Easily Testable Realizations for Generalized Reed-Muller Expressions

Highly Testable Finite State Machines Based on EXOR Logic

It is well-known that AND/EXOR circuits are more easily testable than AND/OR circuits. Therefore, in this paper, we primarily propose to use AND/EXOR realizations for implementation of the combinational logic parts of finite state machines. Then, we investigate the effect of different state assignments (i.e. one-hot, gray-code, etc.) and that of using different types of registers (i.e. D-type, ...

Double Fixed-Polarity Reed-Muller Expressions: A New Class of AND-EXOR Expressions for Compact and Testable Realization

As classes of AND-EXOR expressions, PPRMs, FPRMs, and ESOPs are well-known. In this paper, a new class of AND-EXOR expressions, Double Fixed-Polarity Reed-Muller Expressions (DFPRMs), is proposed. DFPRMs are generalized expressions of FPRMs, and can be the smallest PLA among all the classes of AND-EXOR expressions. We discuss their properties: the relation to other classes, a compact realizatio...

GRMIN: A Heuristic Simpli cation Algorithm for Generalized Reed-Muller Expressions

| A generalized Reed-Muller expression (GRM) is a type of AND-EXOR expressions. In a GRM, each variable may appear both complemented and uncomplemented. Networks realized using GRMs are easily tested. This paper presents GRMIN, a heuristic simpli cation algorithm for GRMs of multiple-output functions. GRMIN uses eight rules. As the primary objective, it reduces the number of products, and as th...

Generalized State Realizations of Reed-Muller Codes

The Treewidth of MDS and Reed-Muller Codes

The constraint complexity of a graphical realization of a linear code is the maximum dimension of the local constraint codes in the realization. The treewidth of a linear code is the least constraint complexity of any of its cycle-free graphical realizations. This notion provides a useful parametrization of the maximum-likelihood decoding complexity for linear codes. In this paper, we prove the...