An extension of rate-distortion theory to confusion matrices

A discrete confusion matrix is completely specified by a set of transition probabilities, , where and are the input and output symbols, respectively. In this paper we examine the possibility of simulating such a matrix by an available channel with processors at the input and output, when the source is specified beforehand. The central result is to show that such a simulation is always possible when the capacity of the available channel is larger than the mutual information between the source and the desired output. Conversely, such a simulation is not possible if the capacity is less than the mutual information. These results indicate the conditions under which it is physically possible to build transmitter-receiver pairs to approximate a desired discrete confusion matrix.