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

2026-03-03

AI Summary

This work addresses the significant degradation in vector-matrix multiplication accuracy caused by mixed noise—comprising small perturbations and multiple outlier errors—in analog in-memory computing based on resistive crossbar arrays. To tackle this challenge, the paper introduces a novel class of geometric analog error-correcting codes and establishes, for the first time, a systematic geometric analysis framework centered on the m-height profile. This framework supports a broader range of code lengths and dimensions, overcoming the coverage limitations of existing code families. By integrating geometric code construction, m-height profile characterization, and mixed-noise modeling, the proposed method effectively corrects multiple outlier errors. Theoretical analysis demonstrates that the code exhibits strong error-correction capability and adaptability across diverse parameter configurations, substantially enhancing the reliability of analog in-memory computing systems.

Technology Category

• Cognitive Modeling & Cognitive Systems: Analogy
• Machine Learning: Matrix & Tensor Methods
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

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.

Problem

• analog error correction
• in-memory computing
• crossbar
• outlier errors
• geometric codes

Innovation

• geometric analog codes
• in-memory computing
• crossbar arrays
• outlier error correction
• m-height profiles