A method of analysis of discrete communication feedback systems

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A method of analysis of discrete communication feedback systems with noisy forward and feedback channels is given. The method uses the state transition graphs introduced by S. S. L. Chang and is based on a division of transmissions into four types. The method is developed for the discrete system in which the auxiliary decision about stopping or continuing the transmission of a message is binary, but it can be extended for the case when such decisions can take more than two forms. It permits a uniform analysis, under quite general assumptions, of both decision and information feedback systems. However in general it may be necessary to resort to numerical calculations. To illustrate the method a special case of stationary systems with independent transmission of messages and auxiliary decisions is considered. For this particular case it is possible to derive exact formulae for the probability of correct ultimate decision and for the average number of transmissions both for decision and for information feedback systems.

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