A new bound for the capacity of the deletion channel with high deletion probabilities

Details A new bound for the capacity of the deletion channel with high deletion probabilities A new bound for the capacity of the deletion channel with high deletion probabilities

2010-04-02

arxiv.org/abs/1004.0400v2

Computer Science

Information Theory

ISIT 2011, the first draft contained an error in some expressions (a log(n) in place of log(n+1))

Scientific paper

Let $C(d)$ be the capacity of the binary deletion channel with deletion probability $d$. It was proved by Drinea and Mitzenmacher that, for all $d$, $C(d)/(1-d)\geq 0.1185 $. Fertonani and Duman recently showed that $\limsup_{d\to 1}C(d)/(1-d)\leq 0.49$. In this paper, it is proved that $\lim_{d\to 1}C(d)/(1-d)$ exists and is equal to $\inf_{d}C(d)/(1-d)$. This result suggests the conjecture that the curve $C(d)$ my be convex in the interval $d\in [0,1]$. Furthermore, using currently known bounds for $C(d)$, it leads to the upper bound $\lim_{d\to 1}C(d)/(1-d)\leq 0.4143$.

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