Error-latency Trade-off for Asynchronous Stochastic Computing with ΣΔ Streams for the IoT

Asynchronous stochastic computing (ASC) using continuous-time-asynchronous $\Sigma\Delta$ modulators $(\mathrm{S}\mathrm{C}-\mathrm{A}\Sigma\Delta \mathrm{M})$ has the potential to enable ultra-low-power, on-node machine learning algorithms for the next generation of sensors for the Internet of Things $(\mathrm{I}\mathrm{o}\mathrm{T})$. Similar to synchronous stochastic computing $(\mathrm{S}\mathrm{S}\mathrm{C}^{\mathrm{I}})$1, in $\mathrm{S}\mathrm{C}-\mathrm{A}\Sigma\Delta \mathrm{M}$ complex processing units can be implemented with simple gates because numbers are represented with streams. For example a multiplier is implemented with a XNOR gate, yielding savings in power and area of 90% compared with the typical binary approach. Previous work demonstrated that $\mathrm{S}\mathrm{C}-\mathrm{A}\Sigma\Delta \mathrm{M}$ leverages SSC advantages and addresses its drawbacks, achieving significant savings in energy, power and latency. In this work, we study a theoretical model to determine the fundamental limits of accuracy and computing time for SC- $\mathrm{A}\Sigma\Delta \mathrm{M}$. Since the $\Sigma\Delta$ streams are periodic the final computing error is non-zero and depends on the period of the input streams. We validate our theoretical model with Spice-level simulations and evaluate the power and energy consumption using a standard FinFetlX2 technology for two cases: 1) multiplication and 2) gamma correction, an image processing algorithm. Our work determines circuit design guidelines for $\mathrm{S}\mathrm{C}-\mathrm{A}\Sigma\Delta \mathrm{M}$ and shows that multiplication with $\mathrm{S}\mathrm{C}-\mathrm{A}\Sigma\Delta \mathrm{M}$ requires at least 6X less time than SSC. The latency reduction and novel architecture positively impacts the overall energy consumption in the $\mathrm{I}\mathrm{o}\mathrm{T}$ node, enabling savings in energy of 79% compared with the binary approach.1SC is by definition a synchronous approach, thus we use SSC to differentiate it from asynchronous stochastic computing2In modern technologies the node number does not refer to any one feature in the process, and foundries use slightly different conventions; we use lx to denote the 14/16nm FinFET nodes offered by the foundry.