Scaled-CBSC: scaled counting-based stochastic computing multiplication for improved accuracy

Stochastic computing (SC) can lead area-efficient implementation of logic designs. Existing SC multiplication, however, suffers a long-standing problem: large multiplication error with small inputs due to its intrinsic nature of bit-stream based computing. In this article, we propose a new scaled counting-based SC multiplication approach, called Scaled-CBSC, to mitigate this issue by introducing scaling bits to ensure the bit '1' density of the stochastic number is sufficiently large. The idea is to convert the "small" inputs to "large" inputs, thus improve the accuracy of SC multiplication. But different from an existing stream-bit based approach, the new method uses the binary format and does not require stochastic addition as the SC multiplication always starts with binary numbers. Furthermore, Scaled-CBSC only requires all the numbers to be larger than 0.5 instead of arbitrary defined threshold, which leads to integer numbers only for the scaling term. The experimental results show that the 8-bit Scaled-CBSC multiplication with 3 scaling bits can achieve up to 46.6% and 30.4% improvements in mean error and standard deviation, respectively; reduce the peak relative error from 100% to 1.8%; and improve 12.6%, 51.5%, 57.6%, 58.4% in delay, area, area-delay product, energy consumption, respectively, over the state of art work. Furthermore, we evaluate the proposed multiplication approach in a discrete cosine transformation (DCT) application. The results show that with 3 scaling bits, 8-bit scaled counting-based SC multiplication can improve the image quality with 5.9dB upon the state of art work in average.