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Title: The Complexity of Bit Retrieval

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:
ORCiD logo [1]
  1. Cornell Univ., Ithaca, NY (United States). Dept. of Physics
Publication Date:
Grant/Contract Number:
SC0005827; AC02-76SF00515; FG02-11ER16210
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
Research Org:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org:
USDOE; Simons Foundation
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Phase retrieval; periodic autocorrelation; reconstruction algorithms
OSTI Identifier:
1417635

Elser, Veit. The Complexity of Bit Retrieval. United States: N. p., Web. doi:10.1109/TIT.2017.2754485.
Elser, Veit. The Complexity of Bit Retrieval. United States. doi:10.1109/TIT.2017.2754485.
Elser, Veit. 2018. "The Complexity of Bit Retrieval". United States. doi:10.1109/TIT.2017.2754485.
@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 = {2018},
month = {9}
}