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Exact Free Distance and Trapping Set Growth Rates for LDPC Convolutional Codes

Mitchell, David G.M. ; Pusane, Ali Emre ; Lentmaier, Michael LU and Costello Jr., Daniel J. (2011) IEEE International Symposium on Information Theory, 2011 p.1096-1100
Abstract
Ensembles of (J,K)-regular low-density parity-check convolutional (LDPCC) codes are known to be asymptotically good, in the sense that the minimum free distance grows linearly with the constraint length. In this paper, we use a protograph-based analysis of terminated LDPCC codes to obtain an upper bound on the free distance growth rate of ensembles of periodically time-varying LDPCC codes. This bound is compared to a lower bound and evaluated numerically. It is found that, for a sufficiently large period, the bounds coincide. This approach is then extended to obtain bounds on the trapping set numbers, which define the size of the smallest, non-empty trapping sets, for these asymptotically good, periodically time-varying LDPCC code... (More)
Ensembles of (J,K)-regular low-density parity-check convolutional (LDPCC) codes are known to be asymptotically good, in the sense that the minimum free distance grows linearly with the constraint length. In this paper, we use a protograph-based analysis of terminated LDPCC codes to obtain an upper bound on the free distance growth rate of ensembles of periodically time-varying LDPCC codes. This bound is compared to a lower bound and evaluated numerically. It is found that, for a sufficiently large period, the bounds coincide. This approach is then extended to obtain bounds on the trapping set numbers, which define the size of the smallest, non-empty trapping sets, for these asymptotically good, periodically time-varying LDPCC code ensembles. (Less)
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author
; ; and
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
spatial coupling, LDPC codes, LDPC convolutional codes, trapping sets
host publication
2011 IEEE International Symposium on Information Theory Proceedings
pages
1096 - 1100
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
conference name
IEEE International Symposium on Information Theory, 2011
conference location
Saint Petersburg, Russian Federation
conference dates
2011-07-31 - 2011-08-05
external identifiers
  • scopus:80054815545
ISSN
2157-8095
2157-8117
ISBN
978-1-4577-0596-0
DOI
10.1109/ISIT.2011.6033700
language
English
LU publication?
no
id
57386ea7-f709-4be3-8856-a34f52a09e2e (old id 3731146)
date added to LUP
2016-04-01 09:57:05
date last changed
2024-01-06 04:04:26
@inproceedings{57386ea7-f709-4be3-8856-a34f52a09e2e,
  abstract     = {{Ensembles of (J,K)-regular low-density parity-check convolutional (LDPCC) codes are known to be asymptotically good, in the sense that the minimum free distance grows linearly with the constraint length. In this paper, we use a protograph-based analysis of terminated LDPCC codes to obtain an upper bound on the free distance growth rate of ensembles of periodically time-varying LDPCC codes. This bound is compared to a lower bound and evaluated numerically. It is found that, for a sufficiently large period, the bounds coincide. This approach is then extended to obtain bounds on the trapping set numbers, which define the size of the smallest, non-empty trapping sets, for these asymptotically good, periodically time-varying LDPCC code ensembles.}},
  author       = {{Mitchell, David G.M. and Pusane, Ali Emre and Lentmaier, Michael and Costello Jr., Daniel J.}},
  booktitle    = {{2011 IEEE International Symposium on Information Theory Proceedings}},
  isbn         = {{978-1-4577-0596-0}},
  issn         = {{2157-8095}},
  keywords     = {{spatial coupling; LDPC codes; LDPC convolutional codes; trapping sets}},
  language     = {{eng}},
  pages        = {{1096--1100}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  title        = {{Exact Free Distance and Trapping Set Growth Rates for LDPC Convolutional Codes}},
  url          = {{https://lup.lub.lu.se/search/files/1416999/3731149.pdf}},
  doi          = {{10.1109/ISIT.2011.6033700}},
  year         = {{2011}},
}