Second- and Third-Order Asymptotics of the Continuous-Time Poisson Channel
| Autor: | Sakai, Yuta, Tan, Vincent Y. F., Kovačević, Mladen |
|---|---|
| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | IEEE Trans. Inform. Theory, vol. 66, no. 8, pp. 4742-4760, Aug. 2020 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1109/TIT.2020.2987788 |
| Popis: | 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. Comment: 26 pages, to appear in the IEEE Transactions on Information Theory, vol. 66, 2020 |
| Databáze: | arXiv |
| Externí odkaz: |
|