A partial ordering of discrete, memoryless channels
Hermann J. Helgert · IEEE Transactions on Information Theory · 1967
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 ifK_{1}andK_{2}are channels such thatK_{1}includesK_{2}, then if a code exists forK_{2}, there exists a code forK_{1}, whose probability of error is never greater than that of the code forK_{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.