Exploration and Analysis of Combinations of Hamming Codes in 32-bit Memories

TL;DR

This paper analyzes various configurations of Hamming codes in 32-bit memories to improve error correction capabilities in spatial applications, demonstrating that larger Hamming codes significantly enhance simple error correction rates.

Contribution

It introduces and evaluates different Hamming code configurations, including combinations, for 32-bit memories, providing insights into their effectiveness in error correction.

Findings

Ham(31,26) corrects nearly 97% of simple errors

Ham(15,11) and Ham(7,4) configurations have lower correction rates

Combining multiple Hamming codes improves overall error correction performance

Abstract

Reducing the threshold voltage of electronic devices increases their sensitivity to electromagnetic radiation dramatically, increasing the probability of changing the memory cells' content. Designers mitigate failures using techniques such as Error Correction Codes (ECCs) to maintain information integrity. Although there are several studies of ECC usage in spatial application memories, there is still no consensus in choosing the type of ECC as well as its organization in memory. This work analyzes some configurations of the Hamming codes applied to 32-bit memories in order to use these memories in spatial applications. This work proposes the use of three types of Hamming codes: Ham(31,26), Ham(15,11), and Ham(7,4), as well as combinations of these codes. We employed 36 error patterns, ranging from one to four bit-flips, to analyze these codes. The experimental results show that the Ham(31,26) configuration, containing five bits of redundancy, obtained the highest rate of simple error correction, almost 97\%, with double, triple, and quadruple error correction rates being 78.7\%, 63.4\%, and 31.4\%, respectively. While an ECC configuration encompassed four Ham(7.4), which uses twelve bits of redundancy, only fixes 87.5\% of simple errors.