High-rate LDPC codes from partially balanced incomplete block designs

This paper presents a combinatorial construction of low-density parity-check (LDPC) codes from partially balanced incomplete block designs. Since Gallager’s construction of LDPC codes by randomly allocating bits in a sparse parity-check matrix, many researchers have used a variety of more structured...

Full description

Saved in:

Bibliographic Details
Published in:	Journal of algebraic combinatorics Vol. 55; no. 1; pp. 259 - 275
Main Authors:	Donovan, Diane, Price, Aiden, Rao, Asha, Üsküplü, Elif, ŞYazıcı, Emine
Format:	Journal Article
Language:	English
Published:	New York Springer US 01-02-2022 Springer Nature B.V
Subjects:	Binary system Codes Combinatorial analysis Combinatorics Computer Science Convex and Discrete Geometry Error correcting codes Group Theory and Generalizations Lattices Low density parity check codes Mathematics Mathematics and Statistics Order Ordered Algebraic Structures Parity Combinatorial construction Difference covering arrays LDPC codes Partial BIBDs
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	This paper presents a combinatorial construction of low-density parity-check (LDPC) codes from partially balanced incomplete block designs. Since Gallager’s construction of LDPC codes by randomly allocating bits in a sparse parity-check matrix, many researchers have used a variety of more structured combinatorial approaches. Many of these constructions start with the Galois field; however, this limits the choice of parameters of the constructed codes. Here we present a construction of LDPC codes of length 4 n 2 - 2 n for all n using the cyclic group of order 2 n . These codes achieve high information rate (greater than 0.8) for n ≥ 8 , have girth at least 6 and have minimum distance 6 for n odd. The results provide proof of concept and lay the groundwork for potential high performing codes
ISSN:	0925-9899 1572-9192
DOI:	10.1007/s10801-021-01111-0