Fault-tolerant design of analogic CNN templates and algorithms-Part I: The binary output case

This paper addresses the issue of designing a class of fault-tolerant cellular neural network (CNN) templates that, combined with CNN analogic algorithms, work correctly and reliably on given CNN universal machine (CNN-UM) chips. In particular, a generic method for finding nonpropagating binary-output CNN templates is proposed. This method is based on measurements of actual CNN-UM chips and combines adaptive optimization and decomposition of theoretically ideal CNN templates in order to correct the erroneous behavior of actual CNN-UM chips, which is mainly caused by imperfections introduced during fabrication. More specifically, the entire array of cells in a CNN-UM chip is modeled by a single feed-forward virtual cell whose optimal parameters are found by a simple and effective gradient-based method. In the case of binary input-output uncoupled templates (or Boolean operators), a systematic template decomposition method is applied whenever optimization fails to find a correctly working CNN template for all possible combinations of local 3×3 binary input patterns. The resulting templates are finally combined, yielding a simple CNN analogic algorithm. Examples are presented for both binary- and analog-input operators, using two concrete stored-program CNN-UM chips to demonstrate the effectiveness of the proposed method, whose advantages and limitations are also discussed