2016
Stinner, Markus; Olmos, Pablo M
On the Waterfall Performance of Finite-Length SC-LDPC Codes Constructed From Protographs Artículo de revista
En: IEEE Journal on Selected Areas in Communications, vol. 34, no 2, pp. 345–361, 2016, ISSN: 0733-8716.
Resumen | Enlaces | BibTeX | Etiquetas: Analytical models, capacity-achieving codes, Complexity theory, Couplings, Decoding, Encoding, finite-length analysis, Iterative decoding, Low-density parity-check (LDPC) codes, spatially coupled LDPC codes constructed from prot
@article{Stinner2016,
title = {On the Waterfall Performance of Finite-Length SC-LDPC Codes Constructed From Protographs},
author = {Markus Stinner and Pablo M Olmos},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7339427},
doi = {10.1109/JSAC.2015.2504279},
issn = {0733-8716},
year = {2016},
date = {2016-02-01},
journal = {IEEE Journal on Selected Areas in Communications},
volume = {34},
number = {2},
pages = {345--361},
abstract = {An analysis of spatially coupled low-density parity-check (SC-LDPC) codes constructed from protographs is proposed. Given the protograph used to generate the SC-LDPC code ensemble, a set of scaling parameters to characterize the average finite-length performance in the waterfall region is computed. The error performance of structured SC-LDPC code ensembles is shown to follow a scaling law similar to that of unstructured randomly constructed SC-LDPC codes. Under a finite-length perspective, some of the most relevant SC-LDPC protograph structures proposed to date are compared. The analysis reveals significant differences in their finite-length scaling behavior, which is corroborated by simulation. Spatially coupled repeat-accumulate codes present excellent finite-length performance, as they outperform in the waterfall region SC-LDPC codes of the same rate and better asymptotic thresholds.},
keywords = {Analytical models, capacity-achieving codes, Complexity theory, Couplings, Decoding, Encoding, finite-length analysis, Iterative decoding, Low-density parity-check (LDPC) codes, spatially coupled LDPC codes constructed from prot},
pubstate = {published},
tppubtype = {article}
}
An analysis of spatially coupled low-density parity-check (SC-LDPC) codes constructed from protographs is proposed. Given the protograph used to generate the SC-LDPC code ensemble, a set of scaling parameters to characterize the average finite-length performance in the waterfall region is computed. The error performance of structured SC-LDPC code ensembles is shown to follow a scaling law similar to that of unstructured randomly constructed SC-LDPC codes. Under a finite-length perspective, some of the most relevant SC-LDPC protograph structures proposed to date are compared. The analysis reveals significant differences in their finite-length scaling behavior, which is corroborated by simulation. Spatially coupled repeat-accumulate codes present excellent finite-length performance, as they outperform in the waterfall region SC-LDPC codes of the same rate and better asymptotic thresholds.
2015
Stinner, Markus; Olmos, Pablo M
Finite-Length Performance of Multi-Edge Protograph-Based Spatially Coupled LDPC Codes Proceedings Article
En: 2015 IEEE International Symposium on Information Theory (ISIT), pp. 889–893, IEEE, Hong Kong, 2015, ISBN: 978-1-4673-7704-1.
Resumen | Enlaces | BibTeX | Etiquetas: binary erasure channel, Block codes, Couplings, Decoding, Error analysis, finite length performance, finite-length performance, graph theory, Iterative decoding, low density parity check codes, multiedge protograph, parity check codes, spatially coupled LDPC codes, spatially-coupled LDPC codes, Steady-state
@inproceedings{Stinner2015,
title = {Finite-Length Performance of Multi-Edge Protograph-Based Spatially Coupled LDPC Codes},
author = {Markus Stinner and Pablo M Olmos},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7282583},
doi = {10.1109/ISIT.2015.7282583},
isbn = {978-1-4673-7704-1},
year = {2015},
date = {2015-06-01},
booktitle = {2015 IEEE International Symposium on Information Theory (ISIT)},
pages = {889--893},
publisher = {IEEE},
address = {Hong Kong},
abstract = {The finite-length performance of multi-edge spatially coupled low-density parity-check (SC-LDPC) codes over the binary erasure channel (BEC) is analyzed. Existing scaling laws are extended to arbitrary protograph base matrices that include puncturing patterns and multiple edges between nodes. A regular protograph-based SC-LDPC construction based on the (4; 8)-regular LDPC block code works well in the waterfall region compared to more involved rate-1/2 structures proposed to improve the threshold to minimum distance trade-off. Scaling laws are also used for code design and to estimate the block length of a given SC-LDPC code ensemble to match the performance of some other code. Estimates on the performance degradation are developed if the chain length varies.},
keywords = {binary erasure channel, Block codes, Couplings, Decoding, Error analysis, finite length performance, finite-length performance, graph theory, Iterative decoding, low density parity check codes, multiedge protograph, parity check codes, spatially coupled LDPC codes, spatially-coupled LDPC codes, Steady-state},
pubstate = {published},
tppubtype = {inproceedings}
}
The finite-length performance of multi-edge spatially coupled low-density parity-check (SC-LDPC) codes over the binary erasure channel (BEC) is analyzed. Existing scaling laws are extended to arbitrary protograph base matrices that include puncturing patterns and multiple edges between nodes. A regular protograph-based SC-LDPC construction based on the (4; 8)-regular LDPC block code works well in the waterfall region compared to more involved rate-1/2 structures proposed to improve the threshold to minimum distance trade-off. Scaling laws are also used for code design and to estimate the block length of a given SC-LDPC code ensemble to match the performance of some other code. Estimates on the performance degradation are developed if the chain length varies.
