Asymptotic improvement of GV bound - Yip, Jose Zheng Ho (Nanyang Technological University, 2022)
The Gilbert-Varshamov (GV) bound is a well-known lower bound in coding theory that claims that for any given code with relative distance $δ$, 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 $2\log φ - \log τ$, where $τ$ is the asymptotic of the total ball size for the RLL(0,1) constrained system