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arXiv 2011.05931cs.ITmath.IT
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有记忆离散Poisson信道上的比特传输

Transmission of a Bit over a Discrete Poisson Channel with Memory

Niloufar Ahmadypour, Amin Gohari

摘要:

用于比特传输的编码方案将给定比特映射到信道输入序列(称为与传输比特相关联的码字)。在本文中,我们研究的问题设计的最佳码的离散泊松信道的记忆(峰值功率和总功率约束下)。具有记忆的离散泊松信道的输出是泊松分布的随机变量,其平均值包括固定的加性噪声和过去输入符号的线性组合。假设一个最大似然(ML)解码器,我们搜索一个码本,具有最小的可能的错误概率。这个问题是具有挑战性的,因为代码的错误概率不具有封闭形式的解析表达式。对于只有一个总功率约束的情况下,最佳的代码结构,得到的条件是块长度大于存储长度的信道。对于只有一个峰值功率约束的情况下,最佳的代码推导出任意的内存和块长度在高功率政权。对于同时具有峰值功率和总功率约束的情况,当总功率和峰值功率界都很大时,推导出了无记忆泊松信道的最优编码。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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