Joint Optimization of Input Spike Rate and Receiver Decision Threshold to Maximize Achievable Bit Rate of Neuro-Spike Communication Channel

Abstract

Nano-networks employ novel nano-scale communication techniques. These techniques are inspired by biological systems. Neuro-spike communication is an example of this communication paradigm. A new example of nano-networks is the artificial neural system where nano-machines are linked to neurons to treat the neurodegenerative diseases. In these networks, nano-machines are used to replace the damaged segments of the nervous system and they behave exactly like biological entities. In this paper, by considering a point-to-point model for the neuro-spike communication which contains several sources of randomness such as the axonal noise, random amplitude, and the synaptic noise, we analyze the achievable bit rate of the neuro-spike communication channel. This model can be divided into two main parts. The first part is the axonal pathway and the second one encompasses the synaptic transmission and the spike generation. First, we focus on the axonal pathway and we model this part as a binary channel through defining the axonal shot noise probability. Next, we investigate the synaptic transmission part to model this part as a binary channel. Then, we consider the neuro-spike communication channel as two cascaded binary channels to obtain its error probability and achievable bit rate. To enhance the achievable bit rate of the neuro-spike communication, we design an optimum spike detection receiver and also we propose an optimum input spike rate. We derive closed-form descriptions for the decision threshold of the optimum receiver and the optimum input spike rate. Since they are coupled, we propose a recursive scheme to derive their optimum values. Finally, simulation results are used to investigate the impact of the axonal noise, the synaptic noise, and modifications of the spikes' shape due to propagation along the axon on the achievable bit rate of the neuro-spike communication channel.