  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.

Quantitative Methods