Graduate Theses, Dissertations, and Problem Reports 2013 Optimization of a Coded-Modulation System with Shaped Constellation Xingyu Xiang West Virginia University Follow this and additional works at: https://researchrepository.wvu.edu/etd Recommended Citation Xiang, Xingyu, "Optimization of a Coded-Modulation System with Shaped Constellation" (2013). Graduate Theses, Dissertations, and Problem Reports. 207. https://researchrepository.wvu.edu/etd/207 This Dissertation is protected by copyright and/or related rights. It has been brought to you by the The Research Repository @ WVU with permission from the rights-holder(s). You are free to use this Dissertation in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you must obtain permission from the rights-holder(s) directly, unless additional rights are indicated by a Creative Commons license in the record and/ or on the work itself. This Dissertation has been accepted for inclusion in WVU Graduate Theses, Dissertations, and Problem Reports collection by an authorized administrator of The Research Repository @ WVU. For more information, please contact [email protected]. Optimization of a Coded-Modulation System with Shaped Constellation by Xingyu Xiang Dissertation submitted to the College of Engineering and Mineral Resources at West Virginia University in partial fulfillment of the requirements for the degree of Ph.D. in Electrical Engineering Brian D. Woerner, Ph.D. Daryl S. Reynolds, Ph.D. John Goldwasser, Ph.D. Natalia A. Schmid, Ph.D. Matthew C. Valenti, Ph.D., Chair Lane Department of Computer Science and Electrical Engineering Morgantown, West Virginia 2013 Keywords: Information Theory, Constellation Shaping, Capacity, LDPC code, Optimization, EXIT chart Copyright 2013 Xingyu Xiang Abstract Optimization of a Coded-Modulation System with Shaped Constellation by Xingyu Xiang Ph.D. in Electrical Engineering West Virginia University Matthew C. Valenti, Ph.D., Chair Conventional communication systems transmit signals that are selected from a signal constellation with uniform probability. However, information-theoretic results suggest that performance may be improved by shaping the constellation such that lower-energy signals are selected more frequently than higher-energy signals. This dissertation presents an energy- efficient approach for shaping the constellations used by coded-modulation systems. The focus is on designing shaping techniques for systems that use a combination of amplitude- phase shift keying (APSK) and low-density parity check (LDPC) coding. Such a combination is typical of modern satellite communications, such as the system used by the DVB-S2 standard. The system implementation requires that a subset of the bits at the output of the LDPC encoder are passed through a nonlinear shaping encoder whose output bits are more likely to be a zero than a one. The constellation is partitioned into a plurality of sub-constellations, each with a different average signal energy, and the shaping bits are used to select the sub-constellation. An iterative receiver exchanges soft information among the demodulator, LDPC decoder, and shaping decoder. Parameters associated with the modulation and shap- ing code are optimized with respect to information rate, while the design of the LDPC code is optimized for the shaped modulation with the assistance of extrinsic-information transfer (EXIT) charts. The rule for labeling the constellation with bits is optimized using a novel hybrid cost function and a binary switching algorithm. Simulation results show that the combination of constellation shaping, LDPC code op- timization, and optimized bit labeling can achieve a gain in excess of 1 dB in an additive white Gaussian noise (AWGN) channel at a rate of 3 bits/symbol compared with a system that adheres directly to the DVB-S2 standard. iii Acknowledgements This dissertation could never be finished without the assistants and contributions from a great many people around. I would like to extend my appreciation especially to the following. First and foremost, my deepest gratitude is to my dissertation committee chairman and advisor, Dr. Matthew C. Valenti, who is my first foreign advisor and also the best advisor I have ever met. I can still remember the exciting scene that I received the email from Dr. Valenti about his research plan together with the official invitation. His excellent guidance, patience, and enthusiasm attitude made me overcome the problems came across the whole graduate career. He provides the support in almost every possible way, I appreciate his time, idea, editing and funding in the completion of this and other documents. It is an honor to work with him and his instructions will continue benefit my future lives. To the other members of my committee, Dr. Brian