Second- and Third-Order Asymptotics of the Continuous-Time Poisson Channel
Second- and Third-Order Asymptotics of the Continuous-Time Poisson Channel
复制标题
连续时间泊松通道的二阶和三阶渐近
DOI：
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发表时间：
2019
影响因子：
2.5
通讯作者：
Mladen Kovačević
中科院分区：
文献类型：
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作者：
Yuta Sakai;V. Tan;Mladen Kovačević
该纸是连续时间泊松通道的最佳二阶编码率证明是由Wyner离散的渠道引起的新型输出分布的构造，以及适当的$ epsilon $ -NET的构建，而成就证明了一般性的概率。程序以证明Polyanskiy提出的非敏感离散无内存渠道的三阶术语，几种非标准技术 - 例如，使用对数Sobolev不平等的典型集合的新定义和界限，可用于处理连续的性质频道。
The paper derives the optimal second-order coding rate for the continuous-time Poisson channel. We also obtain bounds on the third-order coding rate. This is the first instance of a second-order result for a continuous-time channel. The converse proof hinges on a novel construction of an output distribution induced by Wyner’s discretized channel and the construction of an appropriate $epsilon $ -net of the input probability simplex. While the achievability proof follows the general program to prove the third-order term for non-singular discrete memoryless channels put forth by Polyanskiy, several non-standard techniques—such as new definitions and bounds on the probabilities of typical sets using logarithmic Sobolev inequalities—are employed to handle the continuous nature of the channel.