Computing the Feedback Capacity of Finite State Channels using Reinforcement Learning. In this paper, we propose a novel method to compute the feedback capacity of channels with memory using reinforcement learning (RL). In RL, one seeks to maximize cumulative rewards collected in a sequential decisionmaking environment. This is done by collecting samples of the underlying environment and using them to learn the optimal decision rule. The main advantage of this approach is its computational efficiency, even in high dimensional problems. Hence, RL can be used to estimate numerically the feedback capacity of unifilar finite state channels (FSCs) with large alphabet size. The outcome of the RL algorithm sheds light on the properties of the optimal decision rule, which in our case, is the optimal input distribution of the channel. These insights can be converted into analytic, singleletter capacity expressions by solving corresponding lower and upper bounds. We demonstrate the efficiency of this method by analytically solving the feedback capacity of the wellknown Ising channel with a ternary alphabet. We also provide a simple coding scheme that achieves the feedback capacity.

Computing ClassicalQuantum Channel Capacity Using Blahutxe2x80x93Arimoto Type Algorithm: A Theoretical and Numerical Analysis Based on Arimotoxe2x80x99s work in 1972, we propose an iterative algorithm for computing the capacity of a discrete memoryless classicalquantum channel with a finite input alphabet and a finite dimensional output, which we call the Blahutxe2x80x93Arimoto algorithm for classicalquantum channel, and an input cost constraint is considered. We show that, to reach    e    accuracy, the iteration complexity of the algorithm is upper bounded by      log n log e  e     where n is the size of the input alphabet. In particular, when the output state        xcfx81 x     x xe2x88x88 X      is linearly independent in complex matrix space, the algorithm has a geometric convergence. We also show that the algorithm reaches an    e    accurate solution with a complexity of     O (    m 3  log n log e  e  )    , and     O (  m 3  log e  log  ( 1  xcexb4 )    e  D (  p *     p  N 0   )   )     in the special case, where m is the output dimension,     D (  p *     p  N 0   )     is the relative entropy of two distributions, and    xcexb4    is a positive number. Numerical experiments were performed and an approximate solution for the binary twodimensional case was analysed.