  Positive correlations in the activity of neurons are widely observed in the
brain. Previous studies have shown these correlations to be detrimental to the
fidelity of population codes or at best marginally favorable compared to
independent codes. Here, we show that positive correlations can enhance coding
performance by astronomical factors. Specifically, the probability of
discrimination error can be suppressed by many orders of magnitude. Likewise,
the number of stimuli encoded--the capacity--can be enhanced by similarly large
factors. These effects do not necessitate unrealistic correlation values and
can occur for populations with a few tens of neurons. We further show that both
effects benefit from heterogeneity commonly seen in population activity. Error
suppression and capacity enhancement rest upon a pattern of correlation. In the
limit of perfect coding, this pattern leads to a `lock-in' of response
probabilities that eliminates variability in the subspace relevant for stimulus
discrimination. We discuss the nature of this pattern and suggest experimental
tests to identify it.
