Capacity and Error Probability Analysis of Neuro-Spike Communication Exploiting Temporal Modulation

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.