Information and control: matching channels

Let /spl Xscr/ serve as input alphabet and let /spl Yscr/ serve as output alphabet. By adding dummy letters we can always assume that /spl Xscr//spl sub//spl Yscr/. The transmission of letters is ruled by a class /spl Wscr/ of stochastic matrices with |/spl Xscr/| rows and |/spl Yscr/| columns. In addition to the sender and receiver, there is a third person (or device) called controller who decides which matrix W/spl isin//spl Wscr/={(w(/spl middot/|/spl middot/|s):s/spl isin/S) shall govern the transmission of a letter by the sender. The controller knows which codeword the sender wants to transmit. The receiver has no knowledge about the actions of the controller. As code concept appropriate for this situation we introduce a matching code.