Correlation properties of cyclic sequences

Citation

Titsworth, Robert C. (1962) Correlation properties of cyclic sequences. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/XE6F-BM96. https://resolver.caltech.edu/CaltechETD:etd-09092005-130635

Abstract

In the unconstrained channel with additive Gaussian noise, where the optimum detector is based on correlation or matched filters, the quality of a code can be expressed as a function of the correlation values between code words. For a cyclic-sequence code, optimality reduces to a criterion to be met by the autocorrelation function of the sequence. Methods are presented here for determining cyclic sequences with given correlation properties.

When the amount of equipment in the receiver is limited, matched filtering is no longer the optimal detection scheme. A better system, as is shown here, is one which, by the use of a Boolean function, combines several "component" sequences to generate the transmitted signal; the receiver consists of filters matched to each component. The logic, the number of components, the requirements of the component sequences to optimize the system, and a general method for treating Boolean logics are given in this work.

Item Type:	Thesis (Dissertation (Ph.D.))
Subject Keywords:	cyclic codes, ranging codes, rademacher-walsh transform
Degree Grantor:	California Institute of Technology
Division:	Engineering and Applied Science
Major Option:	Electrical Engineering
Thesis Availability:	Public (worldwide access)
Research Advisor(s):	Golomb, Solomon W. (advisor) Martel, Hardy Cross (advisor)
Thesis Committee:	Golomb, Solomon W. (chair) Martel, Hardy Cross Hall, Marshall Jr.
Defense Date:	1 January 1962
Non-Caltech Author Email:	robert.c.tausworthe (AT) ieee.org
Additional Information:	The results of this thesis were applied to the first interplanetary ranging system, in which the range from Goldstone, CA to the Mariner V spacecraft was tracked to an accuracy of 10m as it passed the planet Venus in 1967. The codes used were those now used in GPS transmissions.
Record Number:	CaltechETD:etd-09092005-130635
Persistent URL:	https://resolver.caltech.edu/CaltechETD:etd-09092005-130635
DOI:	10.7907/XE6F-BM96
Default Usage Policy:	No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:	3399
Collection:	CaltechTHESIS
Deposited By:	Imported from ETD-db
Deposited On:	12 Sep 2005
Last Modified:	21 Dec 2019 04:51

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