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Asymptotic Analysis of Spatially Coupled MacKay-Neal and Hsu-Anastasopoulos LDPC Codes

Mitchell, David G.M.; Kasai, Kenta; Lentmaier, Michael LU and Costello Jr., Daniel J. (2012) International Symposium on Information Theory and its Applications (ISITA'12) In [Host publication title missing] p.337-341
Abstract
MacKay-Neal (MN) and Hsu-Anastasopoulos (HA) low-density parity-check (LDPC) codes are known to achieve the capacity of memoryless binary-input symmetric-output channels under maximum likelihood (ML) decoding with bounded col- umn and row weight in their associated parity-check matrices. Recently, Kasai and Sakaniwa showed that spatially coupled (SC) versions of the MN and HA LDPC codes have belief propagation (BP) iterative decoding thresholds that approach capacity on the binary erasure channel (BEC) as the coupling length increases.

In this paper, we extend the results of Kasai and Sakaniwa to the additive white Gaussian noise (AWGN) channel and show that the thresholds of the SC-MN and SC-HA ensembles approach capacity with... (More)
MacKay-Neal (MN) and Hsu-Anastasopoulos (HA) low-density parity-check (LDPC) codes are known to achieve the capacity of memoryless binary-input symmetric-output channels under maximum likelihood (ML) decoding with bounded col- umn and row weight in their associated parity-check matrices. Recently, Kasai and Sakaniwa showed that spatially coupled (SC) versions of the MN and HA LDPC codes have belief propagation (BP) iterative decoding thresholds that approach capacity on the binary erasure channel (BEC) as the coupling length increases.

In this paper, we extend the results of Kasai and Sakaniwa to the additive white Gaussian noise (AWGN) channel and show that the thresholds of the SC-MN and SC-HA ensembles approach capacity with bounded density as the coupling length increases, i.e., the number of edges per information bit approaches a finite value as the estimated BP threshold approaches the Shannon limit. We also perform an asymptotic weight enumerator analysis and show that, provided the density parameters are chosen to be sufficiently large, the SC-MN and SC-HA ensembles are asymptotically good. Further, for certain selections of parameters, some of these ensembles are shown to have both excellent thresholds and good distance properties. (Less)
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author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
spatial coupling, LDPC codes
in
[Host publication title missing]
pages
337 - 341
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
conference name
International Symposium on Information Theory and its Applications (ISITA'12)
external identifiers
  • Scopus:84873543578
ISBN
978-1-4673-2521-9
language
English
LU publication?
no
id
1d949692-9a49-4bba-9494-e96c67356361 (old id 3404948)
alternative location
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6400949
date added to LUP
2013-04-26 08:26:42
date last changed
2017-01-01 07:59:17
@inproceedings{1d949692-9a49-4bba-9494-e96c67356361,
  abstract     = {MacKay-Neal (MN) and Hsu-Anastasopoulos (HA) low-density parity-check (LDPC) codes are known to achieve the capacity of memoryless binary-input symmetric-output channels under maximum likelihood (ML) decoding with bounded col- umn and row weight in their associated parity-check matrices. Recently, Kasai and Sakaniwa showed that spatially coupled (SC) versions of the MN and HA LDPC codes have belief propagation (BP) iterative decoding thresholds that approach capacity on the binary erasure channel (BEC) as the coupling length increases.<br/><br>
In this paper, we extend the results of Kasai and Sakaniwa to the additive white Gaussian noise (AWGN) channel and show that the thresholds of the SC-MN and SC-HA ensembles approach capacity with bounded density as the coupling length increases, i.e., the number of edges per information bit approaches a finite value as the estimated BP threshold approaches the Shannon limit. We also perform an asymptotic weight enumerator analysis and show that, provided the density parameters are chosen to be sufficiently large, the SC-MN and SC-HA ensembles are asymptotically good. Further, for certain selections of parameters, some of these ensembles are shown to have both excellent thresholds and good distance properties.},
  author       = {Mitchell, David G.M. and Kasai, Kenta and Lentmaier, Michael and Costello Jr., Daniel J.},
  booktitle    = {[Host publication title missing]},
  isbn         = {978-1-4673-2521-9},
  keyword      = {spatial coupling,LDPC codes},
  language     = {eng},
  pages        = {337--341},
  publisher    = {IEEE--Institute of Electrical and Electronics Engineers Inc.},
  title        = {Asymptotic Analysis of Spatially Coupled MacKay-Neal and Hsu-Anastasopoulos LDPC Codes},
  year         = {2012},
}