IEEE International Symposium on Information Theory (ISIT)

Minimum distance bounds of irregular QC-LDPC codes and their applications

Min-Ho Shin, Joon‐Sung Kim, Hong‐Yeop Song

Published Dec 23, 2004• 3 citations

Abstract

We consider a design of quasicyclic LDPC codes which have irregular column weights. We derive bit-oriented bound and parity-oriented bound on the minimum distances of irregular quasicyclic codes using a similar technique to Tanner's simple lower bound

DOI: 10.1109/isit.2004.1365348

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IEEE International Symposium on Information Theory (ISIT)

Minimum distance bounds of irregular QC-LDPC codes and their applications

Min-Ho Shin, Joon‐Sung Kim, Hong‐Yeop Song

Published Dec 23, 2004• 3 citations

Publisher

Abstract

DOI: 10.1109/isit.2004.1365348

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IEEE Communications LettersMar 1, 20057 citations

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We investigate the minimum distance of structured binary Low-Density Parity-Check (LDPC) codes whose parity-check matrices are of the form

[\mathbf{C} \vert \mathbf{M}]

where

\mathbf{C}

is circulant and of column weight

2

, and

\mathbf{M}

has fixed column weight

r \geq 3

and row weight at least

1

. These codes are of interest because they are LDPC codes which come with a natural linear-time encoding algorithm. We show that the minimum distance of these codes is in

O(n^{\frac{r-2}{r-1} + ε})

, where

n

is the code length and

ε> 0

is arbitrarily small. This improves the previously known upper bound in

O(n^{\frac{r-1}{r}})

on the minimum distance of such codes.