Combinatorial Neural Codes from a Mathematical Coding Theory Perspective

Authors

Carina Curto, University of Nebraska - LincolnFollow
Vladimir Itskov, University of Nebraska-LincolnFollow
Katherine Morrison, University of Nebraska - LincolnFollow
Zachary Roth, University of Nebraska - LincolnFollow
Judy L. Walker, University of Nebraska - LincolnFollow

Document Type

Article

Date of this Version

2013

Citation

Neural Computation 25, 1891–1925 (2013).

Comments

Copyright 2013 Massachusetts Institute of Technology

Abstract

Shannon’s seminal 1948 work gave rise to two distinct areas of research: information theory and mathematical coding theory. While information theory has had a strong influence on theoretical neuroscience, ideas from mathematical coding theory have received considerably less attention. Here we take a new look at combinatorial neural codes from a mathematical coding theory perspective, examining the error correction capabilities of familiar receptive field codes (RF codes).We find, perhaps surprisingly, that the high levels of redundancy present in these codes do not support accurate error correction, although the error-correcting performance of receptive field codes catches up to that of random comparison codes when a small tolerance to error is introduced. However, receptive field codes are good at reflecting distances between represented stimuli, while the random comparison codes are not. We suggest that a compromise in error correcting capability may be a necessary price to pay for a neural code whose structure serves not only error correction, but must also reflect relationships between stimuli.