Title :
Capacity-Achieving Distributions for the Discrete-Time Poisson Channel—Part I: General Properties and Numerical Techniques
Author :
Jihai Cao ; Hranilovic, Steve ; Jun Chen
Author_Institution :
Dept. of Electr. & Comput. Eng., McMaster Univ., Hamilton, ON, Canada
Abstract :
Despite being an accepted model for a wide variety of optical channels, few general results on optimal signalling for discrete-time Poisson (DTP) channels are known. Among the most significant is that under simultaneous peak and average constraints, the capacity-achieving distributions are discrete with a finite number of mass points. In this paper, several fundamental properties of capacity-achieving distributions for DTP channels are established. In particular, we demonstrate that all capacity-achieving distributions of the DTP channel have zero as a mass point. In the case of only a peak constraint, it is further shown that the optimal distribution always has a mass point at the maximum amplitude. Finally, under solely an average power constraint, it is shown that a finite number of mass points are insufficient to achieve the capacity. In addition to these analytical results, a numerical algorithm based on deterministic annealing is presented which can efficiently compute both the channel capacity and the associated optimal input distribution under peak and average power constraints. Numerical lower bounds based on the envelope of information rates induced by the maxentropic distributions are also shown to be extremely close to the capacity, especially in the low power regime.
Keywords :
channel capacity; wireless channels; DTP channels; average power constraint; capacity-achieving distributions; channel capacity; deterministic annealing; discrete-time Poisson channel; maxentropic distributions; maximum amplitude; optical channels; optimal input distribution; Annealing; Channel capacity; Channel models; Dark current; Mutual information; Photonics; Upper bound; Discrete-time Poisson channel; capacity-achieving distributions; deterministic annealing;
Journal_Title :
Communications, IEEE Transactions on
DOI :
10.1109/TCOMM.2013.112513.130142