A metric space approach to the information capacity of spike trains

Abstract

Classical information theory can be either discrete or continuous, corresponding to discrete or continuous random variables. However, although spike times in a spike train are described by continuous variables, the information content is usually calculated using discrete information theory. This is because the number of spikes, and hence, the number of variables, varies from spike train to spike train, making the continuous theory difficult to apply.It is possible to avoid this problem by using a metric space approach to spike trains. A metric gives a distance between different spike trains. The continuous version of information theory is then rephrased in terms of metric quantities and used to estimate the information capacity of spike trains. This method works by matching the distribution of distances between responses to the same stimulus to a -distribution: the -distribution is the length distribution for a vector of Gaussian variables. This defines a noise dimension for the spike train and gives a bound on the channel capacity.