Limit on the Addressability of Fault-Tolerant Nanowire Decoders

Although prone to fabrication error, the nanowire crossbar is a promising candidate compoent for next generation nanometer-scale circuits. In the nanowire crossbar architecture, nanowires are addressed by controlling voltages on the mesowires. For area efficiency, we are interested in the maximum number of nanowires N(m,e) that can be addressed by m mesowires, in the face of up to e fabrication errors. Asymptotically tight bounds on N(m,e) are established in this paper. In particular, it is shown that N(m,e) = Theta(2^m / m^epsiv+1/2). Interesting observations are made on the equivalence between this problem and the problem of constructing optimal EC/AUED codes, superimposed distance codes, pooling designs, and diffbounded set systems. Results in this paper also improve upon those in the EC/AUEC codes literature.