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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)
Please use this url to cite or link to this publication:
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
2157-8117
2157-8095
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
2020-10-20 03:11:05
@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         = {2157-8117},
  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/ws/files/1416999/3731149.pdf},
  doi          = {10.1109/ISIT.2011.6033700},
  year         = {2011},
}