The effect of correlations on the fisher information of population codes

We study the effect of correlated noise on the accuracy of population coding using a model of a population of neurons that are broadly tuned to an angle in two-dimension. The fluctuations in the neuronal activity is modeled as a Gaussian noise with pairwise correlations which decays exponentially with the difference between the preferred orientations of the pair. By calculating the Fisher information of the system, we show that in the biologically relevant regime of parameters positive correlations decrease the estimation capability of the network relative to the uncorrelated population. Moreover strong positive correlations result in information capacity which saturates to a finite value as the number of cells in the population grows. In contrast, negative correlations substantially increase the information capacity of the neuronal population.