مرکز منطقه ای اطلاع رساني علوم و فناوري - A partial ordering of discrete, memoryless channels

Abstract :

This paper is concerned with the structure of a partial ordering of discrete, memoryless communication channels. These are identified with equivalence classes of stochastic matrices into which the set of all stochastic matrices is partitioned by a relation of matrix inclusion. The relation carries over to channels and induces a partial ordering on them, having the property that if $K_{1}$ and $K_{2}$ are channels such that $K_{1}$ includes $K_{2}$ , then if a code exists for $K_{2}$ , there exists a code for $K_{1}$ , whose probability of error is never greater than that of the code for $K_{2}$ . Results are derived which specify the equivalence classes of stochastic matrices corresponding to the binary and the symmetric channels and resolve the structure of the partial ordering between them.