COMPACT: Flow-Based Computing on Nanoscale Crossbars with Minimal Semiperimeter

Abstract

In-memory computing is a promising solution strategy for data-intensive applications to circumvent the von Neumann bottleneck. Flow-based computing is the concept of performing in-memory computing using sneak paths in nanoscale crossbar arrays. The limitation of previous work is that the resulting crossbar representations have large dimensions. In this paper, we present a framework called COMPACT for mapping Boolean functions to crossbar representations with minimal semiperimeter (the number of wordlines plus bitlines). The COMPACT framework is based on an analogy between binary decision diagrams (BDDs) and nanoscale memristor crossbar arrays. More specifically, nodes and edges in a BDD correspond to wordlines/bitlines and memristors in a crossbar array, respectively. The relation enables a function represented by a BDD with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$n$</tex> nodes and an odd cycle transversal of size <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k$</tex> to be mapped to a crossbar with a semiperimeter of n+k. The <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k$</tex> extra wordlines/bitlines are introduced due to crossbar connection constraints, i.e. wordlines (bitlines) cannot directly be connected to wordlines (bitlines). For multi-input multi-output functions, COMPACT can also be applied to shared binary decision diagrams (SBDDs), which further reduces the size of the crossbar representations. Compared with the state-of-the-art mapping technique, the semiperimeter is reduced from 2.13n to 1.09n on the average, which translates into crossbar representations with 78% smaller area. The power consumption and the computation delay are on the average reduced by 7% and 52%, respectively.

Topics & Concepts