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Spatially Coupled LDPC Codes Constructed From Protographs

Mitchell, David G.M.; Lentmaier, Michael LU and Costello Jr., Daniel J. (2015) In IEEE Transactions on Information Theory 61(9). p.4866-4889
Abstract
In this paper, we construct protograph-based spatially coupled low-density parity-check (LDPC) codes by coupling together a series of L disjoint, or uncoupled, LDPC code Tanner graphs into a single coupled chain. By varying L, we obtain a flexible family of code ensembles with varying rates and frame lengths that can share the same encoding and decoding architecture for arbitrary L. We demonstrate that the resulting codes combine the best features of optimized irregular and regular codes in one design: capacity approaching iterative belief propagation (BP) decoding thresholds and linear growth of minimum distance with block length. In particular, we show that, for sufficiently large L, the BP thresholds on both the binary erasure channel... (More)
In this paper, we construct protograph-based spatially coupled low-density parity-check (LDPC) codes by coupling together a series of L disjoint, or uncoupled, LDPC code Tanner graphs into a single coupled chain. By varying L, we obtain a flexible family of code ensembles with varying rates and frame lengths that can share the same encoding and decoding architecture for arbitrary L. We demonstrate that the resulting codes combine the best features of optimized irregular and regular codes in one design: capacity approaching iterative belief propagation (BP) decoding thresholds and linear growth of minimum distance with block length. In particular, we show that, for sufficiently large L, the BP thresholds on both the binary erasure channel and the binary-input additive white Gaussian noise channel saturate to a particular value significantly better than the BP decoding threshold and numerically indistinguishable from the optimal maximum a posteriori decoding threshold of the uncoupled LDPC code. When all variable nodes in the coupled chain have degree greater than two, asymptotically the error probability converges at least doubly exponentially with decoding iterations and we obtain sequences of asymptotically good LDPC codes with fast convergence rates and BP thresholds close to the Shannon limit. Further, the gap to capacity decreases as the density of the graph increases, opening up a new way to construct capacity achieving codes on memoryless binary-input symmetric-output channels with low-complexity BP decoding. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
decoding thresholds, minimum distance, capacity achieving codes, density evolution, belief propagation, iterative decoding, spatially coupled codes, LDPC convolutional codes, Low-density parity-check (LDPC) codes
in
IEEE Transactions on Information Theory
volume
61
issue
9
pages
4866 - 4889
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • wos:000360015900021
  • scopus:84939817317
ISSN
0018-9448
DOI
10.1109/TIT.2015.2453267
language
English
LU publication?
yes
id
abc8b412-5f6d-46b5-b70c-6894305643db (old id 7765358)
date added to LUP
2015-08-21 14:12:25
date last changed
2017-10-08 04:07:01
@article{abc8b412-5f6d-46b5-b70c-6894305643db,
  abstract     = {In this paper, we construct protograph-based spatially coupled low-density parity-check (LDPC) codes by coupling together a series of L disjoint, or uncoupled, LDPC code Tanner graphs into a single coupled chain. By varying L, we obtain a flexible family of code ensembles with varying rates and frame lengths that can share the same encoding and decoding architecture for arbitrary L. We demonstrate that the resulting codes combine the best features of optimized irregular and regular codes in one design: capacity approaching iterative belief propagation (BP) decoding thresholds and linear growth of minimum distance with block length. In particular, we show that, for sufficiently large L, the BP thresholds on both the binary erasure channel and the binary-input additive white Gaussian noise channel saturate to a particular value significantly better than the BP decoding threshold and numerically indistinguishable from the optimal maximum a posteriori decoding threshold of the uncoupled LDPC code. When all variable nodes in the coupled chain have degree greater than two, asymptotically the error probability converges at least doubly exponentially with decoding iterations and we obtain sequences of asymptotically good LDPC codes with fast convergence rates and BP thresholds close to the Shannon limit. Further, the gap to capacity decreases as the density of the graph increases, opening up a new way to construct capacity achieving codes on memoryless binary-input symmetric-output channels with low-complexity BP decoding.},
  author       = {Mitchell, David G.M. and Lentmaier, Michael and Costello Jr., Daniel J.},
  issn         = {0018-9448},
  keyword      = {decoding thresholds,minimum distance,capacity achieving codes,density evolution,belief propagation,iterative decoding,spatially coupled codes,LDPC convolutional codes,Low-density parity-check (LDPC) codes},
  language     = {eng},
  number       = {9},
  pages        = {4866--4889},
  publisher    = {IEEE--Institute of Electrical and Electronics Engineers Inc.},
  series       = {IEEE Transactions on Information Theory},
  title        = {Spatially Coupled LDPC Codes Constructed From Protographs},
  url          = {http://dx.doi.org/10.1109/TIT.2015.2453267},
  volume       = {61},
  year         = {2015},
}