Two Approximate Voting Schemes for Reliable Computing

This paper relies on the principles of inexact computing to alleviate the issues arising in static masking by voting for reliable computing in the nanoscales. Two schemes that utilize in different manners approximate voting, are proposed. The first scheme is referred to as inexact double modular redundancy (IDMR). IDMR does not resort to triplication, thus saving overhead due to modular replication. This scheme is crudely adaptive in its operation, i.e., it allows a threshold to determine the validity of the module outputs. IDMR operates by initially establishing the difference between the values of the outputs of the two modules; only if the difference is below a preset threshold, then the voter calculates the average value of the two module outputs. The second scheme (ITDMR) combines IDMR with TMR (triple modular redundancy) by using novel conditions in the comparison of the outputs of the three modules. Within an inexact framework, the majority is established using different criteria; in ITDMR, adaptive operation is carried further than IDMR to include approximate voting in a pairwise fashion. So, the validity of the three inputs is established and when only two of the three inputs satisfy the threshold condition, the IDMR operation is utilized. An extensive analysis that includes the voting circuits as well as a probabilistic framework is included. The proposed IDMR and ITDMR schemes improve the power dissipation and tolerance to variations compared to a traditional TMR. To further validate the applicability of the proposed schemes, inexact voting has been used in two applications (image processing and FIR filtering); the simulation results show that performance is substantially improved over TMR.