Independent neurons representing a finite set of stimuli: dependence of the mutual information on the number of units sampled

We study the capacity with which a system of independent neuron-like units represents a given set of stimuli. We assume that each neuron provides a fi xed amount of information and that the information provided by different ne urons has a random overlap. We derive analytically the dependence of the mu tual information between the set of stimuli and the neural responses on the number of units sampled. For a large set of stimuli, the mutual informatio n rises linearly with the number of neurons and later saturates exponential ly at its maximum value.