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arXiv 2005.12895cs.ITmath.IT
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通过撕纸通道进行通信

Communicating over the Torn-Paper Channel

Ilan Shomorony, Alireza Vahid

摘要:

我们考虑的问题,通过一个通道,随机“撕裂”的消息块成不同大小的小块和洗牌。对于块长度为$n$、块长度为${\rm Geometric}(p_n)$的二进制撕纸信道,我们将其容量表征为$C = e^{-α}$,其中$α= \lim_{n\to\infty} p_n \log n$。我们的研究结果表明,${\rm Geometric}(p_n)$长度的片段的情况下,和确定性长度的$(1/p_n)$片段的情况下是定性不同的,令人惊讶的是,前者的容量更大。直观地说,这是因为在随机碎片的情况下,有时会观察到大碎片,这会提高容量。

英文摘要:

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 ${\rm Geometric}(p_n)$, we characterize the capacity as $C = e^{-α}$, where $α= \lim_{n\to\infty} p_n \log n$. Our results show that the case of ${\rm Geometric}(p_n)$-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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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