# 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:
- Journal Article: 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. doi:10.1109/TIT.2017.2754485.

```
Elser, Veit. Thu .
"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 = {Thu Sep 20 00:00:00 EDT 2018},

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

}

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