### 2015

Olmos, Pablo M; Mitchell, David G M; Costello, Daniel J

Analyzing the Finite-Length Performance of Generalized LDPC Codes Inproceedings

In: 2015 IEEE International Symposium on Information Theory (ISIT), pp. 2683–2687, IEEE, Hong Kong, 2015, ISBN: 978-1-4673-7704-1.

Abstract | Links | BibTeX | Tags: 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

@inproceedings{Olmos2015b,

title = {Analyzing the Finite-Length Performance of Generalized LDPC Codes},

author = {Pablo M Olmos and David G M Mitchell and Daniel J Costello},

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}

}

Stinner, Markus; Olmos, Pablo M

Finite-Length Performance of Multi-Edge Protograph-Based Spatially Coupled LDPC Codes Inproceedings

In: 2015 IEEE International Symposium on Information Theory (ISIT), pp. 889–893, IEEE, Hong Kong, 2015, ISBN: 978-1-4673-7704-1.

Abstract | Links | BibTeX | Tags: 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}

}

### 2014

Stinner, Markus; Olmos, Pablo M

Analyzing Finite-length Protograph-Based Spatially Coupled LDPC Codes Inproceedings

In: 2014 IEEE International Symposium on Information Theory, pp. 891–895, IEEE, Honolulu, 2014, ISBN: 978-1-4799-5186-4.

Abstract | Links | BibTeX | Tags: binary erasure channel, covariance analysis, covariance evolution, Decoding, degree-one check nodes, Error analysis, finite-length protograph, mean evolution, Monte Carlo methods, parity check codes, peeling decoding, protograph-based SC-LDPC codes, spatially coupled low-density parity-check codes, stable decoding phase, Steady-state, Vectors

@inproceedings{Stinner2014,

title = {Analyzing Finite-length Protograph-Based Spatially Coupled LDPC Codes},

author = {Markus Stinner and Pablo M Olmos},

url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6874961},

isbn = {978-1-4799-5186-4},

year = {2014},

date = {2014-01-01},

booktitle = {2014 IEEE International Symposium on Information Theory},

pages = {891--895},

publisher = {IEEE},

address = {Honolulu},

abstract = {The peeling decoding for spatially coupled low-density parity-check (SC-LDPC) codes is analyzed for a binary erasure channel. An analytical calculation of the mean evolution of degree-one check nodes of protograph-based SC-LDPC codes is given and an estimate for the covariance evolution of degree-one check nodes is proposed in the stable decoding phase where the decoding wave propagates along the chain of coupled codes. Both results are verified numerically. Protograph-based SC-LDPC codes turn out to have a more robust behavior than unstructured random SC-LDPC codes. Using the analytically calculated parameters, the finite-length scaling laws for these constructions are given and verified by numerical simulations.},

keywords = {binary erasure channel, covariance analysis, covariance evolution, Decoding, degree-one check nodes, Error analysis, finite-length protograph, mean evolution, Monte Carlo methods, parity check codes, peeling decoding, protograph-based SC-LDPC codes, spatially coupled low-density parity-check codes, stable decoding phase, Steady-state, Vectors},

pubstate = {published},

tppubtype = {inproceedings}

}

### 2013

Salamanca, Luis; Murillo-Fuentes, Juan Jose; Olmos, Pablo M; Perez-Cruz, Fernando

Improving the BP Estimate over the AWGN Channel Using Tree-Structured Expectation Propagation Inproceedings

In: 2013 IEEE International Symposium on Information Theory, pp. 2990–2994, IEEE, Istanbul, 2013, ISSN: 2157-8095.

Abstract | Links | BibTeX | Tags: Approximation algorithms, Approximation methods, AWGN channels, BEC, belief propagation decoding, BI-AWGN channel, binary additive white Gaussian noise channel, binary erasure channel, BP estimation, Channel Coding, Complexity theory, error rate reduction, error statistics, Expectation, finite-length codes, Iterative decoding, LDPC codes, LDPC decoding, low-density parity-check decoding, Maximum likelihood decoding, parity check codes, posterior distribution, Propagation, TEP algorithm, tree-structured expectation propagation algorithm, trees (mathematics)

