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Correlation Properties of Cyclic Sequences


Titsworth, Robert Clem (1963) Correlation Properties of Cyclic Sequences. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/XE6F-BM96.


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:(Electrical Engineering and Mathematics) ; cyclic codes, ranging codes, rademacher-walsh transform
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Electrical Engineering
Minor Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Golomb, Solomon W.
Thesis Committee:
  • Unknown, Unknown
Defense Date:1962
Non-Caltech Author Email:robert.c.tausworthe (AT)
Additional Information:The author graduated from Caltech under the name Robert Clem Titsworth. His last name later changed, and he became known as Robert C. Tausworthe. 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:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3399
Deposited By: Imported from ETD-db
Deposited On:12 Sep 2005
Last Modified:04 Jan 2024 22:11

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