Improved Upper Bounds and Structural Results on the Capacity of the Discrete-Time Poisson Channel. Cheraghchi, M. & Ribeiro, J. IEEE Transactions on Information Theory, 65(7):4052–4068, 2019. Preliminary version in Proceedings of ISIT 2018.Link Paper doi abstract bibtex New capacity upper bounds are presented for the discrete-time Poisson channel with no dark current and an average-power constraint. These bounds are a consequence of techniques developed for the seemingly unrelated problem of upper bounding the capacity of binary deletion and repetition channels. Previously, the best known capacity upper bound in the regime where the average-power constraint does not approach zero was due to Martinez (JOSA B, 2007), which is re-derived as a special case of the framework developed in this paper. Furthermore, this framework is carefully instantiated in order to obtain a closed-form bound that improves the result of Martinez everywhere. Finally, capacity-achieving distributions for the discrete-time Poisson channel are studied under an average-power constraint and/or a peak-power constraint and arbitrary dark current. In particular, it is shown that the support of the capacity-achieving distribution under an average-power constraint must only be countably infinite. This settles a conjecture of Shamai (IEE Proceedings I, 1990) in the affirmative. Previously, it was only known that the support must be an unbounded set.
@ARTICLE{ref:CR19:poi,
author = {Mahdi Cheraghchi and Jo\~{a}o Ribeiro},
title = {Improved Upper Bounds and Structural Results on the
Capacity of the Discrete-Time {Poisson} Channel},
year = 2019,
journal = {IEEE Transactions on Information Theory},
volume = 65,
number = 7,
pages = {4052--4068},
note = {Preliminary version in Proceedings of {ISIT 2018}.},
doi = {10.1109/TIT.2019.2896931},
url_Link = {https://ieeexplore.ieee.org/document/8632953},
url_Paper = {https://arxiv.org/abs/1801.02745},
abstract = {New capacity upper bounds are presented for the
discrete-time Poisson channel with no dark current
and an average-power constraint. These bounds are a
consequence of techniques developed for the
seemingly unrelated problem of upper bounding the
capacity of binary deletion and repetition
channels. Previously, the best known capacity upper
bound in the regime where the average-power
constraint does not approach zero was due to
Martinez (JOSA B, 2007), which is re-derived as a
special case of the framework developed in this
paper. Furthermore, this framework is carefully
instantiated in order to obtain a closed-form bound
that improves the result of Martinez
everywhere. Finally, capacity-achieving
distributions for the discrete-time Poisson channel
are studied under an average-power constraint and/or
a peak-power constraint and arbitrary dark
current. In particular, it is shown that the support
of the capacity-achieving distribution under an
average-power constraint must only be countably
infinite. This settles a conjecture of Shamai (IEE
Proceedings I, 1990) in the affirmative. Previously,
it was only known that the support must be an
unbounded set. }
}
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These bounds are a consequence of techniques developed for the seemingly unrelated problem of upper bounding the capacity of binary deletion and repetition channels. Previously, the best known capacity upper bound in the regime where the average-power constraint does not approach zero was due to Martinez (JOSA B, 2007), which is re-derived as a special case of the framework developed in this paper. Furthermore, this framework is carefully instantiated in order to obtain a closed-form bound that improves the result of Martinez everywhere. Finally, capacity-achieving distributions for the discrete-time Poisson channel are studied under an average-power constraint and/or a peak-power constraint and arbitrary dark current. In particular, it is shown that the support of the capacity-achieving distribution under an average-power constraint must only be countably infinite. This settles a conjecture of Shamai (IEE Proceedings I, 1990) in the affirmative. 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Previously, the best known capacity upper\n bound in the regime where the average-power\n constraint does not approach zero was due to\n Martinez (JOSA B, 2007), which is re-derived as a\n special case of the framework developed in this\n paper. Furthermore, this framework is carefully\n instantiated in order to obtain a closed-form bound\n that improves the result of Martinez\n everywhere. Finally, capacity-achieving\n distributions for the discrete-time Poisson channel\n are studied under an average-power constraint and/or\n a peak-power constraint and arbitrary dark\n current. In particular, it is shown that the support\n of the capacity-achieving distribution under an\n average-power constraint must only be countably\n infinite. This settles a conjecture of Shamai (IEE\n Proceedings I, 1990) in the affirmative. 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