Correlation properties of cyclic sequences

cyclic codes, ranging codes, rademacher-walsh transform

Titsworth, Robert C. ; Golomb, Solomon W. (advisor)

University:California Institute of Technology

Department:Engineering and Applied Science

关键词: cyclic codes, ranging codes, rademacher-walsh transform;   

Others  :  https://thesis.library.caltech.edu/3399/1/Titsworth_RC_1962.pdf

美国|英语

来源: Caltech THESIS

【 摘 要 】

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.