Date of Award


Publication Type

Doctoral Thesis

Degree Name



Electrical and Computer Engineering


G. A. Jullien




This work considers VLSI implementations for the recently introduced Polynomial Ring Engine (PRE) using small residue rings. To allow for a comprehensive approach to the implementation of the PRE mappings for DSP algorithms, this dissertation introduces novel techniques ranging from system level architectures to transistor level considerations. The Polynomial Ring Engine combines both classical residue mappings and new polynomial mappings. This dissertation develops a systematic approach for generating pipelined systolic/ semi-systolic structures for the PRE mappings. An example architecture is constructed and simulated to illustrate the properties of the new architectures. To simultaneously achieve large computational dynamic range and high throughput rate the basic

building blocks of the PRE architecture use transistor size profiling. Transistor sizing software is developed for profiling the Switching Tree dynamic logic used to build the basic modulo blocks. The software handles complex nFET structures using a simple iterative algorithm. Issues such as convergence of the iterative technique and validity of the sizing formulae have been treated with an appropriate mathematical analysis.

As an illustration of the use of PRE architectures for modem DSP computational problems, a Wavelet Transform for HDTV image compression is implemented. An interesting use is made of the PRE technique of using polynomial indeterminates as 'placeholders' for components of the processed data. In this case we use an indeterminate to symbolically handle the irrational number [square root of 3] of the Daubechie mother wavelet for N = 4.

Finally, a multi-level fault tolerant PRE architecture is developed by combining the classical redundant residue approach and the circuit parity check approach. The proposed architecture uses syndromes to correct faulty residue channels and an embedded parity check to correct faulty computational channels. The architecture offers superior fault detection and correction with online data interruption.