Portland State University. Department of Electrical Engineering.
Marek A. Perkowski
Date of Award
Master of Science (M.S.) in Electrical and Computer Engineering
Electrical and Computer Engineering
1 online resource (2, viii, 77 p.)
Mappings (Mathematics) -- Computer programs, Programmable logic devices, Digital integrated circuits -- Design and construction
The thesis presents a new approach to the decomposition of incompletely specified functions and its application to FPGA (Field Programmable Gate Array) mapping. Five methods: Variable Partitioning, Graph Coloring, Bond Set Encoding, CLB Reusing and Local Transformation are developed in order to efficiently perform decomposition and FPGA (Lookup-Table based FPGA) mapping. 1) Variable Partitioning is a high quality hemistic method used to find the "best" partitions, avoiding the very time consuming testing of all possible decomposition charts, which is impractical when there are many input variables in the input function. 2) Graph Coloring is another high quality heuristic\ used to perform the quasi-optimum don't care assignment, making the program possible to accept incompletely specified function and perform a quasi-optimum assignment to the unspecified part of the function. 3) Bond Set Encoding algorithm is used to simplify the decomposed blocks during the process of decomposition. 4) CLB Reusing algorithm is used to reduce the number of CLBs used in the final mapped circuit. 5) Local Transformation concept is introduced to transform nondecomposable functions into decomposable ones, thus making it possible to apply decomposition method to FPGA mapping. All the above developed methods are incorporated into a program named TRADE, which performs global optimization over the input functions. While most of the existing methods recursively perform local optimization over some kinds of network-like graphs, and few of them can handle incompletely specified functions. Cube calculus is used in the TRADE program, the operations are global and very fast. A short description of the TRADE program and the evaluation of the results are provided at the_ end of the thesis. For many benchmarks the TRADE program gives better results than any program published in the literature.
Wan, Wei, "A New Approach to the Decomposition of Incompletely Specified Functions Based on Graph Coloring and Local Transformation and Its Application to FPGA Mapping" (1992). Dissertations and Theses. Paper 4698.