Multi-Valued Sub-Function Encoding in Functional Decomposition Based on Information Relationships Measures

Functional decomposition is becoming more and more popular, because it is more general than all other known logic synthesis approaches and it seems to be the most effective approach for LUT-based FPGAs, (C)PLDs and complex CMOS-gates. The multi-level functional decomposition can be seen as a recursive splitting of a given function, into two sub-functions: the predecessor (bound-set) function and successor function. Initially, the bound set function is a multi-valued (symbolic) function, where a certain value (symbol) is assigned to each particular input-cube compatibility class of the function being decomposed. To be implemented with binary logic, the multi-valued bound-set function must be expressed as a set of binary functions. This transformation is called the multi-valued sub-function encoding. It can be performed by the binary code assignment to each particular input-cube compatibility class. It determines the resulting binary predecessor and successor sub-functions and therefore influences the quality of the resulting circuit to a high degree. In this paper, a new method of the multi-valued sub-function encoding is presented. The method is based on the information relationship measures. Experimental results from the prototype CAD-tool that implements the method demonstrate that it is able to efficiently construct extremely effective circuits for symmetric functions. Results for asymmetric functions are also very good.