Modulus Computation-Based Techniques for Detecting and Correcting Transmission and Computation Errors in Residue Number System Architectures

Abstract

The Residue Number System (RNS) offers significant advantages in parallel, carry-free arithmetic for highperformance computing but remains critically vulnerable to errors during transmission and computation. Traditional error detection approaches rely on post-processing reverse conversion, which introduces substantial latency and undermines the inherent speed of RNS, making them unsuitable for real-time, reliability-critical applications. This paper proposes a novel architecture for in-situ error detection and correction that operates directly within the residue domain, eliminating the need for costly full reverse conversion. Using an optimized moduli set {2n+1 − 1, 2n + 1, 2n, 2n − 1, 2n−1 − 1}, we develop a hybrid algorithm that combines the Modulus Computation Method (MCM) for rapid reverse estimation with Hamming distance-based majority voting for robust syndrome analysis. The method guarantees single-residue error detection and correction by systematically evaluating residue triples to identify consistent values. Experimental simulations demonstrate a 99.9% correction success rate for realistic fault probabilities (p ≤ 10−4) while maintaining a low-latency, hardwareefficient pipeline. Comparative analysis against state-of-the-art techniques confirms superior performance in area utilization (complexity 5n + 1), detection latency (3 cycles), and flexibility across generalized moduli sets. These results advance the design of fault-tolerant RNS architectures for applications such as cryptography and digital signal processing.