Olmos, Pablo M; Urbanke, Rudiger
A Scaling Law to Predict the Finite-Length Performance of Spatially-Coupled LDPC Codes Artículo de revista
En: IEEE Transactions on Information Theory, vol. 61, no 6, pp. 3164–3184, 2015, ISSN: 0018-9448.
Resumen | Enlaces | BibTeX | Etiquetas: asymptotic analysis, asymptotic properties, binary erasure channel, Channel Coding, Codes on graphs, Couplings, Decoding, Differential equations, error probability, finite length performance, finite length spatially coupled code, finite-length code performance, finite-length performance, Iterative decoding, iterative decoding thresholds, Journal, parity check codes, Probability, SC-LDPC codes, scaling law, Sockets, spatially coupled LDPC codes, spatially-coupled LDPC codes
@article{Olmos2015bb,
title = {A Scaling Law to Predict the Finite-Length Performance of Spatially-Coupled LDPC Codes},
author = {Pablo M Olmos and Rudiger Urbanke},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7086074},
doi = {10.1109/TIT.2015.2422816},
issn = {0018-9448},
year = {2015},
date = {2015-06-01},
journal = {IEEE Transactions on Information Theory},
volume = {61},
number = {6},
pages = {3164--3184},
abstract = {Spatially-coupled low-density parity-check (SC-LDPC) codes are known to have excellent asymptotic properties. Much less is known regarding their finite-length performance. We propose a scaling law to predict the error probability of finite-length spatially coupled code ensembles when transmission takes place over the binary erasure channel. We discuss how the parameters of the scaling law are connected to fundamental quantities appearing in the asymptotic analysis of these ensembles and we verify that the predictions of the scaling law fit well to the data derived from simulations over a wide range of parameters. The ultimate goal of this line of research is to develop analytic tools for the design of SC-LDPC codes under practical constraints.},
keywords = {asymptotic analysis, asymptotic properties, binary erasure channel, Channel Coding, Codes on graphs, Couplings, Decoding, Differential equations, error probability, finite length performance, finite length spatially coupled code, finite-length code performance, finite-length performance, Iterative decoding, iterative decoding thresholds, Journal, parity check codes, Probability, SC-LDPC codes, scaling law, Sockets, spatially coupled LDPC codes, spatially-coupled LDPC codes},
pubstate = {published},
tppubtype = {article}
}
Spatially-coupled low-density parity-check (SC-LDPC) codes are known to have excellent asymptotic properties. Much less is known regarding their finite-length performance. We propose a scaling law to predict the error probability of finite-length spatially coupled code ensembles when transmission takes place over the binary erasure channel. We discuss how the parameters of the scaling law are connected to fundamental quantities appearing in the asymptotic analysis of these ensembles and we verify that the predictions of the scaling law fit well to the data derived from simulations over a wide range of parameters. The ultimate goal of this line of research is to develop analytic tools for the design of SC-LDPC codes under practical constraints.
2011
Olmos, Pablo M; Urbanke, Rudiger
Scaling Behavior of Convolutional LDPC Ensembles over the BEC Proceedings Article
En: 2011 IEEE International Symposium on Information Theory Proceedings, pp. 1816–1820, IEEE, Saint Petersburg, 2011, ISSN: 2157-8095.
Resumen | Enlaces | BibTeX | Etiquetas: BEC, binary codes, binary erasure channel, Bit error rate, convolutional codes, convolutional LDPC ensembles, coupled sparse graph codes, Couplings, Decoding, error probability, Iterative decoding, parity check codes, scaling behavior
@inproceedings{Olmos2011,
title = {Scaling Behavior of Convolutional LDPC Ensembles over the BEC},
author = {Pablo M Olmos and Rudiger Urbanke},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6033863},
issn = {2157-8095},
year = {2011},
date = {2011-01-01},
booktitle = {2011 IEEE International Symposium on Information Theory Proceedings},
pages = {1816--1820},
publisher = {IEEE},
address = {Saint Petersburg},
abstract = {We study the scaling behavior of coupled sparse graph codes over the binary erasure channel. In particular, let 2L+1 be the length of the coupled chain, let M be the number of variables in each of the 2L+1 local copies, let ℓ be the number of iterations, let Pb denote the bit error probability, and let ∈ denote the channel parameter. We are interested in how these quantities scale when we let the blocklength (2L + 1)M tend to infinity. Based on empirical evidence we show that the threshold saturation phenomenon is rather stable with respect to the scaling of the various parameters and we formulate some general rules of thumb which can serve as a guide for the design of coding systems based on coupled graphs.},
keywords = {BEC, binary codes, binary erasure channel, Bit error rate, convolutional codes, convolutional LDPC ensembles, coupled sparse graph codes, Couplings, Decoding, error probability, Iterative decoding, parity check codes, scaling behavior},
pubstate = {published},
tppubtype = {inproceedings}
}
We study the scaling behavior of coupled sparse graph codes over the binary erasure channel. In particular, let 2L+1 be the length of the coupled chain, let M be the number of variables in each of the 2L+1 local copies, let ℓ be the number of iterations, let Pb denote the bit error probability, and let ∈ denote the channel parameter. We are interested in how these quantities scale when we let the blocklength (2L + 1)M tend to infinity. Based on empirical evidence we show that the threshold saturation phenomenon is rather stable with respect to the scaling of the various parameters and we formulate some general rules of thumb which can serve as a guide for the design of coding systems based on coupled graphs.