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

TL;DR

This paper studies a recently proposed family of geometric codes capable of handling multiple outliers, and develops a geometric analysis that characterizes their m-height profiles.

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.

Figures (6)

• Figure 1: An example of dual polygonal codes for $n=3$.
• Figure 2: Icosahedron with a shaded triangular region indicating the fundamental search space.
• Figure 3: Dodecahedron with a shaded triangular region indicating the fundamental search space.
• Figure 4: Triangle $T'$ in $(u,v)$-coordinates and switching lines $L_{2,7}$ and $L_{6,7}$, partitioning $T'$ into three subregions.
• Figure 5: Triangle $T'$ in $(u,v)$-coordinates and switching lines $L_{2,4}$ and $L_{2,7}$, partitioning $T'$ into three subregions.

Theorems & Definitions (18)

• Lemma 3.1
• proof
• Theorem 3.2
• proof
• Lemma 4.1
• proof
• Theorem 4.2
• proof
• Lemma 4.3
• proof