Zig-zag and replacement product graphs and LDPC codes

Christine A Kelley, Deepak Sridhara, Joachim Rosenthal

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

It is known that the expansion property of a graph influences the performance of the corresponding code when decoded using iterative algorithms. Certain graph products may be used to obtain larger expander graphs from smaller ones. In particular, the zig-zag product and replacement product may be used to construct infinite families of constant degree expander graphs. This paper investigates the use of zig-zag and replacement product graphs for the construction of codes on graphs. A modification of the zig-zag product is also introduced, which can operate on two unbalanced biregular bipartite graphs, and a proof of the expansion property of this modified zig-zag product is presented.

Original languageEnglish (US)
Pages (from-to)347-372
Number of pages26
JournalAdvances in Mathematics of Communications
Volume2
Issue number4
DOIs
StatePublished - Nov 1 2008

Fingerprint

Product Graph
LDPC Codes
Zigzag
Replacement
Expander Graphs
Graph Products
Graph in graph theory
Bipartite Graph
Iterative Algorithm

Keywords

  • Codes on graphs
  • Expander graphs
  • LDPC codes
  • Replacement product of a graph
  • Zig-Zag product

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Algebra and Number Theory
  • Applied Mathematics
  • Discrete Mathematics and Combinatorics

Cite this

Zig-zag and replacement product graphs and LDPC codes. / Kelley, Christine A; Sridhara, Deepak; Rosenthal, Joachim.

In: Advances in Mathematics of Communications, Vol. 2, No. 4, 01.11.2008, p. 347-372.

Research output: Contribution to journalArticle

Kelley, Christine A ; Sridhara, Deepak ; Rosenthal, Joachim. / Zig-zag and replacement product graphs and LDPC codes. In: Advances in Mathematics of Communications. 2008 ; Vol. 2, No. 4. pp. 347-372.
@article{1820bdf5d9ee421a86f71f6be1667f20,
title = "Zig-zag and replacement product graphs and LDPC codes",
abstract = "It is known that the expansion property of a graph influences the performance of the corresponding code when decoded using iterative algorithms. Certain graph products may be used to obtain larger expander graphs from smaller ones. In particular, the zig-zag product and replacement product may be used to construct infinite families of constant degree expander graphs. This paper investigates the use of zig-zag and replacement product graphs for the construction of codes on graphs. A modification of the zig-zag product is also introduced, which can operate on two unbalanced biregular bipartite graphs, and a proof of the expansion property of this modified zig-zag product is presented.",
keywords = "Codes on graphs, Expander graphs, LDPC codes, Replacement product of a graph, Zig-Zag product",
author = "Kelley, {Christine A} and Deepak Sridhara and Joachim Rosenthal",
year = "2008",
month = "11",
day = "1",
doi = "10.3934/amc.2008.2.347",
language = "English (US)",
volume = "2",
pages = "347--372",
journal = "Advances in Mathematics of Communications",
issn = "1930-5346",
publisher = "American Institute of Mathematical Sciences",
number = "4",

}

TY - JOUR

T1 - Zig-zag and replacement product graphs and LDPC codes

AU - Kelley, Christine A

AU - Sridhara, Deepak

AU - Rosenthal, Joachim

PY - 2008/11/1

Y1 - 2008/11/1

N2 - It is known that the expansion property of a graph influences the performance of the corresponding code when decoded using iterative algorithms. Certain graph products may be used to obtain larger expander graphs from smaller ones. In particular, the zig-zag product and replacement product may be used to construct infinite families of constant degree expander graphs. This paper investigates the use of zig-zag and replacement product graphs for the construction of codes on graphs. A modification of the zig-zag product is also introduced, which can operate on two unbalanced biregular bipartite graphs, and a proof of the expansion property of this modified zig-zag product is presented.

AB - It is known that the expansion property of a graph influences the performance of the corresponding code when decoded using iterative algorithms. Certain graph products may be used to obtain larger expander graphs from smaller ones. In particular, the zig-zag product and replacement product may be used to construct infinite families of constant degree expander graphs. This paper investigates the use of zig-zag and replacement product graphs for the construction of codes on graphs. A modification of the zig-zag product is also introduced, which can operate on two unbalanced biregular bipartite graphs, and a proof of the expansion property of this modified zig-zag product is presented.

KW - Codes on graphs

KW - Expander graphs

KW - LDPC codes

KW - Replacement product of a graph

KW - Zig-Zag product

UR - http://www.scopus.com/inward/record.url?scp=70349328415&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70349328415&partnerID=8YFLogxK

U2 - 10.3934/amc.2008.2.347

DO - 10.3934/amc.2008.2.347

M3 - Article

VL - 2

SP - 347

EP - 372

JO - Advances in Mathematics of Communications

JF - Advances in Mathematics of Communications

SN - 1930-5346

IS - 4

ER -