On q-ary antipodal matchings and applications

We define a g-ary antipodal matching to be a perfect matching in the bipartite graph with vertices corresponding to words of length ℓ over the integer alphabet Q = {0, 1, ..., q -1}, wherein the left and right vertices are those with respective component sums greater and smaller than ℓ(q -1)/2, and wherein two vertices are connected by an edge if one of the corresponding words dominates the other. We present two different constructions of efficiently computable g-ary antipodal matchings. We then show how such matchings can be used for encoding arbitrary data into n × n arrays over the alphabet Q all of whose row and column sums are at most n(q -1)/2. Such encoders might be useful for mitigating parasitic currents in a next generation memory technology based on crossbar arrays of resistive devices.