DIGITAL HAMMING WEIGHT AND DISTANCE ANALYZERS FOR BINARY VECTORS AND MATRICES

In this paper we explore modules that can analyze binary vectors and matrices and efficiently solve a wide range of problems that involve the computation of Hamming weights or Hamming distances, producing counts and/or comparisons of these, as well as sorting and searching. A set of designs for such modules is proposed and all the designs have been evaluated both theoretically and practically. The practical evaluation involved numerous experiments with hardware implementations using the most recent extensible processing platform that incorporates reconfigurable logic. The objective was to achieve high performance within reasonable resources. As a result, novel solutions for Hamming weight counters/comparators have been identified that have better cost and latency than the best known alternatives. Network-based sorters and searchers with reusable cores are also discussed and these enable high throughput to be achieved with relatively modest resources. The paper shows that similar results cannot be obtained using the best known and most frequently used even-odd merge and bitonic merge networks. Finally, a complete architecture for an analyzer is presented, part of which (covering the modules indicated above) has been completely implemented and prototyped in hardware.