Woerner, Dr. Daryl Reynolds, Dr. Natalia Schmid and Dr. John Goldwasser, thank you for your feedback and suggestions to make this dissertation more thorough and rigorous. I spend most of my professional and personal time in the wireless communication research lab, from where I obtain both friendship and illuminating advice. I am grateful for the colleagues who stayed with me in the past few years: Terry R. Ferret, Mohammad Fanaei, Salvatore Talarico, Aruna Sri and Chandana Nannapaneni. Particularly I would like to acknowledge Terry for helping me settle down on my first day of arrival, he also help Dr. Valenti to maintain the cluster system to provide us the extra computing power. Without all of their contributions to the grid computing, the results of this dissertation would take much more time to be finished. Other graduate students that I have had the pleasure to be alongside of are Jinyu Zuo, Ricky Hussmann, Yuan Li and Wentian Zhou. My time at West Virginia University was enjoyable due to the beautiful environment and the unique graduate student experience, it becomes a part of my life and thanks to all the professors and friends to make it memorable. Special recognition goes out to my family I ACKNOWLEDGEMENTS iv would like thank my parents for all their love and encouragement. They supported me and trusted me unconditionally even in the tough times. Lastly, I want to thank the WVU staff and my friends in China, America and elsewhere for their support and encouragement. iv Contents Acknowledgements iii List of Figures vi List of Tables x 1 Introduction 1 1.1 Digital Communication System Model . .2 1.2 Modulation . .3 1.3 Channel Coding . .4 1.3.1 Convolutional Codes . .5 1.3.2 Turbo Code . .6 1.3.3 Linear Block Codes . .8 1.3.4 Low-Density Parity-Check (LDPC) Codes . .9 1.4 Satellite Communication . 15 1.4.1 DVB-S2 Standard . 16 1.4.2 APSK . 17 1.4.3 TWTA . 18 1.4.4 DVB-S2 Performance . 22 1.5 Thesis Outline . 24 2 Channel Capacity and Constellation Shaping 26 2.1 Channel Capacity . 26 2.1.1 The Unconstrained Capacity . 27 2.1.2 Capacity under Coded Modulation . 30 2.1.3 Capacity Calculation . 34 2.2 Constellation Shaping . 36 2.2.1 Shaping System Model . 38 2.2.2 Shaping Strategies . 41 2.2.3 Shaping for 16-APSK and 32-APSK . 41 2.3 Parameter Optimization . 44 2.4 PAPR Consideration . 49 2.5 Summary . 50 CONTENTS v 3 Constellation Shaping Implementation 52 3.1 Transmitter Structure . 53 3.1.1 Constellation Shaping with 16-PAM . 54 3.1.2 Constellation Shaping with 32-APSK . 54 3.2 Receiver Implementation . 56 3.2.1 The Demodulator . 58 3.2.2 The Shaping Decoder . 59 3.2.3 Receiver with Turbo Decoder . 60 3.2.4 Receiver with LDPC Decoder . 62 3.3 Numerical Results . 63 3.3.1 Results When using Turbo Codes . 64 3.3.2 Results when using LDPC Codes . 68 3.3.3 Receiver Complexity Consideration . 70 3.4 Conclusion . 72 4 EXIT Chart and LDPC Code Optimization 73 4.1 EXIT Charts Based Analysis . 73 4.1.1 Exit Charts for Uniform System . 73 4.1.2 Exit Charts for Shaped System . 81 4.2 LDPC Codes Optimization . 86 4.2.1 Codes Designed for AWGN Channel . 87 4.2.2 Codes Designed for Fading Channel . 93 4.3 Short Cycles in LDPC Codes . 96 4.4 Conclusion . 98 5 Constellation Optimization 99 5.1 Mapping Optimization Strategy . 100 5.1.1 Constellation Labeling Optimization . 105 5.1.2 Binary Switching Algorithm and the Cost Functions . 106 5.1.3 Mapping Optimization for Uniform 32-APSK . 111 5.1.4 Mapping Optimization for Shaped 32-APSK . 112 5.2 Numerical Results with Optimized LDPC Codes and Symbol Mapping . 115 5.3 Optimization of the Input Alphabet . 117 5.4 Conclusion . 122 References 124 vi List of Figures 1.1 Block diagram for a basic digital communication system. .2 1.2 Bit Error Rate of Uncoded Modulations . .5 1.3 Convolutional encoder . .6 1.4 Structure of turbo encoder . .7 1.5 Structure of turbo decoder . .8 1.6 Tanner Graph corresponding to H1, the squares represent check nodes and the circles represent check nodes. 11 1.7 16-APSK . 18 1.8 Caption for LOF . 19 1.9 Distorted 16-QAM on the outputs of non-linear TWTA . 20 1.10 Distorted 32-APSK on the outputs of non-linear TWTA . 20 1.11 Magnitude Predistortion linearizers generate a response opposite to a TWTA's characteristics . 21 1.12 Phase Predistortion linearizers generate a response opposite to a TWTA's characteristics . 21 1.13 Predistorted QAM and 32-APSK on the outputs of non-linear TWTA . 22 1.14 Performance of DVB-S2 standardized LDPC coded over AWGN channel . 23 1.15 Caption for LOF . 24 2.1 Unconstrained AWGN channel capacity and SIR with equiprobable M-QAM(PSK) inputs . 32 2.2 A BICM system structure which contains the CM system. The block `Enc' is the binary channel encoder, ‘Π’ is a bit-level interleaver and ‘Φ’ is a memory- less mapper.