Temporal code versus rate code for binary Information Sources

Neuroscientists formulate very different hypotheses about the nature of neural coding. At one extreme, it has been argued that neurons encode information through relatively slow changes in the arrival rates of individual spikes (rate codes) and that the irregularity in the spike trains reflects the noise in the system. At the other extreme, this irregularity is the code itself (temporal codes) so that 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 the 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 an uncorrelated stochastic process or by a process with a memory, we compare the Information Transmission Rates carried by such spike trains with their firing rates. Here we show that a crucial role in the relation between information transmission and firing rates is played by a factor that we call the “jumping” parameter. This parameter corresponds to the probability of transitions from the no-spike-state to the spike-state and . For low jumping parameter values, the quotient of information and firing rates is a monotonically decreasing function of the firing rate, and there therefore a straightforward, one-to-one, relation between temporal and rate codes. However, it turns out that for large enough values of the jumping parameter this quotient is a non-monotonic function of the firing rate and it exhibits a global maximum, so that in this case there is an 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 a large jumping parameter value is especially important in the context of bursting phenomena.