On pseudo-noise sequences

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 Dere...

Full description

Saved in:
Bibliographic Details
Main Authors: Rubin, Karlyn Anne C., Shi, Yiyin Iris Sy
Format: text
Language:English
Published: Animo Repository 2010
Subjects:
Online Access:https://animorepository.dlsu.edu.ph/etd_bachelors/5338
Tags: Add Tag
No Tags, Be the first to tag this record!
Institution: De La Salle University
Language: English
id oai:animorepository.dlsu.edu.ph:etd_bachelors-5776
record_format eprints
spelling oai:animorepository.dlsu.edu.ph:etd_bachelors-57762022-03-11T01:49:14Z On pseudo-noise sequences Rubin, Karlyn Anne C. Shi, Yiyin Iris Sy 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. 2010-01-01T08:00:00Z text https://animorepository.dlsu.edu.ph/etd_bachelors/5338 Bachelor's Theses English Animo Repository Coding theory Error-correcting codes (Information theory) Mathematics
institution De La Salle University
building De La Salle University Library
continent Asia
country Philippines
Philippines
content_provider De La Salle University Library
collection DLSU Institutional Repository
language English
topic Coding theory
Error-correcting codes (Information theory)
Mathematics
spellingShingle Coding theory
Error-correcting codes (Information theory)
Mathematics
Rubin, Karlyn Anne C.
Shi, Yiyin Iris Sy
On pseudo-noise sequences
description 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.
format text
author Rubin, Karlyn Anne C.
Shi, Yiyin Iris Sy
author_facet Rubin, Karlyn Anne C.
Shi, Yiyin Iris Sy
author_sort Rubin, Karlyn Anne C.
title On pseudo-noise sequences
title_short On pseudo-noise sequences
title_full On pseudo-noise sequences
title_fullStr On pseudo-noise sequences
title_full_unstemmed On pseudo-noise sequences
title_sort on pseudo-noise sequences
publisher Animo Repository
publishDate 2010
url https://animorepository.dlsu.edu.ph/etd_bachelors/5338
_version_ 1772834668450676736