Persistent Link:
http://hdl.handle.net/10150/195483
Title:
Analysis of Failures of Decoders for LDPC Codes
Author:
Chilappagari, Shashi Kiran
Issue Date:
2008
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
Ever since the publication of Shannon's seminal work in 1948, the search for capacity achieving codes has led to many interesting discoveries in channel coding theory. Low-density parity-check (LDPC) codes originally proposed in 1963 were largely forgotten and rediscovered recently. The significance of LDPC codes lies in their capacity approaching performance even when decoded using low complexity sub-optimal decoding algorithms. Iterative decoders are one such class of decoders that work on a graphical representation of a code known as the Tanner graph. Their properties have been well understood in the asymptotic limit of the code length going to infinity. However, the behavior of various decoders for a given finite length code remains largely unknown.An understanding of the failures of the decoders is vital for the error floor analysis of a given code. Broadly speaking, error floor is the abrupt degradation in the frame error rate (FER) performance of a code in the high signal-to-noise ratio domain. Since the error floor phenomenon manifests in the regions not reachable by Monte-Carlo simulations, analytical methods are necessary for characterizing the decoding failures. In this work, we consider hard decision decoders for transmission over the binary symmetric channel (BSC).For column-weight-three codes, we provide tight upper and lower bounds on the guaranteed error correction capability of a code under the Gallager A algorithm by studying combinatorial objects known as trapping sets. For higher column weight codes, we establish bounds on the minimum number of variable nodes that achieve certain expansion as a function of the girth of the underlying Tanner graph, thereby obtaining lower bounds on the guaranteed error correction capability. We explore the relationship between a class of graphs known as cage graphs and trapping sets to establish upper bounds on the error correction capability.We also propose an algorithm to identify the most probable noise configurations, also known as instantons, that lead to error floor for linear programming (LP) decoding over the BSC. With the insight gained from the above analysis techniques, we propose novel code construction techniques that result in codes with superior error floor performance.
Type:
text; Electronic Dissertation
Keywords:
Error floor; Gallager A algorithm; Instantons; LDPC codes; Pseudo-codewords; Trapping sets
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Electrical & Computer Engineering; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Vasic, Bane
Committee Chair:
Vasic, Bane

Full metadata record

DC FieldValue Language
dc.language.isoENen_US
dc.titleAnalysis of Failures of Decoders for LDPC Codesen_US
dc.creatorChilappagari, Shashi Kiranen_US
dc.contributor.authorChilappagari, Shashi Kiranen_US
dc.date.issued2008en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractEver since the publication of Shannon's seminal work in 1948, the search for capacity achieving codes has led to many interesting discoveries in channel coding theory. Low-density parity-check (LDPC) codes originally proposed in 1963 were largely forgotten and rediscovered recently. The significance of LDPC codes lies in their capacity approaching performance even when decoded using low complexity sub-optimal decoding algorithms. Iterative decoders are one such class of decoders that work on a graphical representation of a code known as the Tanner graph. Their properties have been well understood in the asymptotic limit of the code length going to infinity. However, the behavior of various decoders for a given finite length code remains largely unknown.An understanding of the failures of the decoders is vital for the error floor analysis of a given code. Broadly speaking, error floor is the abrupt degradation in the frame error rate (FER) performance of a code in the high signal-to-noise ratio domain. Since the error floor phenomenon manifests in the regions not reachable by Monte-Carlo simulations, analytical methods are necessary for characterizing the decoding failures. In this work, we consider hard decision decoders for transmission over the binary symmetric channel (BSC).For column-weight-three codes, we provide tight upper and lower bounds on the guaranteed error correction capability of a code under the Gallager A algorithm by studying combinatorial objects known as trapping sets. For higher column weight codes, we establish bounds on the minimum number of variable nodes that achieve certain expansion as a function of the girth of the underlying Tanner graph, thereby obtaining lower bounds on the guaranteed error correction capability. We explore the relationship between a class of graphs known as cage graphs and trapping sets to establish upper bounds on the error correction capability.We also propose an algorithm to identify the most probable noise configurations, also known as instantons, that lead to error floor for linear programming (LP) decoding over the BSC. With the insight gained from the above analysis techniques, we propose novel code construction techniques that result in codes with superior error floor performance.en_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.subjectError flooren_US
dc.subjectGallager A algorithmen_US
dc.subjectInstantonsen_US
dc.subjectLDPC codesen_US
dc.subjectPseudo-codewordsen_US
dc.subjectTrapping setsen_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineElectrical & Computer Engineeringen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorVasic, Baneen_US
dc.contributor.chairVasic, Baneen_US
dc.contributor.committeememberMarcellin, Michael W.en_US
dc.contributor.committeememberRyan, William E.en_US
dc.contributor.committeememberLux, Klaus M.en_US
dc.identifier.proquest10120en_US
dc.identifier.oclc659750516en_US
All Items in UA Campus Repository are protected by copyright, with all rights reserved, unless otherwise indicated.