Analytical Algorithm for Capacities of Classical and Classical-Quantum Channels

We derive an analytical algorithm for the channel capacity of a classical channel without any iteration, while its existing algorithms require iterations and the number of iterations depends on the required precision level. Hence, our algorithm is its first analytical algorithm for this task without any iteration, while this algorithm needs several conditions for the channel. We apply the obtained algorithm to examples, and see how the obtained algorithm 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 has also no iteration, and outputs the exactly optimum value.