Distributed detection and coding in information networks

This thesis investigates the distributed information and detection of a binary source through a parallel system of relays. Each relay observes the source output through a noisy channel, and the channel outputs are independent conditional on the source input. The relays forward limited information through a noiseless link to the final destination which makes an optimal decision. The essence of the problem lies in the loss of information at the relays. To solve this problem, the characteristics of the error curve are established and developed as a tool to build a fundamental framework for analysis. For understanding, the simplest non-trivial case of two relays, each forwarding only a single binary digit to the final destination is first studied. If the binary output constraint is removed and the output alphabet size for one relay is M, then no more than M + 1 alphabet symbols are required from the other relay for optimal operation. For arbitrary channels, a number of insights are developed about the structure of the optimal strategies for the relay and final destination. These lead to a characterization of the optimal solution. Furthermore, the complete solution to the Additive Gaussian Noise channel is also provided. Thesis Supervisor: Robert G. Gallager Title: Professor of Electrical Engineering and Computer Science