Randomness and dependencies extraction via polarization

Emmanuel Abbe

doi:10.1109/ITA.2011.5743556

Randomness and dependencies extraction via polarization

Emmanuel Abbe

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

22 Scopus citations

Abstract

The basic polarization phenomenon for i.i.d. sources is extended to a framework allowing dependencies within and between multiple sources. In particular, it is shown that taking the polar transform of a random matrix with i.i.d. columns of arbitrary (correlated) distribution allows to extract the randomness and dependencies. This result is the used to develop polar coding schemes (having low complexity) for: (1) distributed data compression, i.e., Slepian-Wolf coding (without decomposing the problem into single-user problems), (2) compression of sources with memory, (3) compression of sources on finite fields, extending the polarization phenomenon for alphabets of prime cardinality to powers of primes.

Original language	English (US)
Title of host publication	2011 Information Theory and Applications Workshop, ITA 2011 - Conference Proceedings
Pages	8-14
Number of pages	7
DOIs	https://doi.org/10.1109/ITA.2011.5743556
State	Published - 2011
Event	2011 Information Theory and Applications Workshop, ITA 2011 - San Diego, CA, United States Duration: Feb 6 2011 → Feb 11 2011

Publication series

Name	2011 Information Theory and Applications Workshop, ITA 2011 - Conference Proceedings

Other

Other	2011 Information Theory and Applications Workshop, ITA 2011
Country/Territory	United States
City	San Diego, CA
Period	2/6/11 → 2/11/11

All Science Journal Classification (ASJC) codes

Computational Theory and Mathematics
Computer Science Applications
Information Systems

Access to Document

10.1109/ITA.2011.5743556

Cite this

@inproceedings{f4b411abe8fc4c27aa6f942b3ddb4191,

title = "Randomness and dependencies extraction via polarization",

abstract = "The basic polarization phenomenon for i.i.d. sources is extended to a framework allowing dependencies within and between multiple sources. In particular, it is shown that taking the polar transform of a random matrix with i.i.d. columns of arbitrary (correlated) distribution allows to extract the randomness and dependencies. This result is the used to develop polar coding schemes (having low complexity) for: (1) distributed data compression, i.e., Slepian-Wolf coding (without decomposing the problem into single-user problems), (2) compression of sources with memory, (3) compression of sources on finite fields, extending the polarization phenomenon for alphabets of prime cardinality to powers of primes.",

author = "Emmanuel Abbe",

year = "2011",

doi = "10.1109/ITA.2011.5743556",

language = "English (US)",

isbn = "9781457703614",

series = "2011 Information Theory and Applications Workshop, ITA 2011 - Conference Proceedings",

pages = "8--14",

booktitle = "2011 Information Theory and Applications Workshop, ITA 2011 - Conference Proceedings",

note = "2011 Information Theory and Applications Workshop, ITA 2011 ; Conference date: 06-02-2011 Through 11-02-2011",

}

Abbe, E 2011, Randomness and dependencies extraction via polarization. in 2011 Information Theory and Applications Workshop, ITA 2011 - Conference Proceedings., 5743556, 2011 Information Theory and Applications Workshop, ITA 2011 - Conference Proceedings, pp. 8-14, 2011 Information Theory and Applications Workshop, ITA 2011, San Diego, CA, United States, 2/6/11. https://doi.org/10.1109/ITA.2011.5743556

TY - GEN

T1 - Randomness and dependencies extraction via polarization

AU - Abbe, Emmanuel

PY - 2011

Y1 - 2011

N2 - The basic polarization phenomenon for i.i.d. sources is extended to a framework allowing dependencies within and between multiple sources. In particular, it is shown that taking the polar transform of a random matrix with i.i.d. columns of arbitrary (correlated) distribution allows to extract the randomness and dependencies. This result is the used to develop polar coding schemes (having low complexity) for: (1) distributed data compression, i.e., Slepian-Wolf coding (without decomposing the problem into single-user problems), (2) compression of sources with memory, (3) compression of sources on finite fields, extending the polarization phenomenon for alphabets of prime cardinality to powers of primes.

AB - The basic polarization phenomenon for i.i.d. sources is extended to a framework allowing dependencies within and between multiple sources. In particular, it is shown that taking the polar transform of a random matrix with i.i.d. columns of arbitrary (correlated) distribution allows to extract the randomness and dependencies. This result is the used to develop polar coding schemes (having low complexity) for: (1) distributed data compression, i.e., Slepian-Wolf coding (without decomposing the problem into single-user problems), (2) compression of sources with memory, (3) compression of sources on finite fields, extending the polarization phenomenon for alphabets of prime cardinality to powers of primes.

UR - http://www.scopus.com/inward/record.url?scp=79955780858&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79955780858&partnerID=8YFLogxK

U2 - 10.1109/ITA.2011.5743556

DO - 10.1109/ITA.2011.5743556

M3 - Conference contribution

AN - SCOPUS:79955780858

SN - 9781457703614

T3 - 2011 Information Theory and Applications Workshop, ITA 2011 - Conference Proceedings

SP - 8

EP - 14

BT - 2011 Information Theory and Applications Workshop, ITA 2011 - Conference Proceedings

T2 - 2011 Information Theory and Applications Workshop, ITA 2011

Y2 - 6 February 2011 through 11 February 2011

ER -

Randomness and dependencies extraction via polarization

Abstract

Publication series

Other

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this