Correlated activity between sensory neurons governs both the stimulus information conveyed by a neural population and how downstream neurons can extract it. Although previous studies looking at pairs of cells have examined correlations, their functional origin and impact on the neural code are still not understood. Pillow et al. address the question in a complete population of primate retinal ganglion cells. Fitting the physiological data to a model of multi-neuron spike responses, the authors find that a significant fraction of what is usually considered single-cell noise in trial-to-trial response variability can be explained by correlations, and that a significant amount of sensory information can be decoded from the correlation structure. The functional significance of correlated firing in a complete population of macaque parasol retinal ganglion cells using a model of multi-neuron spike responses is analysed. Fitting the physiological data to a model of multi-neuron spike responses, it is found that a significant fraction of what is usually considered single-cell noise in trial-to-trial response variability can be explained by correlations, and that a significant amount of sensory information can be decoded from the correlation structure. Statistical dependencies in the responses of sensory neurons govern both the amount of stimulus information conveyed and the means by which downstream neurons can extract it. Although a variety of measurements indicate the existence of such dependencies1,2,3, their origin and importance for neural coding are poorly understood. Here we analyse the functional significance of correlated firing in a complete population of macaque parasol retinal ganglion cells using a model of multi-neuron spike responses4,5. The model, with parameters fit directly to physiological data, simultaneously captures both the stimulus dependence and detailed spatio-temporal correlations in population responses, and provides two insights into the structure of the neural code. First, neural encoding at the population level is less noisy than one would expect from the variability of individual neurons: spike times are more precise, and can be predicted more accurately when the spiking of neighbouring neurons is taken into account. Second, correlations provide additional sensory information: optimal, model-based decoding that exploits the response correlation structure extracts 20% more information about the visual scene than decoding under the assumption of independence, and preserves 40% more visual information than optimal linear decoding6. This model-based approach reveals the role of correlated activity in the retinal coding of visual stimuli, and provides a general framework for understanding the importance of correlated activity in populations of neurons.