One-Cold Poisson Channel: A Simple Continuous-Time Channel with Zero Dispersion
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914256120709120 |
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| author | Li, Cheuk Ting |
| author_facet | Li, Cheuk Ting |
| contents | We introduce the one-cold Poisson channel (OCPC), where the transmitter chooses one of several frequency bands to attenuate at a time. In particular, the perfect OCPC, where the number of bands is unlimited, is an extremely simple continuous-time memoryless channel. It has a capacity 1, zero channel dispersion, and an information spectrum being the degenerate distribution at 1. It is the only known nontrivial (discrete or continuous-time) memoryless channel with a closed-form formula for its optimal non-asymptotic error probability, making it the simplest channel in this sense. A potential application is optical communication with a tunable band rejection filter. Due to its simplicity, we may use it as a basic currency of information that is infinitely divisible, as an alternative to bits which are not infinitely divisible. OCPC with perfect feedback gives a generalization of prefix codes. We also study non-asymptotic coding and channel simulation results for the general OCPC. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_09894 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | One-Cold Poisson Channel: A Simple Continuous-Time Channel with Zero Dispersion Li, Cheuk Ting Information Theory Signal Processing We introduce the one-cold Poisson channel (OCPC), where the transmitter chooses one of several frequency bands to attenuate at a time. In particular, the perfect OCPC, where the number of bands is unlimited, is an extremely simple continuous-time memoryless channel. It has a capacity 1, zero channel dispersion, and an information spectrum being the degenerate distribution at 1. It is the only known nontrivial (discrete or continuous-time) memoryless channel with a closed-form formula for its optimal non-asymptotic error probability, making it the simplest channel in this sense. A potential application is optical communication with a tunable band rejection filter. Due to its simplicity, we may use it as a basic currency of information that is infinitely divisible, as an alternative to bits which are not infinitely divisible. OCPC with perfect feedback gives a generalization of prefix codes. We also study non-asymptotic coding and channel simulation results for the general OCPC. |
| title | One-Cold Poisson Channel: A Simple Continuous-Time Channel with Zero Dispersion |
| topic | Information Theory Signal Processing |
| url | https://arxiv.org/abs/2601.09894 |