Plotkin-like Bound and Explicit Function-Correcting Code Constructions for Lee Metric Channels

TL;DR

This paper introduces a Plotkin-like bound for Lee-distance codes and constructs explicit function-correcting Lee codes, demonstrating their efficiency in reducing redundancy for protecting function evaluations against errors.

Contribution

It proposes a new bound for Lee-distance codes and provides explicit constructions of function-correcting Lee codes that are optimal in certain cases.

Findings

Explicit FCLCs constructed for specific functions.

Lower bounds on redundancy established for these functions.

FCLCs can significantly reduce redundancy compared to classical Lee codes.

Abstract

Function-Correcting Codes (FCCs) are a novel class of codes designed to protect function evaluations of messages against errors while minimizing redundancy. A theoretical framework for systematic FCCs to channels matched to the Lee metric has been studied recently, which introduced function-correcting Lee codes (FCLCs) and also derived upper and lower bounds on their optimal redundancy. In this paper, we first propose a Plotkin-like bound for irregular Lee-distance codes. We then construct explicit FCLCs for specific classes of functions, including the Lee weight, Lee weight distribution, modular sum and locally bounded function. For these functions, lower bounds on redundancy are obtained, and our constructions are shown to be optimal in certain cases. Finally, a comparative analysis with classical Lee error-correcting codes and codes correcting errors in function values demonstrates that FCLCs can significantly reduce redundancy while preserving function correctness.