Accelerating Stochastic Computing Using Deterministic Halton Sequences

Abstract

Deterministic approaches have recently been developed for accurate computation in stochastic computing (SC). They, however, suffer a long operation time. Fortunately, for applications that do not require completely accurate processing results, such as image processing, the time can significantly be reduced due to the better progressive precision in the bit-streams generated by these approaches. That means a computation can be terminated in time when its output accuracy is acceptable. Due to the fast convergence property of low-discrepancy sequences, we propose three deterministic Halton sequence (DHS)-based stochastic number generators (SNGs) for the first time by using, respectively, prime length, rotation, and clock division for accelerating computation in SC. Experimental results show that the proposed designs are more efficient than their counterparts. For multiplication, the proposed DHS-based designs perform up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$32\times $ </tex-math></inline-formula> faster than prior designs for a mean error of 0.1%. The speedup reaches <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$128\times $ </tex-math></inline-formula> for an edge detection algorithm. Three stochastic circuits are then designed by using the proposed DHS-based SNGs for the Bernsen binarization algorithm, which lead to more accurate results than existing designs at the same bit-stream length. Finally, the proposed designs show an excellent fault-tolerance against bit flipping errors.