IEICE TRANSACTIONS on Fundamentals
An Extension of Gallager Ensemble of Low Density Parity Check Codes
Summary :
Gallager has defined an ensemble of regular low density parity check (LDPC) codes for deriving the ensemble performance of regular LDPC codes. The ensemble is called the Gallager ensemble. In this paper, we define a new ensemble of LDPC codes, called extended Gallager ensemble, which is a natural extension of the Gallager ensemble. It is shown that an extended Gallager ensemble has potential to achieve larger typical minimum distance ratio than that of the original Gallager ensemble. In particular, the extended Gallager ensembles based on the Hamming and extended Hamming codes have typical minimum distance ratio which is very close to the asymptotic Gilbert-Varshamov bound. Furthermore, decoding performance of an instance of an extended Gallager ensemble, called an extended LDPC code, has been examined by simulation. The results show good block error performance of extended LDPC codes.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E85-A No.5 pp.1161-1171
- Publication Date
- 2002/05/01
- Publicized
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- PAPER
- Category
- Coding Theory
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Tadashi WADAYAMA, "An Extension of Gallager Ensemble of Low Density Parity Check Codes" in IEICE TRANSACTIONS on Fundamentals,
vol. E85-A, no. 5, pp. 1161-1171, May 2002, doi: .
Abstract: Gallager has defined an ensemble of regular low density parity check (LDPC) codes for deriving the ensemble performance of regular LDPC codes. The ensemble is called the Gallager ensemble. In this paper, we define a new ensemble of LDPC codes, called extended Gallager ensemble, which is a natural extension of the Gallager ensemble. It is shown that an extended Gallager ensemble has potential to achieve larger typical minimum distance ratio than that of the original Gallager ensemble. In particular, the extended Gallager ensembles based on the Hamming and extended Hamming codes have typical minimum distance ratio which is very close to the asymptotic Gilbert-Varshamov bound. Furthermore, decoding performance of an instance of an extended Gallager ensemble, called an extended LDPC code, has been examined by simulation. The results show good block error performance of extended LDPC codes.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e85-a_5_1161/_p
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@ARTICLE{e85-a_5_1161,
author={Tadashi WADAYAMA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={An Extension of Gallager Ensemble of Low Density Parity Check Codes},
year={2002},
volume={E85-A},
number={5},
pages={1161-1171},
abstract={Gallager has defined an ensemble of regular low density parity check (LDPC) codes for deriving the ensemble performance of regular LDPC codes. The ensemble is called the Gallager ensemble. In this paper, we define a new ensemble of LDPC codes, called extended Gallager ensemble, which is a natural extension of the Gallager ensemble. It is shown that an extended Gallager ensemble has potential to achieve larger typical minimum distance ratio than that of the original Gallager ensemble. In particular, the extended Gallager ensembles based on the Hamming and extended Hamming codes have typical minimum distance ratio which is very close to the asymptotic Gilbert-Varshamov bound. Furthermore, decoding performance of an instance of an extended Gallager ensemble, called an extended LDPC code, has been examined by simulation. The results show good block error performance of extended LDPC codes.},
keywords={},
doi={},
ISSN={},
month={May},}
Copy
TY - JOUR
TI - An Extension of Gallager Ensemble of Low Density Parity Check Codes
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1161
EP - 1171
AU - Tadashi WADAYAMA
PY - 2002
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E85-A
IS - 5
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - May 2002
AB - Gallager has defined an ensemble of regular low density parity check (LDPC) codes for deriving the ensemble performance of regular LDPC codes. The ensemble is called the Gallager ensemble. In this paper, we define a new ensemble of LDPC codes, called extended Gallager ensemble, which is a natural extension of the Gallager ensemble. It is shown that an extended Gallager ensemble has potential to achieve larger typical minimum distance ratio than that of the original Gallager ensemble. In particular, the extended Gallager ensembles based on the Hamming and extended Hamming codes have typical minimum distance ratio which is very close to the asymptotic Gilbert-Varshamov bound. Furthermore, decoding performance of an instance of an extended Gallager ensemble, called an extended LDPC code, has been examined by simulation. The results show good block error performance of extended LDPC codes.
ER -
English
