DISCRETE-TIME POISSON CHANNEL: CAPACITY AND SIGNALLING DESIGN

Abstract

<p>The discrete-time Poisson (DTP) channel models a wide range of optical communication channels. The channel capacity and capacity-achieving distributions are generally unknown. This thesis addresses system design of DTP channels and presents novel contributions to the capacity of DTP channel, properties and closed-form expression of the capacity-achieving distribution under peak and average constraints, signalling design, and sum-capacity-achieving distributions of DTP multiple access channel (MAC) with peak amplitude constraints.</p> <p>Two algorithms are developed to compute the channel capacity of DTP channel as well as the capacity-achieving distribution with average and peak amplitude constraints. Tight lower bounds based on input distributions with simple forms are presented. Non-uniform signalling algorithms to achieve the channel capacity are also demonstrated. Fundamental properties of capacity-achieving distributions for DTP channels are established. Furthermore, necessary and sufficient conditions on the optimality of binary distributions are presented. Analytical expressions for the capacity-achieving distributions of the DTP channel are derived when there is no dark current and when the dark current is large enough. A two-user DTP multiple access channel model is proposed and it is shown that the sum-capacity-achieving distributions under peak amplitude constraints are discrete with a finite number of mass points.</p>