Signal Fluctuations and the Information Transmission Rates in Binary Communication Channels

In the nervous system, information is conveyed by sequence of action potentials, called spikes-trains. As MacKay and McCulloch suggested, spike-trains can be represented as bits sequences coming from Information Sources ([Formula: see text]). Previously, we studied relations between spikes’ Information Transmission Rates [Formula: see text] and their correlations, and frequencies. Now, I concentrate on the problem of how spikes fluctuations affect [Formula: see text]. The [Formula: see text] are typically modeled as stationary stochastic processes, which I consider here as two-state Markov processes. As a spike-trains’ fluctuation measure, I assume the standard deviation [Formula: see text] , which measures the average fluctuation of spikes around the average spike frequency. I found that the character of [Formula: see text] and signal fluctuations relation strongly depends on the parameter s being a sum of transitions probabilities from a no spike state to spike state. The estimate of the Information Transmission Rate was found by expressions depending on the values of signal fluctuations and parameter s. It turned out that for smaller [Formula: see text] , the quotient [Formula: see text] has a maximum and can tend to zero depending on transition probabilities, while for [Formula: see text] , the [Formula: see text] is separated from 0. Additionally, it was also shown that [Formula: see text] quotient by variance behaves in a completely different way. Similar behavior was observed when classical Shannon entropy terms in the Markov entropy formula are replaced by their approximation with polynomials. My results suggest that in a noisier environment [Formula: see text] , to get appropriate reliability and efficiency of transmission, [Formula: see text] with higher tendency of transition from the no spike to spike state should be applied. Such selection of appropriate parameters plays an important role in designing learning mechanisms to obtain networks with higher performance.