Efficient synthesis of AND/XOR networks

Abstract

A new graph-based synthesis method for general Exclusive Sum-of-Product forms (ESOP) is presented in this paper. Previous research has largely concentrated on a class of ESOP's, the Canonical Restricted Fixed/Mixed Polarity Reed-Muller form, also known as Generalized Reed-Muller (GRM) form. However, for many functions, the minimum GRM can be much worse than the ESOP. We have defined a Shared Multiple Rooted XOR-based Decomposition Diagram (XORDD) to represent functions with multiple outputs. By iteratively applying transformations and reductions, we obtain a compact XORDD which gives a minimized ESOP. Our method can synthesize larger circuits than previously possible. The compact ESOP representation provides a form that is easier to synthesize for XOR heavy multilevel circuit, such as arithmetic functions. The method successfully minimized large functions with multiple outputs. Results are also compared to the minimized SOP's obtained from ESPRESSO. Experimental results show that for many circuits ESOP's have considerably more compact form than SOP's.