Fast Polarization for Processes with Memory

Boaz Shuval; Ido Tal

doi:10.1109/ISIT.2018.8437742

Fast Polarization for Processes with Memory

Boaz Shuval, Ido Tal

Electrical and Computer Engineering

Technion - Israel Institute of Technology

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

Abstract

Fast polarization is crucial for the performance guarantees of polar codes. In the memoryless setting, the rate of polarization is known to be exponential in the square root of the block length. A complete characterization of the rate of polarization for models with memory has been missing. We consider polar codes for processes with memory that are characterized by an underlying aperiodic and irreducible finite state Markov chain. We show that the rate of polarization for these processes is the same as in the memoryless setting, both to the high and to the low-entropy sets. Thus, polar codes achieve the Markov capacity in many information-theoretic applications.

Original language	English
Title of host publication	2018 IEEE International Symposium on Information Theory, ISIT 2018
Pages	851-855
Number of pages	5
DOIs	https://doi.org/10.1109/ISIT.2018.8437742
State	Published - 15 Aug 2018
Event	2018 IEEE International Symposium on Information Theory, ISIT 2018 - Vail, United States Duration: 17 Jun 2018 → 22 Jun 2018

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2018-June

Conference

Conference	2018 IEEE International Symposium on Information Theory, ISIT 2018
Country/Territory	United States
City	Vail
Period	17/06/18 → 22/06/18

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Information Systems
Modelling and Simulation
Applied Mathematics

Access to Document

10.1109/ISIT.2018.8437742

Cite this

@inproceedings{bb09279b337443b595f9a62852ad4f4b,

title = "Fast Polarization for Processes with Memory",

abstract = "Fast polarization is crucial for the performance guarantees of polar codes. In the memoryless setting, the rate of polarization is known to be exponential in the square root of the block length. A complete characterization of the rate of polarization for models with memory has been missing. We consider polar codes for processes with memory that are characterized by an underlying aperiodic and irreducible finite state Markov chain. We show that the rate of polarization for these processes is the same as in the memoryless setting, both to the high and to the low-entropy sets. Thus, polar codes achieve the Markov capacity in many information-theoretic applications.",

author = "Boaz Shuval and Ido Tal",

note = "Publisher Copyright: {\textcopyright} 2018 IEEE.; 2018 IEEE International Symposium on Information Theory, ISIT 2018 ; Conference date: 17-06-2018 Through 22-06-2018",

year = "2018",

month = aug,

day = "15",

doi = "10.1109/ISIT.2018.8437742",

language = "الإنجليزيّة",

isbn = "9781538647806",

series = "IEEE International Symposium on Information Theory - Proceedings",

pages = "851--855",

booktitle = "2018 IEEE International Symposium on Information Theory, ISIT 2018",

}

Shuval, B & Tal, I 2018, Fast Polarization for Processes with Memory. in 2018 IEEE International Symposium on Information Theory, ISIT 2018., 8437742, IEEE International Symposium on Information Theory - Proceedings, vol. 2018-June, pp. 851-855, 2018 IEEE International Symposium on Information Theory, ISIT 2018, Vail, United States, 17/06/18. https://doi.org/10.1109/ISIT.2018.8437742

TY - GEN

T1 - Fast Polarization for Processes with Memory

AU - Shuval, Boaz

AU - Tal, Ido

PY - 2018/8/15

Y1 - 2018/8/15

N2 - Fast polarization is crucial for the performance guarantees of polar codes. In the memoryless setting, the rate of polarization is known to be exponential in the square root of the block length. A complete characterization of the rate of polarization for models with memory has been missing. We consider polar codes for processes with memory that are characterized by an underlying aperiodic and irreducible finite state Markov chain. We show that the rate of polarization for these processes is the same as in the memoryless setting, both to the high and to the low-entropy sets. Thus, polar codes achieve the Markov capacity in many information-theoretic applications.

AB - Fast polarization is crucial for the performance guarantees of polar codes. In the memoryless setting, the rate of polarization is known to be exponential in the square root of the block length. A complete characterization of the rate of polarization for models with memory has been missing. We consider polar codes for processes with memory that are characterized by an underlying aperiodic and irreducible finite state Markov chain. We show that the rate of polarization for these processes is the same as in the memoryless setting, both to the high and to the low-entropy sets. Thus, polar codes achieve the Markov capacity in many information-theoretic applications.

UR - http://www.scopus.com/inward/record.url?scp=85052466091&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2018.8437742

DO - 10.1109/ISIT.2018.8437742

M3 - منشور من مؤتمر

SN - 9781538647806

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 851

EP - 855

BT - 2018 IEEE International Symposium on Information Theory, ISIT 2018

T2 - 2018 IEEE International Symposium on Information Theory, ISIT 2018

Y2 - 17 June 2018 through 22 June 2018

ER -

Fast Polarization for Processes with Memory

Abstract

Publication series

Conference

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Cite this