In this paper, we consider a neuro-spike communication system between two neurons where nano-machines are used to enhance ability of neurons. Nano-machines can be employed for stimulation tasks when neurons have lost their ability to communicate. In the assumed system, information is conveyed via the time intervals between the input spikes train. For efficiency evaluation of temporal coding, we model the neuro-spike communication system by an additive Gamma noise channel. We present this model by considering different time distortion factors in the neuro-spike system. Then, we derive upper and lower bounds on the channel capacity. We analyze the channel capacity bounds as functions of the time intervals between the input spikes and the firing threshold of the target neuron. Moreover, we propose maximum likelihood and maximum a posteriori receivers and derive the resulting bit error probability when the system uses binary modulation. In addition, we obtain an upper bound for this error probability. Then, we extend this upper bound to the symbol error probability of the $T$ -ary modulations. Simulation results show that this upper bound is tight. The derived results show that temporal coding has a higher efficiency than spike rate coding in terms of achievable data rate.

中文翻译：

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利用时间调制的神经尖峰通信的容量和错误概率分析

在本文中，我们考虑了两个神经元之间的神经尖峰通信系统，其中使用纳米机器来增强神经元的能力。当神经元失去交流能力时，纳米机器可用于刺激任务。在假设的系统中，信息是通过输入尖峰序列之间的时间间隔来传达的。为了评估时间编码的效率，我们通过加性伽玛噪声通道对神经尖峰通信系统进行建模。我们通过考虑神经尖峰系统中不同的时间失真因素来呈现这个模型。然后，我们推导出信道容量的上限和下限。我们将通道容量边界分析为输入尖峰和目标神经元的激发阈值之间的时间间隔的函数。而且，我们提出了最大似然和最大后验接收器，并推导出系统使用二进制调制时产生的误码概率。此外，我们获得了这个错误概率的上限。然后，我们将此上限扩展到 $T$ -ary 调制的符号错误概率。仿真结果表明这个上限是紧的。推导出的结果表明，就可实现的数据速率而言，时间编码比尖峰速率编码具有更高的效率。