ISSN: 1402-1544 ISBN 978-91-86233-XX-X Se i listan och fyll i siffror där kryssen är DOCTORAL T H E SIS Sara Sandberg Department of Computer Science and Electrical Engineering Division of Systems and Interaction Low-Density Parity-CheckLow-Density Codes - ISSN: 1402-1544 ISBN 978-91-86233-14-3 Low-Density Parity-Check Codes - Luleå University of Technology 2009 Unequal Error Protection and Reduction of Clipping Effects Unequal Error Protection and Reduction of Clipping Effects Sara Sandberg Luleå University of Technology Low-Density Parity-Check Codes - Unequal Error Protection and Reduction of Clipping Effects Sara Sandberg Division of Systems and Interaction Department of Computer Science and Electrical Engineering Lule˚a University of Technology Lule˚a, Sweden Supervisor: Professor James P. LeBlanc Tryck: Universitetstryckeriet, Luleå ISSN: 1402-1544 ISBN 978-91-86233-14-3 Luleå www.ltu.se To Marcus, Miriam, and Jakob iv Abstract The invention of low-density parity-check (LDPC) codes made reliable communication possible at transmission rates very close to the theoretical limit predicted by Shannon. However, communication close to the Shannon limit requires very long codes and results in long delay and high encoder and decoder complexity. In many communication scenar- ios, constraints on delay, complexity and power prohibit communication with arbitrarily low error probability. To achieve good performance it is then important that the code is appropriately matched to the other parts of the communication system. In this thesis, LDPC codes for two different communication scenarios are studied. A common scenario is communication of information bits with unequal importance for the perceptual quality after source decoding. This is the case for example in many networks and for transport of multimedia data, where one frame may consist of a header, some payload and additional payload for increased quality. Errors in the header data may cause the whole frame to be useless, while errors in the additional payload generally cause only a small quality reduction. A code with unequal error protection (UEP) is designed to protect some bits more than others, thus providing a reduced bit-error rate (BER) for the important bits. This work studies design of LDPC codes with UEP capability for bandwidth-efficient higher order constellations. A flexible design algorithm for irregular UEP-LDPC codes is proposed, which is applicable to arbitrary signal constellations, an arbitrary number of classes of bits with different importance and arbitrary sizes of the classes. Simulations using 8-PSK modulation show that the overall BER is reduced if codes are properly designed for the modulation scheme, compared to the BER achieved by standard UEP codes designed for BPSK modulation. Codes designed by the proposed algorithm also provide more UEP capability, especially at high SNR. Moreover, further work shows that the UEP capability of an irregular LDPC code is not only dependent on the variable node degrees as is widely believed. The LDPC construction algorithms, that place the edges in the graph according to the degree distributions, also play a critical role for the UEP behavior of an LDPC code. The differences in UEP capability are explained by introduction of detailed check node degree distributions that describe differences in the code structure. v vi LDPC codes for the orthogonal frequency division multiplexing (OFDM) system are also studied. OFDM enables simple equalization and has been adopted in several stan- dards. However, OFDM is sensitive to frequency-selective fading and introduces a large peak-to-average power ratio (PAPR) of the transmitted signal. These problems can be alleviated by pre-multiplying the OFDM block with a spreading matrix that both reduces the PAPR of the transmitted signal and increases the frequency diversity. Simulation of an OFDM system with clipping shows that the performance gain by spreading is substan- tial also when an LDPC code, which on its own improves the performance significantly, is applied to the OFDM system. PAPR reduction may also be achieved by deliberate clip- ping of the signal, prior to the transmitter high-power amplifier. Clipping will however introduce losses and receiver methods to mitigate such clipping losses are investigated. We consider Bayesian estimation of the unclipped signal as well as statistical character- ization of the clipping distortion, that is fed to the LDPC decoder. The results show that for an LDPC coded OFDM system, the improvement by these clipping mitigation methodsisminimal. Contents Part I - General Introduction xiii Chapter 1–Thesis Introduction 1 1.1Motivation................................... 1 1.2ADigitalCommunicationSystem...................... 