基于超几何分解的随机运算系统分析方法

Analysis Method of Stochastic Computing System Based on Hypergeometric Decomposition

基于Bernoulli分布的方差及期望传递方程一直是随机运算系统的数学基础,针对这种传统分析方法在实际应用中的不准确性和片面性,该文提出一种全新的数学方法:超几何分解(hypergeometic decomposition),用来解决在更复杂情况下期望与方差在随机运算系统中的传播规律。基于超几何分解,提出4组更加精确的期望及方差传递方程,在数学上证明了随机运算体系更加广泛的适用性,并且通过随机运算系统在图像处理中的应用,提出了基于方差的系统评价方法,相比于传统按位仿真方法,基于方差的系统分析方法具有耗时短、准确和全面的优点。新的方差传递方程首次将随机信号源的类型引入性能分析,证明了具有特定码流长度的随机序列可以使系统性能达到最优。

As mathematical fundamental of stochastic computing system, transfer function of variance and expected value based on Bernoulli distribution is not accurate and general in system analysis. A novel mathematic method, hypergeometric decomposition is proposed to solve this problem; it offers a general way to calculate transfer function of expected value and variance under more complicated circumstance. There are four groups of transfer function proposed here, which proves the effectiveness of stochastic computing system in a more general way; also they offer a better way to evaluate stochastic system. Compared with traditional bit-level simulation, evaluation method based on variance is time saving, accurate and comprehensive. New variance transfer function includes type of input random stream into performance analysis for the first time, which proves that specific length of stochastic sequence can maximize system performance.