Improved Upper Bounds and Structural Results on the Capacity of the Discrete-Time Poisson Channel
Improved Upper Bounds and Structural Results on the Capacity of the Discrete-Time Poisson Channel
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DOI：
10.1109/tit.2019.2896931
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发表时间：
2019-07-01
影响因子：
2.5
通讯作者：
Ribeiro, Joao
中科院分区：
文献类型：
--
作者：
Cheraghchi, Mahdi;Ribeiro, Joao
为离散时间泊松通道提供了新的容量上限，没有暗电流和平均功率约束。这些界限是针对看似无关的二进制缺失和重复渠道能力的看似无关的问题而开发的技术的结果。以前，在平均值限制下未接近零的制度中，最著名的容量上限是由于马丁内斯（Josa B，2007年）引起的，后者是本文开发的框架的特殊情况。此外，该框架是仔细实例化的，以获得封闭形式的结合，以改善Martinez到处的结果。最后，在平均功率约束和/或峰值限制和任意黑电流下研究了离散时间泊松通道的容量调整分布。特别是，这表明在平均功率约束下的能力成绩分布的支持必须仅是无限的。这解决了Shamai的猜想（IEE会议记录I，1990年）。以前，只知道支持必须是无限的集合。
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.