Critical size of neural population for reliable information transmission

Abstract

It is known that the probability of decoding error has a phase transition at information rate equal to the channel capacity. The corresponding thermodynamic limit requires infinite coding dimension, hence making the actual decoding practically impossible. In this letter we analyze finite-size effects that occur in limited neural populations. We report that the achievable rate approaches the asymptote in a remarkably non-linear manner with the population size. Qualitatively, our findings do not seem to depend on the details of the model.