Date of Award

6-1994

Degree Type

Thesis

Degree Name

Doctor of Philosophy (PhD)

Department

Electrical and Computer Engineering

Supervisor

D. P. Taylor

Abstract

This thesis reports my research work in the area of trellis coded continuous phase frequency shift keying (CPFSK). Previous approaches [1, 2, 3, 4, 5] applied binary convolutional codes to CPFSK to achieve power and bandwidth efficiency. However, the work in [6] and part of this thesis show that no single approach among previous approaches can be outperformed by the others if only binary convolutional codes are considered.

A new coding scheme based on cnovolutional codes on the ring of integers modulo-P is shown to be a natural way to apply trellis coding to CPFSK [7]. Recent work has decomposed CPFSK into two parts; a linear encoder with memory, called the continuous phase encoder (CPE), and a memoryless modulator (MM), where the CPE often has a code structure defined over the ring of integers modulo-P. The combination of modulo-P convolutional channel encoder (CE) and the CPE, is a linear modulo-P encoder. Design examples are given for rate 1/2 coded quaternary CPFSK with modulation indices 1/2 and 1/4, and rate-2/3 coded octal CPFSK with modulation index 1/8. Combinations are optimized in the normalized minimum Euclidean distance sense for a given total number of states in the overall maximum likelihood sequence estimation (MLSE) receiver. Numerical results show that this new coding scheme consistently achieves better performance than previous schemes. [1, 2, 3, 4, 5].

An upper bound on the bit error probability (BER) for ring convolutionally encoded CPFSK is derived. The bound shows that feedback-free CPFSK usually has a smaller error coefficient than CPFSK. The minimum Eucildean distance is a good parameter for estimating performance, and the ring convolutionally encoded CPFSK has a good BER for both moderate and practical signal to noise ratio.