We consider the problem of communicating over a channel that randomly “tears” the message block into small pieces of different sizes and shuffles them. For the binary torn-paper channel with block length n and pieces of length Geometric(pn), we characterize the capacity as $C = e^{-lpha}$, where $lpha=lim_{nightarrowinfty}p_{n}log n$, Our results show that the case of Geometric (Pn)-length fragments and the case of deterministic length-($1/p_{n}$) fragments are qualitatively different and, surprisingly, the capacity of the former is larger. Intuitively, this is due to the fact that, in the random fragments case, large fragments are sometimes observed, which boosts the capacity.
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机译：我们考虑在一条频道上沟通的问题，随机将消息块“撕裂”到小块不同尺寸并将其洗牌。对于具有块长度n的二进制撕纸通道，几何长度（p n ），我们表征了容量 $ c = e ^ { - alpha} $ ， 在哪里 $ alpha = lim_ { n lightarrow infty} p_ {n} log n $ 我们的结果表明，几何的情况（p n ） - 长碎片和确定性长度的情况 - （ $ 1 / p_ {n} $ ）碎片是定性不同的，令人惊讶的是，前者的能力更大。直观地，这是由于，在随机碎片情况下，有时观察大碎片，促进了容量。
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