A New Class of Geometric Analog Error Correction Codes for Crossbar Based In-Memory Computing

TL;DR

This paper introduces a new class of geometric analog error correction codes designed for resistive crossbar in-memory computing, addressing multiple outliers and expanding code options.

Contribution

It develops a geometric analysis of a recently proposed family of codes capable of correcting multiple outliers, broadening the range of available code parameters.

Findings

Characterization of m-height profiles of geometric codes.

Extension of code families to handle multiple outliers.

Enhanced understanding of geometric code capabilities in analog computing.

Abstract

Analog error correction codes have been proposed for analog in-memory computing on resistive crossbars, which can accelerate vector-matrix multiplication for machine learning. Unlike traditional communication or storage channels, this setting involves a mixed noise model with small perturbations and outlier errors. A number of analog codes have been proposed for handling a single outlier, and several constructions have also been developed to address multiple outliers. However, the set of available code families remains limited, covering only a narrow range of code lengths and dimensions. In this paper, we study a recently proposed family of geometric codes capable of handling multiple outliers, and develop a geometric analysis that characterizes their m-height profiles.