Error-Correcting Decision Diagrams for Multiple-Valued Functions

Abstract

Decision diagrams are an efficient way of representing switching functions and they are easily mapped to technology. The layout of a circuit is directly determined by the shape of the decision diagram. By combining the theory of error-correcting codes with decision diagrams, it is possible to form robust circuit layouts, which can detect and correct errors. The method of constructing robust decision diagrams is analogous to the decoding process of linear codes, and can be based on simple matrix and look-up operations. In this paper, we focus on error-correcting decision diagrams for multiple-valued functions, considering them for both the Hamming metric and the Lee metric. The performance of robust decision diagrams is analyzed by determining the error probabilities for such constructions. Depending on the error-correcting properties of the code used in the construction, the error probability of a circuit can be significantly decreased by a robust decision diagram.