On The Capacities of Discrete Memoryless Thresholding Channels

In this paper, we study the channel capacity of discrete memoryless thresholding channels (DMTCs) that are used in Pulse Amplitude Modulation (PAM) for LED free-space transmissions. Although capacities of discrete memoryless channels (DMC) are well-studied, and can be determined by various algorithms, the capacity of a DMTC is less explored and its capacity is more difficult to obtain. This is due to the fact that, unlike a typical DMC channel whose the capacity is a function input distribution, the capacity of a DTMC channel is a function of both input distribution and decision thresholds. To resolve this problem, we propose an algorithm for finding the channel capacity of a DMTC. Both theoretical and numerical results are provided to verify our approach.