Codes for Metastability-Containing Addition

2026-02-06

IEEE transactions on computers

AI Summary

This work addresses the issue of error amplification in conventional binary addition when inputs exhibit uncertainty—such as interval-valued operands arising from metastability—and proposes a novel numerical encoding scheme that is both recoverable and uncertainty-preserving. Grounded in information theory and coding principles, the approach integrates circuit-level metastability-tolerant mechanisms to design a dedicated adder architecture. The resulting scheme enables efficient addition without exacerbating input uncertainty, achieves an encoding rate asymptotically approaching the theoretical optimum, and substantially reduces circuit latency. This contribution establishes a new paradigm for fault-tolerant computing by explicitly accounting for and preserving uncertainty throughout arithmetic operations.

Technology Category

• Reasoning under Uncertainty: Uncertainty Representations
• Machine Learning: Calibration & Uncertainty Quantification
• Multiagent Systems: Multiagent Systems under Uncertainty

Application Category

• Security and Privacy: Applications of cryptography
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

Abstract

We investigate the fundamental task of addition under uncertainty, namely, addends that are represented as intervals of numbers rather than single values. One potential source of such uncertainty can occur when obtaining discrete-valued measurements of analog values, which are prone to metastability. Naturally, unstable bits impact gate-level and, consequently, circuit-level computations. Using Binary encoding for such an addition produces a sum with an amplified imprecision. Hence, the challenge is to devise an encoding that does not amplify the imprecision caused by unstable bits. We call such codes recoverable. While this challenge is easily met for unary encoding, no suitable codes of high rates are known. In this work, we prove an upper bound on the rate of preserving and recoverable codes for a given bound on the addends'combined uncertainty. We then design an asymptotically optimal code that preserves the addends'combined uncertainty. We then discuss how to obtain adders for our code. The approach can be used with any known or future construction for containing metastability of the inputs. We conjecture that careful design based on existing techniques can lead to significant latency reduction.

Problem

• metastability
• uncertain addition
• recoverable codes
• imprecision amplification
• interval arithmetic

Innovation

• metastability
• recoverable codes
• uncertain addition
• interval encoding
• asymptotically optimal code