Population encoding is a means by which information about something is encoded in a group of neurons. In population encoding, each neuron has a distribution of responses over some set of inputs, and the responses of many neurons may be combined to determine some value about the inputs. In one classic example in primary motor cortex, Georgopoulos and colleagues trained monkeys to move a joystick in one of multiple directions towards a lit LED. Neurons in primary motor cortex responded maximally during movements to their preferred direction, and their response decreased if the animal made movements towards directions increasingly different from the preferred direction. Kenneth Johnson originally derived that if each neuron represents movement in its preferred direction, and the vector sum of all neurons is calculated (each neuron has a firing rate and a preferred direction), the sum points in the direction of motion. In this manner, the population of neurons codes the signal for the motion. This particular population code is referred to as population vector coding. This particular study divided the field of motor physiologists between Evarts' "upper motor neuron" group, which followed the hypothesis that motor cortex neurons contributed to control of single muscles, and the Georgopoulos group studying the representation of movement directions in cortex.
Typically an encoding function has a peak value such that activity of the neuron is greatest if the perceptual value is close to the peak value, and becomes reduced accordingly for values less close to the peak value.
If follows that the actual perceived value can be reconstructed from the overall pattern of activity in the set of neurons. One specific mathematical technique for performing such a reconstruction is the method of maximum likelihood, although the Johnson/Georgopoulos vector coding is an example of simple averaging.
Contrast this with sparse coding.