Error Correction via Restorative Feedback in M-ary Logic Circuits
Chris Winstead, Yi Luo, Eduardo Monzon and Abiezer Tejeda
This paper presents an error correction method known as restorative feedback (RFB) that provides error-correction for both permanent and temporal logic faults in any M-ary logic system. The RFB method is a variant of triple modular redundancy (TMR), which achieves error correction in logic circuits by using three-fold redundancy. Unlike TMR, the RFB method has well-defined application to arbitrary M-ary logic systems as well as conventional binary logic circuits. The RFB method also uses a feedback mechanism to suppress transient errors, resulting in a lower error probability than TMR when considering transient upsets. The underlying theory of RFB is presented as an adaptation of stochastic error correction theory. Two circuit-level proof-of-concept demonstrations are presented, which include a binary implementation using Muller C-elements, and a ternary implementation based on Semi-Floating Gate logic circuits. The error-correcting performance of these circuits is evaluated using logic-level simulations as well as device-level simulations in Spectre. Bit and symbol error rates are also computed using Monte Carlo simulations which demonstrate that the RFB method is superior to traditional TMR for a variety of cases. An application of the RFB method is also demonstrated using redundant gate-level synthesis of multiple-valued ripple-carry adder circuits. The application circuits are simulated using an abstract noisy-logic model, and the RFB method is shown to significantly improve the circuits’ noise immunity.
Keywords: Error correction, restorative feedback, triple modular redundancy, reliability.