A Number-Theoretic Error-Correcting Code

TL;DR

This paper introduces a novel number-theoretic error-correcting code inspired by cryptography, which offers a unique approach to error detection and correction through modular products and lattice reduction, with efficiency advantages in specific scenarios.

Contribution

The paper presents a new ECC design based on number theory and cryptographic principles, differing from traditional codes by using modular products and lattice techniques.

Findings

The new ECC can detect and correct errors using modular division.

It is less efficient than Turbo codes but more efficient than some established ECCs for certain parameters.

The approach leverages cryptographic concepts for error correction.

Abstract

In this paper we describe a new error-correcting code (ECC) inspired by the Naccache-Stern cryptosystem. While by far less efficient than Turbo codes, the proposed ECC happens to be more efficient than some established ECCs for certain sets of parameters. The new ECC adds an appendix to the message. The appendix is the modular product of small primes representing the message bits. The receiver recomputes the product and detects transmission errors using modular division and lattice reduction.