3 Chapter 2–Error Control Coding 9 2.1HistoricalDevelopment............................ 9 2.2LinearBlockCodes.............................. 11 2.3ConvolutionalCodes............................. 20 2.4TurboCodes.................................. 24 2.5CodedModulation.............................. 27 2.6PerformanceComparison........................... 29 Chapter 3–Low-Density Parity-Check Codes 33 3.1 Fundamentals of LDPC Codes ........................ 33 3.2DecodingofLDPCCodes.......................... 36 3.3DensityEvolution............................... 40 Part II - Introduction to the Specific Research Topics 47 Chapter 4–Overview of Clipping Mitigation Strategies in OFDM 49 4.1OFDMBasics................................. 49 4.2ReductionofthePeak-To-AveragePowerRatio.............. 52 4.3 Reduction of Clipping Effects in the Receiver ................ 54 4.4SpreadOFDM................................. 55 4.5CodedOFDM................................. 56 Chapter 5–Overview of Unequal Error Protection Codes 59 5.1UEPCodes.................................. 60 5.2UEP-LDPCCodes.............................. 62 5.3IrregularUEP-LDPCCodes......................... 63 vii viii Chapter 6–Research Contributions 67 6.1ClippingMitigationinLDPCCodedOFDMSystems........... 67 6.2DesignofUnequalErrorProtectionLDPCCodes............. 69 Part III - Research Papers 87 Paper A-Performance of LDPC Coded Spread OFDM with Clipping 89 1 Introduction.................................. 91 2 TheOFDMSystem.............................. 92 3 LDPCcodesforOFDMandSOFDM.................... 95 4 Results..................................... 97 5 Conclusions.................................. 100 Paper B-Receiver-oriented Clipping-effect Mitigation in OFDM - A Worthy Approach? 105 1 Introduction.................................. 107 2 SystemDescriptionandChannelModel................... 108 3 CharacterizationofClippingNoise..................... 110 4 BayesianEstimation............................. 112 5 ResultsandDiscussion............................ 113 6 Conclusions.................................. 115 Paper C-Design of Unequal Error Protection LDPC Codes for Higher Order Constellations 119 1 Introduction.................................. 121 2 SystemModel................................. 122 3 Modulation.................................. 123 4 UEP-LDPCCodes.............................. 124 5 SimulationResults.............................. 131 6 Conclusions.................................. 134 Paper D-Design of Bandwidth-Efficient Unequal Error Protection LDPC Codes 137 1 Introduction.................................. 139 2 SystemModel................................. 143 3 UEP-LDPCCodesforHigherOrderConstellations............ 147 4 SimulationResults.............................. 154 5 Conclusions.................................. 160 ix Paper E-On the UEP Capabilities of Several LDPC Construction Algorithms 165 1 Introduction.................................. 167 2 ConstructionAlgorithms........................... 169 3 SimulationResults.............................. 171 4 RelevantGraphProperties.......................... 175 5 ModifiedPEG-ACEConstructionwithIncreasedUEPCapability.... 184 6 Conclusions.................................. 185 x Acknowledgements The first person I would like to express my gratitude to is my supervisor Professor James LeBlanc. Thank you for convincing me that I would find the Ph.D. studies fun and for the guidance and support that you have given me. Because of your enthusiasm and dedication to my education, becoming a Ph.D. student is a choice I have never regretted. Also, many thanks go to my assistant advisor, Professor Bane Vasic from the Univer- sity of Arizona, that has supported me with his coding expertise and interesting ideas. Thanks also for giving me the opportunity to visit you and your group for three months and the hospitality you all showed me and my family. Magnus Lundberg Nordenvaad has been my assistant advisor since 2007. Thank you for your valuable support. During the M-Pipe project, I got to know Neele von Deetzen from Jacobs University Bremen, Germany. Since then we have written three papers together. I have really enjoyed our discussions and collaboration, from which I think both of us have learned a lot. Thanks also for being a good friend. It has been a pleasure to get to know you Neele! I would also like to thank all my colleagues at the department of computer science and electrical engineering. All together you make up a friendly and inspiring atmosphere that makes it enjoyable to go to work. I would especially like to thank my friends in the A3200-corridor for joining me in the coffee room and Johan Carlson for providing the LATEX template for this thesis. Acknowledgments also to the European Commission for co-funding