channels with side information at the receiver. We study the mutual information function and some of its analytical properties such as strict concavity and continuity. For this purpose, we use the weak * topology and establish necessary and sufficient conditions for strict concavity and continuity of the mutual information based on the weak * topology. We then raise the issue of capacity analysis and address necessary and sufficient conditions for the existence, uniqueness, and the expression of capacity-achieving measure