Coding for the ℓ∞-limited permutation channel

Michael Langberg; Moshe Schwartz; Eitan Yaakobi

doi:10.1109/ISIT.2015.7282793

Coding for the ℓ_∞-limited permutation channel

Michael Langberg, Moshe Schwartz, Eitan Yaakobi

Ben-Gurion University of the Negev, Technion - Israel Institute of Technology

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

Abstract

In this work we consider the communication of information in the presence of synchronization errors. Specifically, we consider permutation channels in which a transmitted codeword x = (x₁,⋯, x_n) is corrupted by a permutation π ϵ S_n to yield the received word y = (y₁,⋯, y_n) where y_i = x_π(i). We initiate the study of worst case (or zero error) communication over permutation channels that distort the information by applying permutations π which are limited to displacing any symbol by at most r locations, i.e. permutations π with weight at most r in the ℓ_∞-metric. We present direct and recursive constructions, as well as bounds on the rate of such channels for binary and general alphabets. Specific attention is given to the case of r = 1.

Original language	English
Title of host publication	Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1936-1940
Number of pages	5
ISBN (Electronic)	9781467377041
DOIs	https://doi.org/10.1109/ISIT.2015.7282793
State	Published - 28 Sep 2015
Event	IEEE International Symposium on Information Theory, ISIT 2015 - Hong Kong, Hong Kong Duration: 14 Jun 2015 → 19 Jun 2015

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2015-June

Conference

Conference	IEEE International Symposium on Information Theory, ISIT 2015
Country/Territory	Hong Kong
City	Hong Kong
Period	14/06/15 → 19/06/15

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Information Systems
Modelling and Simulation
Applied Mathematics

Access to Document

10.1109/ISIT.2015.7282793

Cite this

Langberg, M., Schwartz, M., & Yaakobi, E. (2015). Coding for the ℓ_∞-limited permutation channel. In Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015 (pp. 1936-1940). Article 7282793 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2015-June). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2015.7282793

@inproceedings{5c6da34ee8be405da58645e7ba9c6401,

title = "Coding for the ℓ∞-limited permutation channel",

abstract = "In this work we consider the communication of information in the presence of synchronization errors. Specifically, we consider permutation channels in which a transmitted codeword x = (x1,⋯, xn) is corrupted by a permutation π ϵ Sn to yield the received word y = (y1,⋯, yn) where yi = xπ(i). We initiate the study of worst case (or zero error) communication over permutation channels that distort the information by applying permutations π which are limited to displacing any symbol by at most r locations, i.e. permutations π with weight at most r in the ℓ∞-metric. We present direct and recursive constructions, as well as bounds on the rate of such channels for binary and general alphabets. Specific attention is given to the case of r = 1.",

author = "Michael Langberg and Moshe Schwartz and Eitan Yaakobi",

note = "Publisher Copyright: {\textcopyright} 2015 IEEE.; IEEE International Symposium on Information Theory, ISIT 2015 ; Conference date: 14-06-2015 Through 19-06-2015",

year = "2015",

month = sep,

day = "28",

doi = "10.1109/ISIT.2015.7282793",

language = "الإنجليزيّة",

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

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "1936--1940",

booktitle = "Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015",

address = "الولايات المتّحدة",

}

Langberg, M, Schwartz, M & Yaakobi, E 2015, Coding for the ℓ_∞-limited permutation channel. in Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015., 7282793, IEEE International Symposium on Information Theory - Proceedings, vol. 2015-June, Institute of Electrical and Electronics Engineers Inc., pp. 1936-1940, IEEE International Symposium on Information Theory, ISIT 2015, Hong Kong, Hong Kong, 14/06/15. https://doi.org/10.1109/ISIT.2015.7282793

Coding for the ℓ_∞-limited permutation channel. / Langberg, Michael; Schwartz, Moshe ; Yaakobi, Eitan.
Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015. Institute of Electrical and Electronics Engineers Inc., 2015. p. 1936-1940 7282793 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2015-June).

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

TY - GEN

T1 - Coding for the ℓ∞-limited permutation channel

AU - Langberg, Michael

AU - Schwartz, Moshe

AU - Yaakobi, Eitan

PY - 2015/9/28

Y1 - 2015/9/28

N2 - In this work we consider the communication of information in the presence of synchronization errors. Specifically, we consider permutation channels in which a transmitted codeword x = (x1,⋯, xn) is corrupted by a permutation π ϵ Sn to yield the received word y = (y1,⋯, yn) where yi = xπ(i). We initiate the study of worst case (or zero error) communication over permutation channels that distort the information by applying permutations π which are limited to displacing any symbol by at most r locations, i.e. permutations π with weight at most r in the ℓ∞-metric. We present direct and recursive constructions, as well as bounds on the rate of such channels for binary and general alphabets. Specific attention is given to the case of r = 1.

AB - In this work we consider the communication of information in the presence of synchronization errors. Specifically, we consider permutation channels in which a transmitted codeword x = (x1,⋯, xn) is corrupted by a permutation π ϵ Sn to yield the received word y = (y1,⋯, yn) where yi = xπ(i). We initiate the study of worst case (or zero error) communication over permutation channels that distort the information by applying permutations π which are limited to displacing any symbol by at most r locations, i.e. permutations π with weight at most r in the ℓ∞-metric. We present direct and recursive constructions, as well as bounds on the rate of such channels for binary and general alphabets. Specific attention is given to the case of r = 1.

UR - http://www.scopus.com/inward/record.url?scp=84969750172&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2015.7282793

DO - 10.1109/ISIT.2015.7282793

M3 - منشور من مؤتمر

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 1936

EP - 1940

BT - Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - IEEE International Symposium on Information Theory, ISIT 2015

Y2 - 14 June 2015 through 19 June 2015

ER -