Advanced

Spatially Coupled Turbo-Like Codes

Moloudi, Saeedeh LU (2018)
Abstract
The focus of this thesis is on proposing and analyzing a powerful class of codes on graphs—with trellis constraints—that can simultaneously approach capacity
and achieve very low error floor. In particular, we propose the concept of spatial coupling for turbo-like code (SC-TC) ensembles and investigate the impact of
coupling on the performance of these codes. The main elements of this study can be summarized by the following four major topics.
First, we considered the spatial coupling of parallel concatenated codes (PCCs), serially concatenated codes (SCCs), and hybrid concatenated codes (HCCs).
We also proposed two extensions of braided convolutional codes (BCCs) to higher coupling memories.
Second, we investigated the... (More)
The focus of this thesis is on proposing and analyzing a powerful class of codes on graphs—with trellis constraints—that can simultaneously approach capacity
and achieve very low error floor. In particular, we propose the concept of spatial coupling for turbo-like code (SC-TC) ensembles and investigate the impact of
coupling on the performance of these codes. The main elements of this study can be summarized by the following four major topics.
First, we considered the spatial coupling of parallel concatenated codes (PCCs), serially concatenated codes (SCCs), and hybrid concatenated codes (HCCs).
We also proposed two extensions of braided convolutional codes (BCCs) to higher coupling memories.
Second, we investigated the impact of coupling on the asymptotic behavior of the proposed ensembles in term of the decoding thresholds. For that, we derived
the exact density evolution (DE) equations of the proposed SC-TC ensembles over the binary erasure channel. Using the DE equations, we found the thresholds
of the coupled and uncoupled ensembles under belief propagation (BP) decoding for a wide range of rates. We also computed the maximum a-posteriori (MAP)
thresholds of the underlying uncoupled ensembles. Our numerical results confirm that TCs have excellent MAP thresholds, and for a large enough coupling
memory, the BP threshold of an SC-TC ensemble improves to the MAP threshold of the underlying TC ensemble. This phenomenon is called threshold
saturation and we proved its occurrence for SC-TCs by use of a proof technique based on the potential function of the ensembles.
Third, we investigated and discussed the performance of SC-TCs in the finite length regime. We proved that under certain conditions the minimum distance of
an SC-TCs is either larger or equal to that of its underlying uncoupled ensemble. Based on this fact, we performed a weight enumerator (WE) analysis for the
underlying uncoupled ensembles to investigate the error floor performance of the SC-TC ensembles. We computed bounds on the error rate performance and
minimum distance of the TC ensembles. These bounds indicate very low error floor for SCC, HCC, and BCC ensembles, and show that for HCC, and BCC
ensembles, the minimum distance grows linearly with the input block length. The results from the DE and WE analysis demonstrate that the performance of
TCs benefits from spatial coupling in both waterfall and error floor regions. While uncoupled TC ensembles with close-to-capacity performance exhibit a high
error floor, our results show that SC-TCs can simultaneously approach capacity and achieve very low error floor.
Fourth, we proposed a unified ensemble of TCs that includes all the considered TC classes. We showed that for each of the original classes of TCs, it is possible
to find an equivalent ensemble by proper selection of the design parameters in the unified ensemble. This unified ensemble not only helps us to understand the (Less)
Please use this url to cite or link to this publication:
author
opponent
  • Professor Narayanan, Krishna, Texas A&M University, USA
organization
publishing date
type
Thesis
publication status
published
subject
publisher
Electrical and Information Technology, Lund University
defense location
lecture hall E:1406, building E, Ole Römers väg 3, Lund University, Faculty of Engineering LTH, Lund
defense date
2018-06-11 09:15
ISBN
ISBN 978-91-7753-647-5
ISBN 978-91-7753-648-2
language
English
LU publication?
yes
id
6373aa40-e380-4983-8176-24fea7001fdd
date added to LUP
2018-05-15 16:24:59
date last changed
2018-05-29 11:14:26
@phdthesis{6373aa40-e380-4983-8176-24fea7001fdd,
  abstract     = {The focus of this thesis is on proposing and analyzing a powerful class of codes on graphs—with trellis constraints—that can simultaneously approach capacity<br/>and achieve very low error floor. In particular, we propose the concept of spatial coupling for turbo-like code (SC-TC) ensembles and investigate the impact of<br/>coupling on the performance of these codes. The main elements of this study can be summarized by the following four major topics.<br/>First, we considered the spatial coupling of parallel concatenated codes (PCCs), serially concatenated codes (SCCs), and hybrid concatenated codes (HCCs).<br/>We also proposed two extensions of braided convolutional codes (BCCs) to higher coupling memories.<br/>Second, we investigated the impact of coupling on the asymptotic behavior of the proposed ensembles in term of the decoding thresholds. For that, we derived<br/>the exact density evolution (DE) equations of the proposed SC-TC ensembles over the binary erasure channel. Using the DE equations, we found the thresholds<br/>of the coupled and uncoupled ensembles under belief propagation (BP) decoding for a wide range of rates. We also computed the maximum a-posteriori (MAP)<br/>thresholds of the underlying uncoupled ensembles. Our numerical results confirm that TCs have excellent MAP thresholds, and for a large enough coupling<br/>memory, the BP threshold of an SC-TC ensemble improves to the MAP threshold of the underlying TC ensemble. This phenomenon is called threshold<br/>saturation and we proved its occurrence for SC-TCs by use of a proof technique based on the potential function of the ensembles.<br/>Third, we investigated and discussed the performance of SC-TCs in the finite length regime. We proved that under certain conditions the minimum distance of<br/>an SC-TCs is either larger or equal to that of its underlying uncoupled ensemble. Based on this fact, we performed a weight enumerator (WE) analysis for the<br/>underlying uncoupled ensembles to investigate the error floor performance of the SC-TC ensembles. We computed bounds on the error rate performance and<br/>minimum distance of the TC ensembles. These bounds indicate very low error floor for SCC, HCC, and BCC ensembles, and show that for HCC, and BCC<br/>ensembles, the minimum distance grows linearly with the input block length. The results from the DE and WE analysis demonstrate that the performance of<br/>TCs benefits from spatial coupling in both waterfall and error floor regions. While uncoupled TC ensembles with close-to-capacity performance exhibit a high<br/>error floor, our results show that SC-TCs can simultaneously approach capacity and achieve very low error floor.<br/>Fourth, we proposed a unified ensemble of TCs that includes all the considered TC classes. We showed that for each of the original classes of TCs, it is possible<br/>to find an equivalent ensemble by proper selection of the design parameters in the unified ensemble. This unified ensemble not only helps us to understand the},
  author       = {Moloudi, Saeedeh},
  isbn         = {ISBN 978-91-7753-647-5},
  language     = {eng},
  publisher    = {Electrical and Information Technology, Lund University},
  school       = {Lund University},
  title        = {Spatially Coupled Turbo-Like Codes},
  year         = {2018},
}