Combinatorial neural codes from a mathematical coding theory perspective

TL;DR

This paper analyzes neural codes using mathematical coding theory, revealing that receptive field codes have limited error correction but effectively reflect stimulus relationships, suggesting a trade-off in neural coding functions.

Contribution

It provides a novel perspective by applying coding theory to neural codes, highlighting their error correction limits and their ability to encode stimulus relationships.

Findings

RF codes have high redundancy but limited error correction.

RF codes accurately reflect stimulus distances.

Error correction and stimulus relationship encoding may involve trade-offs.

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 does not support accurate error correction, although the error-correcting performance of RF codes "catches up" to that of random comparison codes when a small tolerance to error is introduced. On the other hand, RF 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.