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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書目詳細資料
主要作者: Yip, Jose Zheng Ho
其他作者: Kiah Han Mao
格式: Final Year Project
語言:English
出版: Nanyang Technological University 2022
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在線閱讀:https://hdl.handle.net/10356/156922
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總結: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