Torn-Paper Coding
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 <inline-formula> <tex-math notation="LaTeX">n </tex-math>&...
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Published in | IEEE transactions on information theory Vol. 67; no. 12; pp. 7904 - 7913 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
New York
IEEE
01.12.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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Abstract | 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 <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> and pieces of length <inline-formula> <tex-math notation="LaTeX">{\mathrm{ Geometric}}(p_{n}) </tex-math></inline-formula>, we characterize the capacity as <inline-formula> <tex-math notation="LaTeX">C = e^{-\alpha } </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">\alpha = \lim _{n\to \infty } p_{n} \log n </tex-math></inline-formula>. Our results show that the case of <inline-formula> <tex-math notation="LaTeX">{\mathrm{ Geometric}}(p_{n}) </tex-math></inline-formula>-length fragments and the case of deterministic length-<inline-formula> <tex-math notation="LaTeX">(1/p_{n}) </tex-math></inline-formula> 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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AbstractList | 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 <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> and pieces of length <inline-formula> <tex-math notation="LaTeX">{\mathrm{ Geometric}}(p_{n}) </tex-math></inline-formula>, we characterize the capacity as <inline-formula> <tex-math notation="LaTeX">C = e^{-\alpha } </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">\alpha = \lim _{n\to \infty } p_{n} \log n </tex-math></inline-formula>. Our results show that the case of <inline-formula> <tex-math notation="LaTeX">{\mathrm{ Geometric}}(p_{n}) </tex-math></inline-formula>-length fragments and the case of deterministic length-<inline-formula> <tex-math notation="LaTeX">(1/p_{n}) </tex-math></inline-formula> 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. 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 [Formula Omitted] and pieces of length [Formula Omitted], we characterize the capacity as [Formula Omitted], where [Formula Omitted]. Our results show that the case of [Formula Omitted]-length fragments and the case of deterministic length-[Formula Omitted] 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. |
Author | Shomorony, Ilan Vahid, Alireza |
Author_xml | – sequence: 1 givenname: Ilan orcidid: 0000-0001-5077-2269 surname: Shomorony fullname: Shomorony, Ilan email: ilans@illinois.edu organization: Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign (UIUC), Urbana, IL, USA – sequence: 2 givenname: Alireza orcidid: 0000-0002-5079-4617 surname: Vahid fullname: Vahid, Alireza email: alireza.vahid@ucdenver.edu organization: Department of Electrical Engineering, University of Colorado Denver, Denver, CO, USA |
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Snippet | 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... 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... |
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StartPage | 7904 |
SubjectTerms | Codes Communication data storage Decoding DNA DNA storage Encoding Fragments Indexes Sequential analysis Torn paper Transmitters unordered communication |
Title | Torn-Paper Coding |
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