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

机译：具有辅助信息的连续字母通道的容量分析，第一部分：通用框架

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摘要

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 analytical 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.
机译：在接收器处具有辅助信息的信道的容量分析一直是人们关注的领域。对于有限字母通道的情况，已经很好地研究了此问题。但是，由于连续字母固有的分析困难，因此结果不容易推广到连续字母通道的情况。在这个由两部分组成的论文的第一部分中，我们提出了一个分析框架，用于对带有接收器边信息的连续字母通道进行容量分析。为此，我们为相互信息的弱连续性和严格凹度建立了新颖的充要条件。这些条件用于调查能力获得措施的存在和唯一性。此外，我们得出了必要和充分的条件，这些条件表征了接收方带有辅助信息的连续字母信道的容量值和容量实现措施。

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