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Spatially Coupled Turbo-Like Codes

Moloudi, Saeedeh LU ; Lentmaier, Michael LU and Graell i Amat, Alexandre (2017) In IEEE Transactions on Information Theory 63(10). p.6199-6215
Abstract
In this paper, we introduce the concept of spatially coupled turbo-like codes (SC-TCs) as the spatial coupling of a number of turbo-like code ensembles. In particular, we consider the spatial coupling of parallel concatenated codes, introduced by Berrou et al., and that of serially concatenated codes (SCCs), introduced by Benedetto et al. Furthermore, we propose two extensions of braided convolutional codes (BCCs), and a class of turbo-like codes which have an inherent spatially coupled structure, to higher coupling memories, and show that these yield improved belief propagation (BP) thresholds as compared with the original BCC ensemble. We derive the exact density evolution (DE) equations for SC-TCs and analyze their asymptotic behavior... (More)
In this paper, we introduce the concept of spatially coupled turbo-like codes (SC-TCs) as the spatial coupling of a number of turbo-like code ensembles. In particular, we consider the spatial coupling of parallel concatenated codes, introduced by Berrou et al., and that of serially concatenated codes (SCCs), introduced by Benedetto et al. Furthermore, we propose two extensions of braided convolutional codes (BCCs), and a class of turbo-like codes which have an inherent spatially coupled structure, to higher coupling memories, and show that these yield improved belief propagation (BP) thresholds as compared with the original BCC ensemble. We derive the exact density evolution (DE) equations for SC-TCs and analyze their asymptotic behavior on the binary erasure channel. We also consider the construction of families of rate-compatible SC-TC ensembles. Our numerical results show that the threshold saturation of the BP decoding threshold to the maximum a posteriori threshold of the underlying uncoupled ensembles occurs for large enough coupling memory. The improvement of the BP threshold is especially significant for SCCs and BCCs, whose uncoupled ensembles suffer from a poor BP threshold. For a wide range of code rates, SC-TCs show close-to-capacity performance as the coupling memory increases. We further give a proof of threshold saturation for SC-TC ensembles with identical component encoders. In particular, we show that the DE of SC-TC ensembles with identical component encoders can be properly rewritten as a scalar recursion. This allows us to define potential functions and prove threshold saturation using the proof technique recently introduced by Yedla et al. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
IEEE Transactions on Information Theory
volume
63
issue
10
pages
6199 - 6215
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • scopus:85028988980
  • wos:000411021000007
ISSN
0018-9448
DOI
10.1109/TIT.2017.2735965
language
English
LU publication?
yes
id
b68cf365-55c8-410f-842b-f09871eabed6
date added to LUP
2017-09-18 08:51:46
date last changed
2018-05-29 12:06:34
@article{b68cf365-55c8-410f-842b-f09871eabed6,
  abstract     = {In this paper, we introduce the concept of spatially coupled turbo-like codes (SC-TCs) as the spatial coupling of a number of turbo-like code ensembles. In particular, we consider the spatial coupling of parallel concatenated codes, introduced by Berrou et al., and that of serially concatenated codes (SCCs), introduced by Benedetto et al. Furthermore, we propose two extensions of braided convolutional codes (BCCs), and a class of turbo-like codes which have an inherent spatially coupled structure, to higher coupling memories, and show that these yield improved belief propagation (BP) thresholds as compared with the original BCC ensemble. We derive the exact density evolution (DE) equations for SC-TCs and analyze their asymptotic behavior on the binary erasure channel. We also consider the construction of families of rate-compatible SC-TC ensembles. Our numerical results show that the threshold saturation of the BP decoding threshold to the maximum a posteriori threshold of the underlying uncoupled ensembles occurs for large enough coupling memory. The improvement of the BP threshold is especially significant for SCCs and BCCs, whose uncoupled ensembles suffer from a poor BP threshold. For a wide range of code rates, SC-TCs show close-to-capacity performance as the coupling memory increases. We further give a proof of threshold saturation for SC-TC ensembles with identical component encoders. In particular, we show that the DE of SC-TC ensembles with identical component encoders can be properly rewritten as a scalar recursion. This allows us to define potential functions and prove threshold saturation using the proof technique recently introduced by Yedla et al.},
  author       = {Moloudi, Saeedeh and Lentmaier, Michael and Graell i Amat, Alexandre},
  issn         = {0018-9448},
  language     = {eng},
  number       = {10},
  pages        = {6199--6215},
  publisher    = {IEEE--Institute of Electrical and Electronics Engineers Inc.},
  series       = {IEEE Transactions on Information Theory},
  title        = {Spatially Coupled Turbo-Like Codes},
  url          = {http://dx.doi.org/10.1109/TIT.2017.2735965},
  volume       = {63},
  year         = {2017},
}