Coding for the ℓ∞-Limited Permutation Channel

Michael Langberg; Moshe Schwartz; Eitan Yaakobi

doi:10.1109/TIT.2017.2762676

Coding for the ℓ_∞-Limited Permutation Channel

Michael Langberg, Moshe Schwartz, Eitan Yaakobi

Department of Electrical & Computer Engineering

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

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 S_n to yield the received word y=(y₁,..,y_n), where y_i=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 ℓmetric. 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
Article number	8067503
Pages (from-to)	7676-7686
Number of pages	11
Journal	IEEE Transactions on Information Theory
Volume	63
Issue number	12
DOIs	https://doi.org/10.1109/TIT.2017.2762676
State	Published - 1 Dec 2017

Keywords

Permutation channel
ℓ-metric

ASJC Scopus subject areas

Information Systems
Computer Science Applications
Library and Information Sciences

Access to Document

10.1109/TIT.2017.2762676

Cite this

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title = "Coding for the ℓ∞-Limited Permutation Channel",

abstract = "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 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 ℓmetric. 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.",

keywords = "Permutation channel, ℓ-metric",

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

note = "Funding Information: Manuscript received May 26, 2016; revised March 3, 2017; accepted October 3, 2017. Date of publication October 13, 2017; date of current version November 20, 2017. M. Langberg was supported by BSF under Grant 2010075. M. Schwartz was supported by the Israel Science Foundation (ISF) under Grant 130/14. E. Yaakobi was supported by ISF under Grant 1624/14. The work was presented in part at the 2014 IEEE International Symposium on Information Theory [16]. Publisher Copyright: {\textcopyright} 1963-2012 IEEE.",

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AU - Schwartz, Moshe

AU - Yaakobi, Eitan

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N2 - 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 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 ℓmetric. 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 - 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 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 ℓmetric. 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.

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