Evaluating the Connectivity of Self-Assembled Networks of Nano-scale Processing Elements

Architectures built using bottom-up self-assembly of nanoelectronic devices will need to tolerate defect rates that are orders of magnitude higher than those found in current CMOS technologies. In this paper, we describe and evaluate an approach to provide defect isolation in such an architecture that consists of a large number of simple computational nodes, each of which can communicate with four neighbors on single-bit asynchronous links. Our approach does not require an external defect map, nor does it require redundancy of complex computational circuits, either of which will limit the scalability of the system. We use the reverse path forwarding broadcast routing algorithm, commonly used in wide-area networks, to map out defective nodes at startup. The algorithm guarantees two things (a) the broadcast eventually terminates and (b) all functional nodes that have a path to the broadcast source will receive it. Thus, all functional and reachable nodes are connected through a broadcast tree, resulting in defect isolation. Simulations show that, for a fail-stop model of node failure, the broadcast connects all nodes that are reachable from the source. In case of low defect rates ( 10%), the broadcast reaches more than 97% of non-defective nodes. For a network of nodes in the form of a grid, our results show that, in most cases, the time taken to complete the broadcast is proportional to the square root of the number of nodes in the system. Finally, we also present an analysis of the characteristics of the trees generated by our broadcast mechanism.