How far can neural correlations reduce uncertainty? Comparison of Information Transmission Rates for Markov and Bernoulli processes
The nature of neural codes is central to neuroscience. Do neurons encode information through relatively slow changes in the emission rates of individual spikes (rate code), or by the precise timing of every spike (temporal codes)? Here we compare the loss of information due to correlations for these two possible neural codes. The essence of Shannon's definition of information is to combine information with uncertainty: the higher the uncertainty of a given event, the more information is conveyed by that event. Correlations can reduce uncertainty or the amount of information, but by how much? In this paper we address this question by a direct comparison of the information per symbol conveyed by the words coming from a binary Markov source (temporal codes) with the information per symbol coming from the corresponding Bernoulli source (uncorrelated, rate code source). In a previous paper we found that a crucial role in the relation between Information Transmission Rates (ITR) and Firing Rates is played by a parameter s, which is the sum of transitions probabilities from the no-spike-state to the spike-state and vice versa. It turned out that also in this case a crucial role is played by the same parameter s. We found bounds of the quotient of ITRs for these sources, i.e. this quotient's minimal and maximal values. Next, making use of the entropy grouping axiom, we determined the loss of information in a Markov source in relation to its corresponding Bernoulli source for a given length of word. Our results show that in practical situations in the case of correlated signals the loss of information is relatively small, thus temporal codes, which are more energetically efficient, can replace the rate code effectively. These phenomena were confirmed by experiments.