Temporal code versus rate code for binary Information Sources

Neuroscientists formulate very different hypotheses about the nature of neural code. At one extreme, it has been argued that neurons encode information in relatively slow changes of individual spikes arriving rates (rates codes) and the irregularity in the spike trains reflects noise in the system, while in the other extreme this irregularity is the code itself (temporal codes) thus the precise timing of every spike carries additional information about the input. It is well known that in the estimation of Shannon information transmission rate the patterns and temporal structures are taken into account, while the ”rate code” is already determined by the firing rate, i.e. by spike frequency. In this paper we compare these two types of codes for binary Information Sources which model encoded spike-trains. Assuming that the information transmitted by a neuron is governed by uncorrelated stochastic process or by process with a memory we compare the information transmission rates carried by such spike-trains with their firing rates. We showed that the crucial role in studying the relation between information and firing rates is played by a quantity which we call ”jumping” parameter. It corresponds to the probabilities of transitions from no-spike-state to the spike-state and vice versa. For low values of jumping parameter the quotient of information and firing rates is monotonically decreasing function of firing rate, thus there is straightforward, one-to-one, relation between temporal ∗Corresponding author Email address: [email protected] (Janusz Szczepanski ) Preprint submitted to Elsevier March 10, 2016 ar X iv :1 60 3. 02 79 8v 1 [ qbi o. N C ] 9 M ar 2 01 6 and rate codes. On the contrary, it turns out that for large enough jumping parameter this quotient is non-monotonic function of firing rate and it exhibits a global maximum, i.e. in this case there exists the optimal firing rate. Moreover, there is no one-to-one relation between information and firing rates, so the temporal and rate codes differ qualitatively. This leads to the observation that the behavior of the quotient of information and firing rates for large jumping parameter is especially important in the context of bursting phenomena.