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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| Format: | Final Year Project |
| Language: | English |
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Nanyang Technological University
2022
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| Online Access: | https://hdl.handle.net/10356/156922 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | 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 |
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