Empirical Verification of Fault Models for FPGAs Operating in the Subcritical Voltage Region

We present a rigorous empirical study of the bit-level error behavior of field programmable gate arrays operating in the subcricital voltage region. This region is of significant interest as voltage-scaling under normal circumstances is halted by the first occurrence of errors. However, accurate fault models might provide insight that would allow subcritical scaling by changing digital design practices or by simply accepting errors if possible. To facilitate further work in this direction, we present probabilistic error models that allow us to link error behavior with statistical properties of the binary signals, and based on a two-FPGA setup we experimentally verify the correctness of candidate models. For all experiments, the observed error rates exhibit a polynomial dependency on outcome probability of the binary inputs, which corresponds to the behavior predicted by the proposed timing error model. Furthermore, our results show that the fault mechanism is fully deterministic - mimicking temporary stuck-at errors. As a result, given knowledge about a given signal, errors are fully predictable in the subcritical voltage region.