Alternating Optimization Approach for Computing $\hat{I}\pm$-Mutual Information and $\hat{I}\pm$-Capacity

Abstract

This study presents alternating optimization (AO) algorithms for computing $\hat{I}\pm$-mutual information ($\hat{I}\pm$-MI) and $\hat{I}\pm$-capacity based on variational characterizations of $\hat{I}\pm$-MI using a reverse channel. Specifically, we derive several variational characterizations of Sibson, Arimoto, Augustin--Csisz{\' a}r, and Lapidoth--Pfister MI and introduce novel AO algorithms for computing $\hat{I}\pm$-MI and $\hat{I}\pm$-capacity; their performances for computing $\hat{I}\pm$-capacity are also compared. The comparison results show that the AO algorithm based on the Sibson MI's characterization has the fastest convergence speed.