On the Structure of Real-Time Encoders and Decoders in a Multi-Terminal Communication System

Details On the Structure of Real-Time Encoders and Decoders in a Multi-Terminal Communication System On the Structure of Real-Time Encoders and Decoders in a Multi-Terminal Communication System

2009-10-26

arxiv.org/abs/0910.4955v1

Computer Science

Information Theory

Scientific paper

A real-time communication system with two encoders communicating with a single receiver over separate noisy channels is considered. The two encoders make distinct partial observations of a Markov source. Each encoder must encode its observations into a sequence of discrete symbols. The symbols are transmitted over noisy channels to a finite memory receiver that attempts to reconstruct some function of the state of the Markov source. Encoding and decoding must be done in real-time, that is, the distortion measure does not tolerate delays. Under the assumption that the encoders' observations are conditionally independent Markov chains given an unobserved time-invariant random variable, results on the structure of optimal real-time encoders and the receiver are obtained. It is shown that there exist finite-dimensional sufficient statistics for the encoders. The problem with noiseless channels and perfect memory at the receiver is then considered. A new methodology to find the structure of optimal real-time encoders is employed. A sufficient statistic with a time-invariant domain is found for this problem. This methodology exploits the presence of common information between the encoders and the receiver when communication is over noiseless channels.

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