Torn-Paper Coding

We consider the problem of communicating over a channel that randomly “tears” message block into small pieces different sizes and shuffles them. For binary torn-paper with length $n$ notation="LaTeX">${\mathrm{ Geometric}}(p_{n})$ , we characterize capacity as notation="LaTeX">$C = e^{-\alpha }$ where notation="LaTeX">$\alpha \lim _{n\to \infty } p_{n} \log n$ . Our results show case -length fragments deterministic length- notation="LaTeX">$(1/p_{n})$ are qualitatively and, surprisingly, former is larger. Intuitively, this due to fact that, in random case, large sometimes observed, which boosts capacity.