Optimal coding of a random stimulus by a population of parallel neuron models

We examine the question of how a population of independently noisy sensory neurons should be configured to optimize the encoding of a random stimulus into sequences of neural action potentials. For the case where firing rates are the same in all neurons, we consider the problem of optimizing the noise distribution for a known stimulus distribution, and the converse problem of optimizing the stimulus for a given noise distribution. This work is related to suprathreshold stochastic resonance (SSR). It is shown that, for a large number of neurons, the SSR model is equivalent to a single rate-coding neuron with multiplicative output noise.