@inproceedings{Salamanca2013,

title = {Improving the BP Estimate over the AWGN Channel Using Tree-Structured Expectation Propagation},

author = {Luis Salamanca and Juan Jose Murillo-Fuentes and Pablo M Olmos and Fernando Perez-Cruz},

url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6620774},

issn = {2157-8095},

year = {2013},

date = {2013-01-01},

booktitle = {2013 IEEE International Symposium on Information Theory},

pages = {2990--2994},

publisher = {IEEE},

address = {Istanbul},

abstract = {In this paper, we propose the tree-structured expectation propagation (TEP) algorithm for low-density parity-check (LDPC) decoding over the binary additive white Gaussian noise (BI-AWGN) channel. By approximating the posterior distribution by a tree-structure factorization, the TEP has been proven to improve belief propagation (BP) decoding over the binary erasure channel (BEC). We show for the AWGN channel how the TEP decoder is also able to capture additional information disregarded by the BP solution, which leads to a noticeable reduction of the error rate for finite-length codes. We show that for the range of codes of interest, the TEP gain is obtained with a slight increase in complexity over that of the BP algorithm. An efficient way of constructing the tree-like structure is also described.},

keywords = {Approximation algorithms, Approximation methods, AWGN channels, BEC, belief propagation decoding, BI-AWGN channel, binary additive white Gaussian noise channel, binary erasure channel, BP estimation, Channel Coding, Complexity theory, error rate reduction, error statistics, Expectation, finite-length codes, Iterative decoding, LDPC codes, LDPC decoding, low-density parity-check decoding, Maximum likelihood decoding, parity check codes, posterior distribution, Propagation, TEP algorithm, tree-structured expectation propagation algorithm, trees (mathematics)},

pubstate = {published},

tppubtype = {inproceedings}

}

### 2012

Olmos, Pablo M; Perez-Cruz, Fernando; Salamanca, Luis; Murillo-Fuentes, Juan Jose

Finite-Length Analysis of the TEP Decoder for LDPC Ensembles over the BEC Inproceedings

In: 2012 IEEE International Symposium on Information Theory Proceedings, pp. 2346–2350, IEEE, Cambridge, MA, 2012, ISSN: 2157-8095.

Abstract | Links | BibTeX | Tags: Approximation methods, BEC, binary codes, binary erasure channel, Decoding, Error analysis, error probability, finite-length analysis, LDPC ensembles, low-density parity check ensembles, parity check codes, TEP decoder, Trajectory, tree-expectation propagation algorithm, waterfall region

@inproceedings{Olmos2012a,

title = {Finite-Length Analysis of the TEP Decoder for LDPC Ensembles over the BEC},

author = {Pablo M Olmos and Fernando Perez-Cruz and Luis Salamanca and Juan Jose Murillo-Fuentes},

url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6283932},

issn = {2157-8095},

year = {2012},

date = {2012-01-01},

booktitle = {2012 IEEE International Symposium on Information Theory Proceedings},

pages = {2346--2350},

publisher = {IEEE},

address = {Cambridge, MA},

abstract = {In this work, we analyze the finite-length performance of low-density parity check (LDPC) ensembles decoded over the binary erasure channel (BEC) using the tree-expectation propagation (TEP) algorithm. In a previous paper, we showed that the TEP improves the BP performance for decoding regular and irregular short LDPC codes, but the perspective was mainly empirical. In this work, given the degree-distribution of an LDPC ensemble, we explain and predict the range of code lengths for which the TEP improves the BP solution. In addition, for LDPC ensembles that present a single critical point, we propose a scaling law to accurately predict the performance in the waterfall region. These results are of critical importance to design practical LDPC codes for the TEP decoder.},

keywords = {Approximation methods, BEC, binary codes, binary erasure channel, Decoding, Error analysis, error probability, finite-length analysis, LDPC ensembles, low-density parity check ensembles, parity check codes, TEP decoder, Trajectory, tree-expectation propagation algorithm, waterfall region},

pubstate = {published},

tppubtype = {inproceedings}

}

### 2011

Olmos, Pablo M; Urbanke, Rudiger

Scaling Behavior of Convolutional LDPC Ensembles over the BEC Inproceedings

In: 2011 IEEE International Symposium on Information Theory Proceedings, pp. 1816–1820, IEEE, Saint Petersburg, 2011, ISSN: 2157-8095.

Abstract | Links | BibTeX | Tags: 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}

}

Salamanca, Luis; Olmos, Pablo M; Murillo-Fuentes, Juan Jose; Perez-Cruz, Fernando

MAP Decoding for LDPC Codes over the Binary Erasure Channel Inproceedings

In: 2011 IEEE Information Theory Workshop, pp. 145–149, IEEE, Paraty, 2011, ISBN: 978-1-4577-0437-6.

Abstract | Links | BibTeX | Tags: 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)

@inproceedings{Salamanca2011a,

title = {MAP Decoding for LDPC Codes over the Binary Erasure Channel},

author = {Luis Salamanca and Pablo M Olmos and Juan Jose Murillo-Fuentes and Fernando Perez-Cruz},

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}

}