Asymptotic Analysis of Spatially Coupled MacKay-Neal and Hsu-Anastasopoulos LDPC Codes
Författare
Summary, in English
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.
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.
Publiceringsår
2012
Språk
Engelska
Sidor
337-341
Publikation/Tidskrift/Serie
2012 International Symposium on Information Theory and its Applications
Fulltext
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Länkar
Dokumenttyp
Konferensbidrag
Förlag
IEEE - Institute of Electrical and Electronics Engineers Inc.
Ämne
- Electrical Engineering, Electronic Engineering, Information Engineering
Nyckelord
- spatial coupling
- LDPC codes
Conference name
International Symposium on Information Theory and its Applications (ISITA'12)
Conference date
2012-10-28 - 2012-10-31
Status
Published
Forskningsgrupp
- Telecommunication Theory
ISBN/ISSN/Övrigt
- ISBN: 978-1-4673-2521-9