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.

翻译：本文介绍了一种单冷泊松信道（OCPC），其发射器每次选择多个频带中的一个进行衰减。特别地，当频带数量不受限制时，完美OCPC是一种极其简单的连续时间无记忆信道。其信道容量为1，信道色散为零，信息谱为在1处的退化分布。这是目前已知唯一具有闭式最优非渐近误码率公式的非平凡（离散或连续时间）无记忆信道，在此意义上它是最简单的信道。一个潜在的应用场景是采用可调谐带阻滤波器的光通信。由于其简单性，我们可以将其作为一种无限可分的基本信息度量单位，作为不可无限分割的比特的替代方案。具有完美反馈的OCPC可推广前缀码的概念。本文还研究了通用OCPC的非渐近编码与信道仿真结果。