Neural coding is a field of study that concerns how sensory information is represented in the brain by networks of neurons. The link between external stimulus and neural response can be studied from two parallel points of view. The first, neural encoding, refers to the mapping from stimulus to response. It focuses primarily on understanding how neurons respond to a wide variety of stimuli and constructing models that accurately describe the stimulus-response relationship. Neural decoding refers to the reverse mapping, from response to stimulus, where the challenge is to reconstruct a stimulus from the spikes it evokes. Since neuronal response is stochastic, a one-to-one mapping of stimuli into neural responses does not exist, causing a mismatch between the two viewpoints of neural coding. Here we use these two perspectives to investigate the question of what rate coding is, in the simple setting of a single stationary stimulus parameter and a single stationary spike train represented by a renewal process. We show that when rate codes are defined in terms of encoding, that is, the stimulus parameter is mapped onto the mean firing rate, the rate decoder given by spike counts or the sample mean does not always efficiently decode the rate codes, but it can improve efficiency in reading certain rate codes when correlations within a spike train are taken into account.

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