Here we show that a simple, highly tractable computational model can capture the fine-grained stimulus dependence and detailed spatiotemporal correlation structure in the light responses of a complete local population of ganglion cells, recorded in primate retina. These correlations strongly influence the precise timing of spike trains, explaining a large fraction of trial-to-trial response variability in individual neurons that otherwise would be attributed to intrinsic noise. The mathematical tractability of the model permits an assessment of the importance of concerted firing by allowing us to perform Bayesian decoding of the stimulus from the spike trains of the complete population (27 cells). We find that exploiting concerted activity across the entire population preserves at least 20% more stimulus-related information than decoding under the assumption of independent encoding. These results provide a unifying framework for understanding the role that correlated activity plays in encoding and decoding sensory signals, and should be applicable to the study of population coding in a wide variety of neural circuits.