On pseudo-noise sequences

Date of Publication

2010

Document Type

Bachelor's Thesis

Degree Name

Bachelor of Science in Mathematics with specialization in Business Applications

Subject Categories

Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics

Thesis Adviser

Ederlina G. Nocon

Defense Panel Chair

Yvette F. Lim

Defense Panel Member

Michele G. Tan
John Vincent S. Morales

Abstract/Summary

The discovery of pseudo-noise sequences is a product of coding theory -- an area of mathematics which deals with the transmission and reception of messages across noisy channels. To give a partial exposition of the article entitled Applications of Coding Theory in Mobile Radio Communications by Derek Smith and Stephanie Perkins [15] is the main aim of this thesis. Also, it aims to discuss in detail the properties of pseudo-noise sequences using the book entitled The Theory of Error-Correcting Codes by Florence MacWilliams and Neil Sloane [10]. In order to give a clear understanding of these properties, basic concepts in abstract algebra, linear algebra, field theory and coding theory are provided. The use of linear feedback shift registers for a fast generation of pseudo-noise sequences is also discussed. Ten properties are verified, and these include properties about pseud-randomness and autocorrelation. It is proven that a pseudo-noise sequence satisfies a certain recurrence and is periodic with period n = 2m - 1, where m is the degree of the primitive irreducible polynomial used for constructing a linear feedback shift register that there are 2m - 1 nonzero states before repeating that each possible nonzero m-tuple is seen only once in a full period of a pseudo-noise sequence and that the sum of any segment (of length n from a pseudo-noise sequence) with a cyclic shift of itself is another cyclic shift of this segment.

Abstract Format

html

Language

English

Format

Print

Accession Number

TU15998

Shelf Location

Archives, The Learning Commons, 12F, Henry Sy Sr. Hall

Physical Description

vii, 103 leaves, illustrations, 28 cm.

Keywords

Coding theory; Error-correcting codes (Information theory)

Embargo Period

4-15-2021

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