Channel Ordering and Supermodularity

This work introduces a new preorder over channels that is monotonic with Shannon’s mutual information for all distributions over the input alphabet. Moreover, this monotonicity also holds when substituting mutual information for quantities relative to Arimoto-Rényi conditional entropies and guessing entropy. Several results connecting this new preorder with others from the literature are proven. This work also discusses an extension of Shannon ordering based on this new preorder, and establishes that channels ordered this way are also ordered with regards to both Shannon and min-capacity.