Combinatorial constructions of low-density parity-check codes for iterative decoding

Bane Vasic; Olgica Milenkovic

doi:10.1109/TIT.2004.828066

Combinatorial constructions of low-density parity-check codes for iterative decoding

Bane Vasic
, Olgica Milenkovic

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

211 Scopus citations

Abstract

This paper introduces several new combinatorial constructions of low-density parity-check (LDPC) codes, in contrast to the prevalent practice of using long, random-like codes. The proposed codes are well structured, and unlike random codes can lend themselves to a very low-complexity implementation. Constructions of regular Gallager codes based on cyclic difference families, cycle-invariant difference sets, and affine 1-configurations are introduced. Several constructions of difference families used for code design are presented, as well as bounds on the minimal distance of the codes based on the concept of a generalized Pasch configuration.

Original language	English (US)
Pages (from-to)	1156-1176
Number of pages	21
Journal	IEEE Transactions on Information Theory
Volume	50
Issue number	6
DOIs	https://doi.org/10.1109/TIT.2004.828066
State	Published - Jun 2004

Keywords

Cyclic difference families
Iterative decoding
Low-density parity-check (LDPC) codes
Pasch configurations

ASJC Scopus subject areas

Information Systems
Computer Science Applications
Library and Information Sciences

Access to Document

10.1109/TIT.2004.828066

Cite this

@article{868d1716fd564e78b4d10c9665a0aa1b,

title = "Combinatorial constructions of low-density parity-check codes for iterative decoding",

abstract = "This paper introduces several new combinatorial constructions of low-density parity-check (LDPC) codes, in contrast to the prevalent practice of using long, random-like codes. The proposed codes are well structured, and unlike random codes can lend themselves to a very low-complexity implementation. Constructions of regular Gallager codes based on cyclic difference families, cycle-invariant difference sets, and affine 1-configurations are introduced. Several constructions of difference families used for code design are presented, as well as bounds on the minimal distance of the codes based on the concept of a generalized Pasch configuration.",

keywords = "Cyclic difference families, Iterative decoding, Low-density parity-check (LDPC) codes, Pasch configurations",

author = "Bane Vasic and Olgica Milenkovic",

note = "Funding Information: We thank Yuan Kuen-Ko for very helpful discussions. This work was performed under contract with the Naval Research Laboratory and was funded by the NASA Hinode program. Hinode is a Japanese mission developed and launched by ISAS/ JAXA, with NAOJ as domestic partner and NASA and STFC (UK) as international partners. It is operated by these agencies in co-operation with ESA and NSC (Norway).",

year = "2004",

month = jun,

doi = "10.1109/TIT.2004.828066",

language = "English (US)",

volume = "50",

pages = "1156--1176",

journal = "IEEE Transactions on Information Theory",

issn = "0018-9448",

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

number = "6",

}

TY - JOUR

T1 - Combinatorial constructions of low-density parity-check codes for iterative decoding

AU - Vasic, Bane

AU - Milenkovic, Olgica

N1 - Funding Information: We thank Yuan Kuen-Ko for very helpful discussions. This work was performed under contract with the Naval Research Laboratory and was funded by the NASA Hinode program. Hinode is a Japanese mission developed and launched by ISAS/ JAXA, with NAOJ as domestic partner and NASA and STFC (UK) as international partners. It is operated by these agencies in co-operation with ESA and NSC (Norway).

PY - 2004/6

Y1 - 2004/6

N2 - This paper introduces several new combinatorial constructions of low-density parity-check (LDPC) codes, in contrast to the prevalent practice of using long, random-like codes. The proposed codes are well structured, and unlike random codes can lend themselves to a very low-complexity implementation. Constructions of regular Gallager codes based on cyclic difference families, cycle-invariant difference sets, and affine 1-configurations are introduced. Several constructions of difference families used for code design are presented, as well as bounds on the minimal distance of the codes based on the concept of a generalized Pasch configuration.

AB - This paper introduces several new combinatorial constructions of low-density parity-check (LDPC) codes, in contrast to the prevalent practice of using long, random-like codes. The proposed codes are well structured, and unlike random codes can lend themselves to a very low-complexity implementation. Constructions of regular Gallager codes based on cyclic difference families, cycle-invariant difference sets, and affine 1-configurations are introduced. Several constructions of difference families used for code design are presented, as well as bounds on the minimal distance of the codes based on the concept of a generalized Pasch configuration.

KW - Cyclic difference families

KW - Iterative decoding

KW - Low-density parity-check (LDPC) codes

KW - Pasch configurations

UR - https://www.scopus.com/pages/publications/2942659753

UR - https://www.scopus.com/pages/publications/2942659753#tab=citedBy

U2 - 10.1109/TIT.2004.828066

DO - 10.1109/TIT.2004.828066

M3 - Article

AN - SCOPUS:2942659753

SN - 0018-9448

VL - 50

SP - 1156

EP - 1176

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 6

ER -

Combinatorial constructions of low-density parity-check codes for iterative decoding

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this