Analytical calculation formulas for capacities of classical and classical-quantum channels

TL;DR

This paper introduces a novel analytical formula for calculating the capacities of classical and classical-quantum channels without iterations, providing exact solutions and improving computational efficiency over existing iterative algorithms.

Contribution

The paper presents the first non-iterative analytical formulas for classical and classical-quantum channel capacities, enabling direct computation of optimal values.

Findings

The formulas accurately compute channel capacities in example cases.

The approach eliminates the need for iterative algorithms, saving computational resources.

Exact capacity values are obtained without approximation or iterative convergence.

Abstract

We derive an analytical calculation formula for the channel capacity of a classical channel without any iteration while its existing algorithms require iterations and the number of iteration depends on the required precision level. Hence, our formula is its first analytical formula without any iteration. We apply the obtained formula to examples and see how the obtained formula works in these examples. Then, we extend it to the channel capacity of a classical-quantum (cq-) channel. Many existing studies proposed algorithms for a cq-channel and all of them require iterations. Our extended analytical algorithm have also no iteration and output the exactly optimum values.