Propagation of Delay in Probabilistic CMOS Systems

Future low voltage noise dominated designs render probabilistic behavior of CMOS. This is acceptable as far as applications’ intrinsic error resilience allows quantified inaccuracy in results to save energy consumption, such as in applications like audio/video processing and sky image formation in radio astronomy. This introduces the trade-off between energy consumption (E) and probability of correctness (p) that provides an opportunity for inexact computing to attain higher energy efficiency. Efforts have been made in the last decade to model probabilistic CMOS (PCMOS) keeping in view the noise variance and to establish its feasibility for error resilient applications focused on the nominal voltage range. However, exploiting the near threshold voltage (NTV) range is quite a promising energy efficient design technique that operates the hardware at relatively slower pace while retaining the deterministic property of computations. We propose to take the advantage of energy efficiency at NTV while retaining the speed as constant, sacrificing p to the extent allowed by applications resilience. In this regard, we investigated the impact of NTV operation on PCMOS where more energy can be saved with less accurate results. Our simulation results of an inverter and a 4-bit ripple carry adder in Cadence showed the shortcomings of current analytical models for probability of correctness at NTV and lower voltage supplies. We further investigated the impact of delay propagation in a digital system composed of probabilistic building blocks, which provides a clear insight of timing delay affecting the higher significant computational bits more than its lower significant counterparts and hence contributing considerably to the total error.