English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This work considers a discrete-time Poisson noise channel with an inputamplitude constraint $\mathsf{A}$ and a dark current parameter $\lambda$. It isknown that the capacity-achieving distribution for this channel is discretewith finitely many points. Recently, for $\lambda=0$, a lower bound of order$\sqrt{\mathsf{A}}$ and an upper bound of order $\mathsf{A} \log^2(\mathsf{A})$have been demonstrated on the cardinality of the support of the optimal inputdistribution.  In this work, we improve these results in several ways. First, we provideupper and lower bounds that hold for non-zero dark current. Second, we producea sharper upper bound with a far simpler technique. In particular, for$\lambda=0$, we sharpen the upper bound from the order of $\mathsf{A}\log^2(\mathsf{A})$ to the order of $\mathsf{A}$. Finally, some otheradditional information about the location of the support is provided.

Improved Bounds on the Number of Support Points of the Capacity-Achieving Input for Amplitude Constrained Poisson Channels