A New Fast Algorithm for Finding Capacity of Discrete Memoryless Thresholding Channels

This paper proposes an efficient algorithm for finding the channel capacity of discrete memoryless thresholding channels (DMTCs) that are typically used in Pulse Amplitude Modulation (PAM). While there are efficient algorithms for determining capacity of a discrete memoryless channel (DMC), it is difficult to obtain the capacity of a DMTC. Unlike a typical DMC channel whose the capacity is a convex function of the input distribution, the capacity of a DMTC is a non-convex function of both the input distribution and decision thresholds. To resolve this problem, we propose an efficient algorithm for approximating the channel capacity of a DMTC using a novel modified k-means algorithm whose computational complexity is reduced by a factor of $ \frac{M}{\log M}$ over the standard k-means algorithm, where M relates to the precision resolution of the solution. Both theoretical and numerical results are provided to verify the proposed algorithm.