The Complexity of Bit Retrieval

Elser, Veit

doi:10.1109/TIT.2017.2754485

Title: The Complexity of Bit Retrieval

Abstract

Bit retrieval is the problem of reconstructing a periodic binary sequence from its periodic autocorrelation, with applications in cryptography and x-ray crystallography. After defining the problem, with and without noise, we describe and compare various algorithms for solving it. A geometrical constraint satisfaction algorithm, relaxed-reflect-reflect, is currently the best algorithm for noisy bit retrieval.

Authors:

^[1]

Cornell Univ., Ithaca, NY (United States). Dept. of Physics

Publication Date:: Thu Sep 20 00:00:00 EDT 2018

Research Org.:: SLAC National Accelerator Lab., Menlo Park, CA (United States)

Sponsoring Org.:: USDOE; Simons Foundation

OSTI Identifier:: 1417635

Grant/Contract Number:: SC0005827; AC02-76SF00515; FG02-11ER16210

Resource Type:: Accepted Manuscript

Journal Name:: IEEE Transactions on Information Theory

Additional Journal Information:: Journal Volume: 64; Journal Issue: 1; Journal ID: ISSN 0018-9448

Publisher:: IEEE

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; Phase retrieval; periodic autocorrelation; reconstruction algorithms

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                    Elser, Veit. The Complexity of Bit Retrieval.  United States: N. p., 2018. 
Web.  doi:10.1109/TIT.2017.2754485.

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                    Elser, Veit. The Complexity of Bit Retrieval.  United States.  https://doi.org/10.1109/TIT.2017.2754485

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                    Elser, Veit. Thu .  
"The Complexity of Bit Retrieval".  United States.  https://doi.org/10.1109/TIT.2017.2754485.  https://www.osti.gov/servlets/purl/1417635.

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@article{osti_1417635,

  title        = {The Complexity of Bit Retrieval},

  author       = {Elser, Veit},

  abstractNote = {Bit retrieval is the problem of reconstructing a periodic binary sequence from its periodic autocorrelation, with applications in cryptography and x-ray crystallography. After defining the problem, with and without noise, we describe and compare various algorithms for solving it. A geometrical constraint satisfaction algorithm, relaxed-reflect-reflect, is currently the best algorithm for noisy bit retrieval.},

  doi          = {10.1109/TIT.2017.2754485},

  journal      = {IEEE Transactions on Information Theory},

  number       = 1,

  volume       = 64,

  place        = {United States},

  year         = {Thu Sep 20 00:00:00 EDT 2018},

  month        = {Thu Sep 20 00:00:00 EDT 2018}

}

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https://doi.org/10.1109/TIT.2017.2754485

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Cited by: 7 works

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Figures / Tables:

Figure 1: Growth in the minimum bit length $P$ required for successful bit retrieval of symmetric Hadamard sequences of length $N$ by the LLL basis reduction algorithm.

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Works referencing / citing this record:

The Douglas–Rachford algorithm for convex and nonconvex feasibility problems
journal, November 2019

Aragón Artacho, Francisco J.; Campoy, Rubén; Tam, Matthew K.
Mathematical Methods of Operations Research, Vol. 91, Issue 2
DOI: 10.1007/s00186-019-00691-9

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Title: The Complexity of Bit Retrieval

Abstract

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Figures / Tables:

The Douglas–Rachford algorithm for convex and nonconvex feasibility problems journal, November 2019

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