Optimum neural tuning curves for information efficiency with rate coding and finite-time window

An important question for neural encoding is what kind of neural systems can convey more information with less energy within a finite time coding window. This paper first proposes a finite-time neural encoding system, where the neurons in the system respond to a stimulus by a sequence of spikes that is assumed to be Poisson process and the external stimuli obey normal distribution. A method for calculating the mutual information of the finite-time neural encoding system is proposed and the definition of information efficiency is introduced. The values of the mutual information and the information efficiency obtained by using Logistic function are compared with those obtained by using other functions and it is found that Logistic function is the best one. It is further found that the parameter representing the steepness of the Logistic function has close relationship with full entropy, and that the parameter representing the translation of the function associates with the energy consumption and noise entropy tightly. The optimum parameter combinations for Logistic function to maximize the information efficiency are calculated when the stimuli and the properties of the encoding system are varied respectively. Some explanations for the results are given. The model and the method we proposed could be useful to study neural encoding system, and the optimum neural tuning curves obtained in this paper might exhibit some characteristics of a real neural system.