Grid cells generate an analog error-correcting code for singularly precise neural computation

Entorhinal grid cells in mammals fire as a function of animal location, with spatially periodic response patterns. This nonlocal periodic representation of location, a local variable, is unlike other neural codes. There is no theoretical explanation for why such a code should exist. We examined how accurately the grid code with noisy neurons allows an ideal observer to estimate location and found this code to be a previously unknown type of population code with unprecedented robustness to noise. In particular, the representational accuracy attained by grid cells over the coding range was in a qualitatively different class from what is possible with observed sensory and motor population codes. We found that a simple neural network can effectively correct the grid code. To the best of our knowledge, these results are the first demonstration that the brain contains, and may exploit, powerful error-correcting codes for analog variables.