Synthesizing Logical Computation on Stochastic Bit Streams

Most digital systems operate on a positional representation of data, such as binary radix. A positional representation is a compact way to encode signal values: in binary radix, 2 distinct values can be represented with n bits. However, operating on it requires complex logic: in each operation such as addition or multiplication, the signal must be “decoded,” with the higher order bits weighted more than the lower order bits. We advocate an alternative representation: random bit streams where the signal value is encoded by the probability of obtaining a one versus a zero. This representation is much less compact than binary radix. However, complex operations can be performed with very simple logic. For instance, multiplication can be performed with a single AND gate. Also, because the representation is uniform, with all bits weighted equally, it is highly tolerant of soft errors (i.e., bit flips). In this paper, we present a general method for synthesizing digital circuitry that computes on such stochastic bit streams. Our method can be used to synthesize arbitrary polynomial functions. Through polynomial approximations, it can also be used to synthesize non-polynomial functions. Experiments on functions used in image processing show that our method produces circuits that are highly tolerant of input errors. The accuracy degrades gracefully with the error rate. For applications that mandate simple hardware, producing relatively low precision computation very reliably, our method is a winning proposition.