Some Problems on Encoders and Channels in Information Theory and Communications

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The principal investigator (PI) proposes to examine two problems in the course of his research. One of these problems involves determining the maximum amount of compression that can be achieved in a message so that it can be reliably transmitted over a communication system. The research will focus on the little understood situation in which the characteristics of both the system and the message- generating device vary with time. The second problem that the PI proposes to explore involves determining the performance of procedures employing feedback for coding sequential data. At present, the only general method for comparing two such procedures is to test to see which of them yields the smaller error. Testing can be eliminated through the use of a formula for the error produced by a general feedback procedure. The search for such a formula is included in the proposed investigation. More specifically, the principal investigator proposes to address communications problems including proving coding theorems for nonstationary communication channels having a variable-length structure, the calculation of the decoding error arising in linear filtering the output sequence of a feedback encoding scheme, and the determination of the optimal average rate at which a nonstationary information source can be encoded via a general class of variable-length source encoder.