Correlation properties of cyclic sequences

• Main Author: Titsworth, Robert C.
• Format: Others
• Published: 1962
• Online Access: https://thesis.library.caltech.edu/3399/1/Titsworth_RC_1962.pdf; 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 <https://resolver.caltech.edu/CaltechETD:etd-09092005-130635>

<p>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.</p> <p>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.</p>