Asymptotic improvement of GV bound

The Gilbert-Varshamov (GV) bound is a well-known lower bound in coding theory that claims that for any given code with relative distance $\delta$, there is a lower bound for the rates possible. This paper will asymptotically improve upon by 1.5$\frac{\log n}{n}$ for unconstrained binary systems. We...

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Main Author:	Yip, Jose Zheng Ho
Other Authors:	Kiah Han Mao
Format:	Final Year Project
Language:	English
Published:	Nanyang Technological University 2022
Subjects:	Science::Mathematics::Discrete mathematics
Online Access:	https://hdl.handle.net/10356/156922
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Institution:	Nanyang Technological University
Language:	English

id	sg-ntu-dr.10356-156922
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spelling	sg-ntu-dr.10356-1569222023-02-28T23:18:56Z Asymptotic improvement of GV bound Yip, Jose Zheng Ho Kiah Han Mao School of Physical and Mathematical Sciences HMKiah@ntu.edu.sg Science::Mathematics::Discrete mathematics The Gilbert-Varshamov (GV) bound is a well-known lower bound in coding theory that claims that for any given code with relative distance $\delta$, there is a lower bound for the rates possible. This paper will asymptotically improve upon by 1.5$\frac{\log n}{n}$ for unconstrained binary systems. We also show that for the RLL(0,1) constrained system, we can achieve rates $2\log \phi - \log \tau$, where $\tau$ is the asymptotic of the total ball size for the RLL(0,1) constrained system Bachelor of Science in Mathematical Sciences 2022-04-28T11:15:30Z 2022-04-28T11:15:30Z 2022 Final Year Project (FYP) Yip, J. Z. H. (2022). Asymptotic improvement of GV bound. Final Year Project (FYP), Nanyang Technological University, Singapore. https://hdl.handle.net/10356/156922 https://hdl.handle.net/10356/156922 en application/pdf Nanyang Technological University
institution	Nanyang Technological University
building	NTU Library
continent	Asia
country	Singapore Singapore
content_provider	NTU Library
collection	DR-NTU
language	English
topic	Science::Mathematics::Discrete mathematics
spellingShingle	Science::Mathematics::Discrete mathematics Yip, Jose Zheng Ho Asymptotic improvement of GV bound
description	The Gilbert-Varshamov (GV) bound is a well-known lower bound in coding theory that claims that for any given code with relative distance $\delta$, there is a lower bound for the rates possible. This paper will asymptotically improve upon by 1.5$\frac{\log n}{n}$ for unconstrained binary systems. We also show that for the RLL(0,1) constrained system, we can achieve rates $2\log \phi - \log \tau$, where $\tau$ is the asymptotic of the total ball size for the RLL(0,1) constrained system
author2	Kiah Han Mao
author_facet	Kiah Han Mao Yip, Jose Zheng Ho
format	Final Year Project
author	Yip, Jose Zheng Ho
author_sort	Yip, Jose Zheng Ho
title	Asymptotic improvement of GV bound
title_short	Asymptotic improvement of GV bound
title_full	Asymptotic improvement of GV bound
title_fullStr	Asymptotic improvement of GV bound
title_full_unstemmed	Asymptotic improvement of GV bound
title_sort	asymptotic improvement of gv bound
publisher	Nanyang Technological University
publishDate	2022
url	https://hdl.handle.net/10356/156922
_version_	1759857945303056384

Asymptotic improvement of GV bound

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