Amplitude Constrained Poisson Noise Channel: Properties of the Capacity-Achieving Input Distribution
Document Type
Conference Proceeding
Publication Date
1-1-2021
Abstract
This work considers a Poisson noise channel with an amplitude constraint. It is well-known that the capacity-achieving input distribution for this channel is discrete with finitely many points. We sharpen this result by introducing upper and lower bounds on the number of mass points. In particular, the upper bound of order A log2(A) and lower bound of order √A are established where A is the constraint on the input amplitude. In addition, along the way, we show several other properties of the capacity and capacity-achieving distribution. For example, it is shown that the capacity is equal to - log P_Y^*(0) where P_Y∗ is the optimal output distribution. Moreover, an upper bound on the values of the probability masses of the capacity-achieving distribution and a lower bound on the probability of the largest mass point are established.
Identifier
85123414092 (Scopus)
ISBN
[9781665403122]
Publication Title
2021 IEEE Information Theory Workshop Itw 2021 Proceedings
External Full Text Location
https://doi.org/10.1109/ITW48936.2021.9611398
Recommended Citation
Dytso, Alex; Barletta, Luca; and Shitz, Shlomo Shamai, "Amplitude Constrained Poisson Noise Channel: Properties of the Capacity-Achieving Input Distribution" (2021). Faculty Publications. 4538.
https://digitalcommons.njit.edu/fac_pubs/4538