Polytope codes against adversaries in networks

Oliver Kosut, Lang Tong, David N C Tse

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

This paper investigates a network coding problem wherein an adversary controls a subset of nodes in the network of limited quantity but unknown location. This problem is shown to be more difficult than that of an adversary controlling a given number of edges in the network, in that linear codes are insufficient. To solve the node problem, the class of polytope codes is introduced. Polytope codes are constant composition codes operating over bounded polytopes in integer vector fields. The polytope structure creates additional complexity, but it induces properties on marginal distributions of code vectors so that validities of codewords can be checked by internal nodes of the network. It is shown that polytope codes achieve a cut-set bound for a class of planar networks. It is also shown that this cut-set bound is not always tight, and a tighter bound is given for an example network.

Original languageEnglish (US)
Article number6781646
Pages (from-to)3308-3344
Number of pages37
JournalIEEE Transactions on Information Theory
Volume60
Issue number6
DOIs
StatePublished - 2014

Fingerprint

Network coding
Chemical analysis
coding

Keywords

  • Active adversaries
  • Byzantine attack
  • network coding
  • network error correction
  • nonlinear codes
  • polytope codes
  • security

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

Cite this

Polytope codes against adversaries in networks. / Kosut, Oliver; Tong, Lang; Tse, David N C.

In: IEEE Transactions on Information Theory, Vol. 60, No. 6, 6781646, 2014, p. 3308-3344.

Research output: Contribution to journalArticle

Kosut, Oliver ; Tong, Lang ; Tse, David N C. / Polytope codes against adversaries in networks. In: IEEE Transactions on Information Theory. 2014 ; Vol. 60, No. 6. pp. 3308-3344.
@article{edf5d25a93ce4ffea4fecc794e00d626,
title = "Polytope codes against adversaries in networks",
abstract = "This paper investigates a network coding problem wherein an adversary controls a subset of nodes in the network of limited quantity but unknown location. This problem is shown to be more difficult than that of an adversary controlling a given number of edges in the network, in that linear codes are insufficient. To solve the node problem, the class of polytope codes is introduced. Polytope codes are constant composition codes operating over bounded polytopes in integer vector fields. The polytope structure creates additional complexity, but it induces properties on marginal distributions of code vectors so that validities of codewords can be checked by internal nodes of the network. It is shown that polytope codes achieve a cut-set bound for a class of planar networks. It is also shown that this cut-set bound is not always tight, and a tighter bound is given for an example network.",
keywords = "Active adversaries, Byzantine attack, network coding, network error correction, nonlinear codes, polytope codes, security",
author = "Oliver Kosut and Lang Tong and Tse, {David N C}",
year = "2014",
doi = "10.1109/TIT.2014.2314642",
language = "English (US)",
volume = "60",
pages = "3308--3344",
journal = "IEEE Transactions on Information Theory",
issn = "0018-9448",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "6",

}

TY - JOUR

T1 - Polytope codes against adversaries in networks

AU - Kosut, Oliver

AU - Tong, Lang

AU - Tse, David N C

PY - 2014

Y1 - 2014

N2 - This paper investigates a network coding problem wherein an adversary controls a subset of nodes in the network of limited quantity but unknown location. This problem is shown to be more difficult than that of an adversary controlling a given number of edges in the network, in that linear codes are insufficient. To solve the node problem, the class of polytope codes is introduced. Polytope codes are constant composition codes operating over bounded polytopes in integer vector fields. The polytope structure creates additional complexity, but it induces properties on marginal distributions of code vectors so that validities of codewords can be checked by internal nodes of the network. It is shown that polytope codes achieve a cut-set bound for a class of planar networks. It is also shown that this cut-set bound is not always tight, and a tighter bound is given for an example network.

AB - This paper investigates a network coding problem wherein an adversary controls a subset of nodes in the network of limited quantity but unknown location. This problem is shown to be more difficult than that of an adversary controlling a given number of edges in the network, in that linear codes are insufficient. To solve the node problem, the class of polytope codes is introduced. Polytope codes are constant composition codes operating over bounded polytopes in integer vector fields. The polytope structure creates additional complexity, but it induces properties on marginal distributions of code vectors so that validities of codewords can be checked by internal nodes of the network. It is shown that polytope codes achieve a cut-set bound for a class of planar networks. It is also shown that this cut-set bound is not always tight, and a tighter bound is given for an example network.

KW - Active adversaries

KW - Byzantine attack

KW - network coding

KW - network error correction

KW - nonlinear codes

KW - polytope codes

KW - security

UR - http://www.scopus.com/inward/record.url?scp=84901275660&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84901275660&partnerID=8YFLogxK

U2 - 10.1109/TIT.2014.2314642

DO - 10.1109/TIT.2014.2314642

M3 - Article

AN - SCOPUS:84901275660

VL - 60

SP - 3308

EP - 3344

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

SN - 0018-9448

IS - 6

M1 - 6781646

ER -