Neural coding and decoding: communication channels and quantization.

We present a novel analytical approach for studying neural encoding. As a first step we model a neural sensory system as a communication channel. Using the method of typical sequence in this context, we show that a coding scheme is an almost bijective relation between equivalence classes of stimulus/response pairs. The analysis allows a quantitative determination of the type of information encoded in neural activity patterns and, at the same time, identification of the code with which that information is represented. Due to the high dimensionality of the sets involved, such a relation is extremely difficult to quantify. To circumvent this problem, and to use whatever limited data set is available most efficiently, we use another technique from information theory--quantization. We quantize the neural responses to a reproduction set of small finite size. Among many possible quantizations, we choose one which preserves as much of the informativeness of the original stimulus/response relation as possible, through the use of an information-based distortion function. This method allows us to study coarse but highly informative approximations of a coding scheme model, and then to refine them automatically when more data become available.