@inproceedings{Olmos2015b,
title = {Analyzing the Finite-Length Performance of Generalized LDPC Codes},
author = {Olmos, Pablo M. and Mitchell, David G. M. and Costello, Daniel J.},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7282943},
doi = {10.1109/ISIT.2015.7282943},
isbn = {978-1-4673-7704-1},
year = {2015},
date = {2015-06-01},
booktitle = {2015 IEEE International Symposium on Information Theory (ISIT)},
pages = {2683--2687},
publisher = {IEEE},
address = {Hong Kong},
abstract = {In this paper, we analyze the performance of finite-length generalized LDPC (GLDPC) block codes constructed from protographs when transmission takes place over the binary erasure channel (BEC). A generalized peeling decoder is proposed and we derive a system of differential equations that gives the expected evolution of the graph degree distribution during decoding. We then show that the finite-length performance of a GLDPC code can be estimated by means of a simple scaling law, where a single scaling parameter represents the finite-length properties of the code. We also show that, as we consider stronger component codes, both the asymptotic threshold and the finite-length scaling parameter are improved.},
keywords = {BEC, binary codes, binary erasure channel, Block codes, Codes on graphs, Decoding, Differential equations, error probability, finite-length generalized LDPC block codes, finite-length performance analysis, generalized LDPC codes, generalized peeling decoder, GLDPC block codes, graph degree distribution, graph theory, Iterative decoding, parity check codes, protographs},
pubstate = {published},
tppubtype = {inproceedings}
}

In this paper, we analyze the performance of finite-length generalized LDPC (GLDPC) block codes constructed from protographs when transmission takes place over the binary erasure channel (BEC). A generalized peeling decoder is proposed and we derive a system of differential equations that gives the expected evolution of the graph degree distribution during decoding. We then show that the finite-length performance of a GLDPC code can be estimated by means of a simple scaling law, where a single scaling parameter represents the finite-length properties of the code. We also show that, as we consider stronger component codes, both the asymptotic threshold and the finite-length scaling parameter are improved.

@inproceedings{Salamanca2011a,
title = {MAP Decoding for LDPC Codes over the Binary Erasure Channel},
author = {Salamanca, Luis and Olmos, Pablo M. and Murillo-Fuentes, Juan Jose and Perez-Cruz, Fernando},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6089364},
isbn = {978-1-4577-0437-6},
year = {2011},
date = {2011-01-01},
booktitle = {2011 IEEE Information Theory Workshop},
pages = {145--149},
publisher = {IEEE},
address = {Paraty},
abstract = {In this paper, we propose a decoding algorithm for LDPC codes that achieves the MAP solution over the BEC. This algorithm, denoted as generalized tree-structured expectation propagation (GTEP), extends the idea of our previous work, the TEP decoder. The GTEP modifies the graph by eliminating a check node of any degree and merging this information with the remaining graph. The GTEP decoder upon completion either provides the unique MAP solution or a tree graph in which the number of parent nodes indicates the multiplicity of the MAP solution. This algorithm can be easily described for the BEC, and it can be cast as a generalized peeling decoder. The GTEP naturally optimizes the complexity of the decoder, by looking for checks nodes of minimum degree to be eliminated first.},
keywords = {binary erasure channel, Channel Coding, computational complexity, Decoding, generalized peeling decoder, generalized tree-structured expectation propagatio, graphical models, Iterative decoding, LDPC codes, MAP decoding, MAP decoding algorithm, Maximum likelihood decoding, parity check codes, TEP decoder, tree graph theory, Tree graphs, tree-structured expectation propagation, trees (mathematics)},
pubstate = {published},
tppubtype = {inproceedings}
}

In this paper, we propose a decoding algorithm for LDPC codes that achieves the MAP solution over the BEC. This algorithm, denoted as generalized tree-structured expectation propagation (GTEP), extends the idea of our previous work, the TEP decoder. The GTEP modifies the graph by eliminating a check node of any degree and merging this information with the remaining graph. The GTEP decoder upon completion either provides the unique MAP solution or a tree graph in which the number of parent nodes indicates the multiplicity of the MAP solution. This algorithm can be easily described for the BEC, and it can be cast as a generalized peeling decoder. The GTEP naturally optimizes the complexity of the decoder, by looking for checks nodes of minimum degree to be eliminated first.