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 xray crystallography. After defining the problem, with and without noise, we describe and compare various algorithms for solving it. A geometrical constraint satisfaction algorithm, relaxedreflectreflect, is currently the best algorithm for noisy bit retrieval.
 Authors:

 Cornell Univ., Ithaca, NY (United States). Dept. of Physics
 Publication Date:
 Research Org.:
 SLAC National Accelerator Lab., Menlo Park, CA (United States)
 Sponsoring Org.:
 USDOE; Simons Foundation
 OSTI Identifier:
 1417635
 Grant/Contract Number:
 SC0005827; AC0276SF00515; FG0211ER16210
 Resource Type:
 Accepted Manuscript
 Journal Name:
 IEEE Transactions on Information Theory
 Additional Journal Information:
 Journal Volume: 64; Journal Issue: 1; Journal ID: ISSN 00189448
 Publisher:
 IEEE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Phase retrieval; periodic autocorrelation; reconstruction algorithms
Citation Formats
Elser, Veit. The Complexity of Bit Retrieval. United States: N. p., 2018.
Web. https://doi.org/10.1109/TIT.2017.2754485.
Elser, Veit. The Complexity of Bit Retrieval. United States. https://doi.org/10.1109/TIT.2017.2754485
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.
@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 xray crystallography. After defining the problem, with and without noise, we describe and compare various algorithms for solving it. A geometrical constraint satisfaction algorithm, relaxedreflectreflect, 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 = {2018},
month = {9}
}
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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
Figures / Tables found in this record:
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