On information theoretical modelling of the communications between neurons and the corresponding information rate

Abstract

Abstract In a nervous system propagation of spikes among neurons can be interpreted as an information transmission process, where, a neural response carries information about the stimulus. Quantification of this information might be of theoretical and practical importance. In this paper, (i) The interaction between two neurons with an electrically coupled transport of ions is modelled mathematically, where the communication through the junction gap between very close neurons occurs with a specific time delay; (ii) then, the connection structure of neurons is proposed based on a particular Rulkov network model. The corresponding process is modelled as a non‐linear binary channel with memory; and (iii) by assuming a recurrence relation for number of available membrane potential changing due to the arrival of the spike to the axonal terminal, the mutual information between channel input and output is obtained and the input range maximizing mutual information, and hence, the information rate of channel is derived.

Keywords

• channel capacity
• information theory
• neural nets
• nonlinear estimation