Mitigating the Correlation Problem in Multi-Layer Stochastic Circuits

Stochastic computing is a low-cost non-standard computer architecture that processes pseudo-random bitstreams. Its effectiveness, and that of other probabilistic methods, requires maintaining desired levels of correlation among interacting input bitstreams, for example, SCC = 0 or SCC = +1, where SCC is the stochastic cross-correlation metric. Correlation errors are systematic (bias-causing) errors that cannot be corrected by increasing bitstream length. A typical stochastic design C
1
only controls correlation at its primary input lines. This is a fairly straightforward task, however it limits the scope of SC to “single layer,” usually combinational, designs. In situations where a second processing layer C
2
follows C
1
, the output correlation of C
1
must satisfy the input correlation needs of C
2
. This can be done by inserting a (sequential) correlation control layer S
12
between C
1
and C
2
, which incurs high area and delay overhead. S
12
transforms intralayer bitstreams Z with unknown or undesired SCC values into numerically equivalent ones Z* with desired correlation. The fundamental problem of designing C
1
to produce Z* directly, thereby dispensing with S
12
, which apparently has not been considered before, is addressed in this paper. We focus on two-layer designs C
1
C
2
requiring SCC = +1 between layers, and present a method called COMAX for (re)designing C
1
so that it outputs bitstreams with correlation that is as close as possible to +1. We demonstrate on a representative image processing application that, compared to alternative correlation control techniques, COMAX reduces area by about 50% without reducing output image quality.