Error Correction via Restorative Feedback in M-ary Logic Circuits

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 devicelevel 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.