# Amplitude Constrained Poisson Noise Channel: Properties of the Capacity-Achieving Input Distribution

Alex Dytso, Luca Barletta, Shlomo Shamai Shitz

نتاج البحث: فصل من :كتاب / تقرير / مؤتمرمنشور من مؤتمرمراجعة النظراء

## ملخص

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.

اللغة الأصلية الإنجليزيّة 2021 IEEE Information Theory Workshop, ITW 2021 - Proceedings 9781665403122 https://doi.org/10.1109/ITW48936.2021.9611398 نُشِر - 2021 2021 IEEE Information Theory Workshop, ITW 2021 - Virtual, Online, اليابانالمدة: ١٧ أكتوبر ٢٠٢١ → ٢١ أكتوبر ٢٠٢١

### سلسلة المنشورات

الاسم 2021 IEEE Information Theory Workshop, ITW 2021 - Proceedings

### !!Conference

!!Conference 2021 IEEE Information Theory Workshop, ITW 2021 اليابان Virtual, Online ١٧/١٠/٢١ → ٢١/١٠/٢١

## All Science Journal Classification (ASJC) codes

• !!Computational Theory and Mathematics
• !!Computer Networks and Communications
• !!Information Systems
• !!Software

## بصمة

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