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Spatially Coupled Generalized LDPC Codes : Asymptotic Analysis and Finite Length Scaling

Mitchell, David G.M. ; Olmos, Pablo M. ; Lentmaier, Michael LU and Costello, Daniel J. (2021) In IEEE Transactions on Information Theory 67(6). p.3708-3723
Abstract

Generalized low-density parity-check (GLDPC) codes are a class of LDPC codes in which the standard single parity check (SPC) constraints are replaced by constraints defined by a linear block code. These stronger constraints typically result in improved error floor performance, due to better minimum distance and trapping set properties, at a cost of some increased decoding complexity. In this paper, we study spatially coupled generalized low-density parity-check (SC-GLDPC) codes and present a comprehensive analysis of these codes, including: (1) an iterative decoding threshold analysis of SC-GLDPC code ensembles demonstrating capacity approaching thresholds via the threshold saturation effect; (2) an asymptotic analysis of the minimum... (More)

Generalized low-density parity-check (GLDPC) codes are a class of LDPC codes in which the standard single parity check (SPC) constraints are replaced by constraints defined by a linear block code. These stronger constraints typically result in improved error floor performance, due to better minimum distance and trapping set properties, at a cost of some increased decoding complexity. In this paper, we study spatially coupled generalized low-density parity-check (SC-GLDPC) codes and present a comprehensive analysis of these codes, including: (1) an iterative decoding threshold analysis of SC-GLDPC code ensembles demonstrating capacity approaching thresholds via the threshold saturation effect; (2) an asymptotic analysis of the minimum distance and free distance properties of SC-GLDPC code ensembles, demonstrating that the ensembles are asymptotically good; and (3) an analysis of the finite-length scaling behavior of both GLDPC block codes and SC-GLDPC codes based on a peeling decoder (PD) operating on a binary erasure channel (BEC). Results are compared to GLDPC block codes, and the advantages and disadvantages of SC-GLDPC codes are discussed.

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author
; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Block codes, Complexity theory, Convolutional codes, Electronic mail, finite length scaling, Generalized LDPC codes, Iterative decoding, iterative decoding thresholds, Maximum likelihood decoding, Message passing, minimum distance, spatially coupled codes
in
IEEE Transactions on Information Theory
volume
67
issue
6
pages
16 pages
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • scopus:85104171015
ISSN
0018-9448
DOI
10.1109/TIT.2021.3071743
language
English
LU publication?
yes
id
4676454c-0381-4b8e-946d-ba6109fe4434
date added to LUP
2021-04-27 09:31:56
date last changed
2022-05-05 01:16:43
@article{4676454c-0381-4b8e-946d-ba6109fe4434,
  abstract     = {{<p>Generalized low-density parity-check (GLDPC) codes are a class of LDPC codes in which the standard single parity check (SPC) constraints are replaced by constraints defined by a linear block code. These stronger constraints typically result in improved error floor performance, due to better minimum distance and trapping set properties, at a cost of some increased decoding complexity. In this paper, we study spatially coupled generalized low-density parity-check (SC-GLDPC) codes and present a comprehensive analysis of these codes, including: (1) an iterative decoding threshold analysis of SC-GLDPC code ensembles demonstrating capacity approaching thresholds via the threshold saturation effect; (2) an asymptotic analysis of the minimum distance and free distance properties of SC-GLDPC code ensembles, demonstrating that the ensembles are asymptotically good; and (3) an analysis of the finite-length scaling behavior of both GLDPC block codes and SC-GLDPC codes based on a peeling decoder (PD) operating on a binary erasure channel (BEC). Results are compared to GLDPC block codes, and the advantages and disadvantages of SC-GLDPC codes are discussed.</p>}},
  author       = {{Mitchell, David G.M. and Olmos, Pablo M. and Lentmaier, Michael and Costello, Daniel J.}},
  issn         = {{0018-9448}},
  keywords     = {{Block codes; Complexity theory; Convolutional codes; Electronic mail; finite length scaling; Generalized LDPC codes; Iterative decoding; iterative decoding thresholds; Maximum likelihood decoding; Message passing; minimum distance; spatially coupled codes}},
  language     = {{eng}},
  month        = {{06}},
  number       = {{6}},
  pages        = {{3708--3723}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  series       = {{IEEE Transactions on Information Theory}},
  title        = {{Spatially Coupled Generalized LDPC Codes : Asymptotic Analysis and Finite Length Scaling}},
  url          = {{http://dx.doi.org/10.1109/TIT.2021.3071743}},
  doi          = {{10.1109/TIT.2021.3071743}},
  volume       = {{67}},
  year         = {{2021}},
}