On LDPC Code Ensembles with Generalized Constraints

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dc.contributor.author Liu, Yanfang
dc.contributor.author Martínez Olmos, Pablo
dc.contributor.author Koch, Tobias Mirco
dc.date.accessioned 2018-02-09T12:56:58Z
dc.date.available 2018-02-09T12:56:58Z
dc.date.issued 2017-08-15
dc.identifier.bibliographicCitation 2017 IEEE International Symposium on Information Theory (ISIT) [Proceedings] , Pp. 371-375
dc.identifier.isbn 978-1-5090-4096-4
dc.identifier.uri http://hdl.handle.net/10016/26210
dc.description Proceeding of: 2017 IEEE International Symposium on Information Theory, Aachen, Germany, 25-30 June, 2017
dc.description.abstract In this paper, we analyze the tradeoff between coding rate and asymptotic performance of a class of generalized low-density parity-check (GLDPC) codes constructed by including a certain fraction of generalized constraint (GC) nodes in the graph. The rate of the GLDPC ensemble is bounded using classical results on linear block codes, namely Hamming bound and Varshamov bound. We also study the impact of the decoding method used at GC nodes. To incorporate both bounded-distance (BD) and Maximum Likelihood (ML) decoding at GC nodes into our analysis without having to resort on multi-edge type of degree distributions (DDs), we propose the probabilistic peeling decoder (P-PD) algorithm, which models the decoding step at every GC node as an instance of a Bernoulli random variable with a success probability that depends on the GC block code and its decoding algorithm. The P-PD asymptotic performance over the BEC can be efficiently predicted using standard techniques for LDPC codes such as density evolution (DE) or the differential equation method. Furthermore, for a class of GLDPC ensembles, we demonstrate that the simulated P-PD performance accurately predicts the actual performance of the GLPDC code. We illustrate our analysis for GLDPC code ensembles using (2, 6) and (2,15) base DDs. In all cases, we show that a large fraction of GC nodes is required to reduce the original gap to capacity.
dc.description.sponsorship This work has been funded in part by the Spanish Ministerio de Economía y Competitividad and the Agencia Española de Investigación under Grant TEC2016-78434-C3-3-R (AEI/FEDER, EU) and by the Comunidad de Madrid in Spain under Grant S2103/ICE-2845. T. Koch has further received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement number 714161), from the 7th European Union Framework Programme under Grant 333680, and from the Spanish Ministerio de Economía y Competitividad under Grants TEC2013-41718-R and RYC-2014-16332. Pablo M. Olmos has further received funding from the Spanish Ministerio de Economía y Competitividad under Grant IJCI-2014-19150.
dc.format.extent 5
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher IEEE
dc.rights © 2017 IEEE
dc.subject.other Generalized low-density parity-check codes
dc.subject.other Codes on graphs
dc.subject.other Peeling decoding
dc.title On LDPC Code Ensembles with Generalized Constraints
dc.type bookPart
dc.type conferenceObject
dc.subject.eciencia Electrónica
dc.subject.eciencia Telecomunicaciones
dc.identifier.doi https://doi.org/10.1109/ISIT.2017.8006552
dc.rights.accessRights openAccess
dc.relation.projectID info:eu-repo/grantAgreement/EC/H2020/714161
dc.relation.projectID info:eu-repo/grantAgreement/EC/FP7/333680
dc.relation.projectID Gobierno de España. TEC2016-78434-C3-3-R (AEI/FEDER, EU)
dc.relation.projectID Gobierno de España. TEC2013-41718-R
dc.relation.projectID Gobierno de España. RYC-2014-16332
dc.relation.projectID Gobierno de España. IJCI-2014-19150
dc.relation.projectID Comunidad de Madrid. S2103/ICE-2845
dc.type.version acceptedVersion
dc.relation.eventdate 2017-06-25
dc.relation.eventplace Aachen, Alemania
dc.relation.eventtitle 2017 IEEE International Symposium on Information Theory
dc.identifier.publicationfirstpage 371
dc.identifier.publicationlastpage 375
dc.identifier.publicationtitle 2017 IEEE International Symposium on Information Theory (ISIT) [Proceedings]
dc.identifier.uxxi CC/0000027312
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