Robust and efficient coding with grid cells

The neuronal code arising from the coordinated population activity of grid cells in the rodent entorhinal cortex can uniquely represent space across large distances but the precise conditions for efficient coding are unknown. Here we present a number-theoretic analysis of grid coding and derive an upper bound on the distance that a population of grid cells can represent without error. We show that in the absence of neuronal noise, the capacity of the system would be extremely sensitive to the choice of the grid periods. However, when the accuracy of the representation is limited by neuronal noise, the capacity becomes gradually more robust against the choice of grid scales as the number of modules increases and remains near optimal even for random scale choices. Our study reveals that robust and efficient coding can be achieved without parameter tuning in the case of grid cell representation.