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Girth Analysis and Design of Periodically Time-Varying SC-LDPC Codes

Battaglioni, Massimo LU ; Chiaraluce, Franco ; Baldi, Marco and Lentmaier, Michael LU (2021) In IEEE Transactions on Information Theory 67(4). p.2217-2235
Abstract

Time-varying spatially coupled low-density parity-check (SC-LDPC) codes with very large period are characterized by significantly better error rate performance and girth properties than their time-invariant counterparts, but the number of parameters they require to be described is usually very large and unpractical. Time-invariant SC-LDPC codes, which can be seen as periodically time-varying codes with unitary period, are represented through a small number of parameters and designed exploiting few degrees of freedom, but their error rate performance and girth properties are sub-optimal. In this paper, we show that the limits of time-invariant SC-LDPC codes can be overcome by transforming them into time-varying SC-LDPC codes with very... (More)

Time-varying spatially coupled low-density parity-check (SC-LDPC) codes with very large period are characterized by significantly better error rate performance and girth properties than their time-invariant counterparts, but the number of parameters they require to be described is usually very large and unpractical. Time-invariant SC-LDPC codes, which can be seen as periodically time-varying codes with unitary period, are represented through a small number of parameters and designed exploiting few degrees of freedom, but their error rate performance and girth properties are sub-optimal. In this paper, we show that the limits of time-invariant SC-LDPC codes can be overcome by transforming them into time-varying SC-LDPC codes with very small period. In particular, we show that periodically time-varying SC-LDPC codes with small period may exhibit significantly better girth properties than the corresponding time-invariant codes by exploiting a larger number of degrees of freedom in the code design, which however scale at most linearly with the product of the code period and the size of the considered base matrix.

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author
; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Convolutional codes, girth, LDPC codes, spatially coupled codes, time-invariant codes, time-varying codes
in
IEEE Transactions on Information Theory
volume
67
issue
4
article number
9354189
pages
19 pages
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • scopus:85101431738
ISSN
0018-9448
DOI
10.1109/TIT.2021.3059414
language
English
LU publication?
yes
id
fdaf5873-ac0b-4309-b2d4-7d1a89e5b834
date added to LUP
2022-02-28 17:22:31
date last changed
2022-05-17 01:46:29
@article{fdaf5873-ac0b-4309-b2d4-7d1a89e5b834,
  abstract     = {{<p>Time-varying spatially coupled low-density parity-check (SC-LDPC) codes with very large period are characterized by significantly better error rate performance and girth properties than their time-invariant counterparts, but the number of parameters they require to be described is usually very large and unpractical. Time-invariant SC-LDPC codes, which can be seen as periodically time-varying codes with unitary period, are represented through a small number of parameters and designed exploiting few degrees of freedom, but their error rate performance and girth properties are sub-optimal. In this paper, we show that the limits of time-invariant SC-LDPC codes can be overcome by transforming them into time-varying SC-LDPC codes with very small period. In particular, we show that periodically time-varying SC-LDPC codes with small period may exhibit significantly better girth properties than the corresponding time-invariant codes by exploiting a larger number of degrees of freedom in the code design, which however scale at most linearly with the product of the code period and the size of the considered base matrix.</p>}},
  author       = {{Battaglioni, Massimo and Chiaraluce, Franco and Baldi, Marco and Lentmaier, Michael}},
  issn         = {{0018-9448}},
  keywords     = {{Convolutional codes; girth; LDPC codes; spatially coupled codes; time-invariant codes; time-varying codes}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{2217--2235}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  series       = {{IEEE Transactions on Information Theory}},
  title        = {{Girth Analysis and Design of Periodically Time-Varying SC-LDPC Codes}},
  url          = {{http://dx.doi.org/10.1109/TIT.2021.3059414}},
  doi          = {{10.1109/TIT.2021.3059414}},
  volume       = {{67}},
  year         = {{2021}},
}