| Abstract: | The conditions are discussed under which two square discrete memoryless channels (DMCs) in cascade commute. Two different types of channel commutativity are considered: matrix commutativity, in which changing the order of two cascaded channels results in an identical overall channel, and capacity commutativity, in which the order of two cascaded channels results in an overall channel with the same capacity as the original cascade. A theorem is presented giving necessary and sufficient conditions for a pair of square DMCs to be matrix commutative and note its implications for a number of example channel cascades. Finally, it is shown that all pairs of r-ary symmetric channels are matrix commutative, regardless of their crossover probabilities. |
