TY - GEN

T1 - Amplitude Constrained Poisson Noise Channel

T2 - 2021 IEEE Information Theory Workshop, ITW 2021

AU - Dytso, Alex

AU - Barletta, Luca

AU - Shitz, Shlomo Shamai

N1 - Publisher Copyright: © 2021 IEEE.

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85123414092&partnerID=8YFLogxK

U2 - https://doi.org/10.1109/ITW48936.2021.9611398

DO - https://doi.org/10.1109/ITW48936.2021.9611398

M3 - منشور من مؤتمر

T3 - 2021 IEEE Information Theory Workshop, ITW 2021 - Proceedings

BT - 2021 IEEE Information Theory Workshop, ITW 2021 - Proceedings

Y2 - 17 October 2021 through 21 October 2021

ER -