Coding for and decomposition of two-way channels

A discrete memoryless two-way channel is defined by a set of transmission probabilities , where and are the transmitted signals, and and are the received signals. Shannon showed that if and are generated independently and without regard to the past, then the rates of information transmitted through the opposite channel directions will lie in a region of of the plane. The present paper investigates whether can be exceeded if the past is allowed to influence the selection of the input signals. Two-way channels are analyzed in order to determine the statistical characteristics of matching signal sources. Appendix I shows how independent messages can be encoded so that during communication the channel signal statistics would approach those caused by sources which generate inputs with arbitrary probabilities Pr and Pr . Under certain natural restrictions, the binary two-way channel can be canonically decomposed into an interconnection of pairs of oppositely oriented memoryless one-way channels connected in cascade to special channels that are noiseless whenever the signal transmitted in the opposite direction is an appropriate one. Three distinct categories are defined into which the totality of all binary channels can be partitioned, according to the type of their decomposition. If the transmission probabilities are symmetrical, equivalent channel representations can be obtained, consisting of interconnections of switches, binary adders, and independent noise sources. In the light of this characteristics of appropriate source signal generation probabilities are discussed and classes of symmetrical channels determined with the conjecture that here the best possible signal sources are memoryless.