Analog Error Correcting Codes with Constant Redundancy

TL;DR

This paper introduces a new family of analog error-correcting codes with constant redundancy, providing improved error correction capabilities for analog vector-matrix computations.

Contribution

It presents an upper bound on the height profile of such codes, a simple decoder for single errors, and constructs codes with smaller height profiles than existing MDS codes.

Findings

Constructed single error-correcting analog ECCs with redundancy three for any length.

Provided an upper bound on the height profile of analog ECCs with unit norm columns.

Demonstrated that the new codes outperform known MDS constructions in height profile.

Abstract

We consider analog error-correcting codes (analog ECCs) that are designed to correct/detect outlying errors arising in analog implementations of vector-matrix multiplication. The error-correction/detection capability of an analog ECC can be characterized by its height profile, which is expected to be as small as possible. In this paper, we consider analog ECCs whose parity check matrix has columns of unit Euclidean norm. We first present an upper bound on the height profile of such codes as well as a simple decoder for correcting a single error. We then construct a family of single error-correcting analog ECCs with redundancy three for any code length, which has smaller height profile compared to the known $[n,n-2]$ MDS constructions.