AI 中文总结
研究有限记忆泊松信道在峰值和平均光强度约束下的i.i.d.约束容量问题，通过对连续状态隐马尔可夫输出过程熵率的研究，证明最大化平稳互信息率的输入分布有有限支撑，采用滤波 - 遗忘估计等方法得出结论。
AI 中文摘要
具有有限符号间干扰的离散时间泊松信道为直接检测光链路提供了自然模型，其中多径记忆和信号相关散粒噪声同时出现。在峰值和平均光强度约束下，我们研究此类信道的独立同分布（i.i.d.）约束容量问题。我们证明，在i.i.d.输入类中最大化平稳互信息率的每个输入分布都具有有限支撑。证明是直接针对由有限记忆信道引起的连续状态隐马尔可夫输出过程的熵率进行的。我们首先建立一个滤波 - 遗忘估计，其常数在所有可允许的i.i.d.输入律上是一致的。然后我们推导熵率的一阶变分，构造相应影响函数的全纯扩展，并将Karush - Kuhn - Tucker条件与超线性增长论证相结合。
英文摘要
Discrete-time Poisson channels with finite intersymbol interference provide a natural model for direct-detection optical links in which multipath memory and signal-dependent shot noise appear simultaneously. Under peak and average optical-intensity constraints, we study the independent and identically distributed (i.i.d.)-constrained capacity problem of such channels. We prove that every input distribution maximizing the stationary mutual information rate within the i.i.d. input class has finite support. The proof is carried out directly on the entropy rate of the continuous-state hidden Markov output process induced by the finite-memory channel. We first establish a filtering-forgetting estimate whose constants are uniform over all admissible i.i.d. input laws. We then derive the entropy-rate first variation, construct a holomorphic extension of the corresponding influence function, and combine the Karush-Kuhn-Tucker condition with a supralinear growth argument.
Comments26 pages, 3 figures
