论文标题
通过内存的离散泊松通道传输一点
Transmission of a Bit over a Discrete Poisson Channel with Memory
论文作者
论文摘要
用于传输位的编码方案给定位映射到一系列通道输入（称为与传输位关联的代码字）。在本文中，我们研究了为带有内存的离散泊松通道设计最佳代码的问题（在峰值和总功率限制下）。带有内存的离散泊松通道的输出是泊松分布式随机变量，其平均值包括固定添加噪声和过去输入符号的线性组合。假设最大样品（ML）解码器，我们搜索具有最小可能的误差概率的代码簿。这个问题是具有挑战性的，因为代码的错误概率没有封闭形式的分析表达式。对于仅具有总功率约束的情况，只要区块长大就大于通道的存储长度，就可以获得最佳代码结构。对于仅具有峰值约束的情况，最佳代码是针对任意内存和高功率制度中的区块长度的。对于具有峰值功率和总功率约束的情况，当总功率和峰值功率边界都大时，无内存的泊松通道会得出最佳代码。
A coding scheme for transmission of a bit maps a given bit to a sequence of channel inputs (called the codeword associated to the transmitted bit). In this paper, we study the problem of designing the best code for a discrete Poisson channel with memory (under peak-power and total-power constraints). The outputs of a discrete Poisson channel with memory are Poisson distributed random variables with a mean comprising of a fixed additive noise and a linear combination of past input symbols. Assuming a maximum-likelihood (ML) decoder, we search for a codebook that has the smallest possible error probability. This problem is challenging because error probability of a code does not have a closed-form analytical expression. For the case of having only a total-power constraint, the optimal code structure is obtained, provided that the blocklength is greater than the memory length of the channel. For the case of having only a peak-power constraint, the optimal code is derived for arbitrary memory and blocklength in the high-power regime. For the case of having both the peak-power and total-power constraints, the optimal code is derived for memoryless Poisson channels when both the total-power and the peak-power bounds are large.
