Function-Correcting Codes

TL;DR

This paper introduces function-correcting codes (FCCs), a new class of codes that protect specific function evaluations against errors, and establishes their theoretical bounds and relationships to irregular-distance codes.

Contribution

It defines FCCs, shows their equivalence to irregular-distance codes, and derives bounds on their redundancy, providing insights into function-specific error correction.

Findings

FCCs are equivalent to irregular-distance codes.

Derived bounds on redundancy depend on the specific function.

Compared FCCs to standard error-correcting codes.

Abstract

In this paper we study function-correcting codes, a new class of codes designed to protect the function evaluation of a message against errors. We show that FCCs are equivalent to irregular-distance codes, i.e., codes that obey some given distance requirement between each pair of codewords. Using these connections, we study irregular-distance codes and derive general upper and lower bounds on their optimal redundancy. Since these bounds heavily depend on the specific function, we provide simplified, suboptimal bounds that are easier to evaluate. We further employ our general results to specific functions of interest and compare our results to standard error-correcting codes, which protect the whole message.