Majority Approximators for Low-Latency Data Bus Inversion

Data bus inversion (DBI) is an encoding technique that saves power in data movement in which the majority function plays an essential role. For a latency optimization, the majority function can be replaced by a majority approximator that allows for a small error in majority voting to obtain a faster encoder that still saves power. In this work, we propose two systematic approaches for finding high-performance majority approximators. First, we perform an exhaustive search of all possible Boolean functions to find an optimal approximator based on a certain circuit structure comprised of fifteen logic gates. The approximator found by the systematic search can be implemented using compound gates, resulting in a latency-efficient design with only two gate levels. Compared with prior works using a heuristic idea, the proposed circuit runs at the same speed but achieves greater switching activity savings. Second, we propose another majority approximator using the average of three randomly permuted copies of the approximator found in the first approach. We show that the second proposed approximator achieves even higher savings in switching activity as its function is closer to a true majority voter. We report various performance metrics of the newly found majority approximators based on syntheses using a 65 nm process.