### 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}

}

### 2011

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

Capacity Achieving LDPC Ensembles for the TEP Decoder in Erasure Channels Inproceedings

In: 2011 IEEE International Symposium on Information Theory Proceedings, pp. 2398–2402, IEEE, St. Petersburg, 2011, ISSN: 2157-8095.

Abstract | Links | BibTeX | Tags: BP threshold, Complexity theory, Decoding, Differential equations, erasure channels, fixed-rate code, Iterative decoding, LDPC, low-density parity-check codes, MAP capacity, MAP threshold, optimisation, Optimization, optimization problem, parity check codes, TEP decoder, tree-expectation propagation decoder

@inproceedings{Olmos2011b,

title = {Capacity Achieving LDPC Ensembles for the TEP Decoder in Erasure Channels},

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

url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6033993},

issn = {2157-8095},

year = {2011},

date = {2011-01-01},

booktitle = {2011 IEEE International Symposium on Information Theory Proceedings},

pages = {2398--2402},

publisher = {IEEE},

address = {St. Petersburg},

abstract = {In this work we address the design of degree distributions (DD) of low-density parity-check (LDPC) codes for the tree-expectation propagation (TEP) decoder. The optimization problem to find distributions to maximize the TEP decoding threshold for a fixed-rate code can not be analytically solved. We derive a simplified optimization problem that can be easily solved since it is based in the analytic expressions of the peeling decoder. Two kinds of solutions are obtained from this problem: we either design LDPC ensembles for which the BP threshold equals the MAP threshold or we get LDPC ensembles for which the TEP threshold outperforms the BP threshold, even achieving the MAP capacity in some cases. Hence, we proved that there exist ensembles for which the MAP solution can be obtained with linear complexity even though the BP threshold does not achieve the MAP threshold.},

keywords = {BP threshold, Complexity theory, Decoding, Differential equations, erasure channels, fixed-rate code, Iterative decoding, LDPC, low-density parity-check codes, MAP capacity, MAP threshold, optimisation, Optimization, optimization problem, parity check codes, TEP decoder, tree-expectation propagation decoder},

pubstate = {published},

tppubtype = {inproceedings}

}