Revisiting Chernoff Information with Likelihood Ratio Exponential Families

Joint Detection and Communication over Type-Sensitive Networks

Due to the difficulty of decentralized inference with conditional dependent observations, and motivated by large-scale heterogeneous networks, we formulate a framework for decentralized detection with coupled observations. Each agent has a state, and the empirical distribution of all agents' states or the type of network dictates the individual agents' behavior. In particular, agents' observations depend on both the underlying hypothesis as well as the empirical distribution of the agents' states. Hence, our framework captures a high degree of coupling, in that an individual agent's behavior depends on both the underlying hypothesis and the behavior of all other agents in the network. Considering this framework, the method of types, and a series of equicontinuity arguments, we derive the error exponent for the case in which all agents are identical and show that this error exponent depends on only a single empirical distribution. The analysis is extended to the multi-class case, and numerical results with state-dependent agent signaling and state-dependent channels highlight the utility of the proposed framework for analysis of highly coupled environments.

Information and Divergence Measures

The present Special Issue of Entropy, entitled Information and Divergence Measures, covers various aspects and applications in the general area of Information and Divergence Measures [...].

The Cauchy Distribution in Information Theory

The Gaussian law reigns supreme in the information theory of analog random variables. This paper showcases a number of information theoretic results which find elegant counterparts for Cauchy distributions. New concepts such as that of equivalent pairs of probability measures and the strength of real-valued random variables are introduced here and shown to be of particular relevance to Cauchy distributions.