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:
-
- 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; 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
Citation Formats
Elser, Veit. The Complexity of Bit Retrieval. United States: N. p., 2018.
Web. doi: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 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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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
Figures / Tables found in this record:
Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.