A Scheme to Design Concurrent Error Detection Techniques for the Fast Fourier Transform Implemented in SRAM-Based FPGAs

Soft errors are an important issue for SRAM-based Field Programmable Gate Arrays (FPGAs), since they result in permanent alterations of the mapped circuit when they affect their configuration memory. Concurrent Error Detection (CED) techniques, such as Dual Modular Redundancy (DMR), are usually employed to detect errors that affect the performance of the circuit. When trying to detect errors produced on the complex Fast Fourier Transform (FFT), the Parseval Sum of Squares (SoS) is a widely used technique. In this paper, we present a scheme to implement CED techniques for the complex FFT implemented in SRAM-based FPGAs. These techniques perform checks based on the relationships existing between one or more of the inputs and the outputs of the algorithm. Three examples of these techniques are provided to further clarify how to construct them. These techniques, along with DMR and SoS, have been tested through fault injection. An analysis on their error detection capabilities shows that they achieve high detection rates with much less resource usage than DMR and SoS. In addition, the number of false error detections for these techniques is lower than that of SoS, which leads to less unnecessary reconfigurations of the device.