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Iterative Decoding for Error Resilient Wireless Data Transmission University of Southern Queensland Faculty of Engineering and Surveying Iterative Decoding for Error Resilient Wireless Data Transmission A dissertation submitted by Tawfiqul Hasan Khan in fulfillment of the requirements of Courses ENG4111 and 4112 Research Project towards the degree of Bachelor of Engineering (Software) Submitted: November, 2006 Abstract Both turbo codes and LDPC codes form two new classes of codes that offer energy efficiencies close to theoretical limit predicted by Claude Shannon. The features of turbo codes include parallel code catenation, recursive convolutional encoders, punctured convolutional codes and an associated decoding algorithm. The features of LDPC codes include code construction, encoding algorithm, and an associated decoding algorithm. This dissertation specifically describes the process of encoding and decoding for both turbo and LDPC codes and demonstrates the performance comparison between theses two codes in terms of some performance factors. In addition, a more general discussion of iterative decoding is presented. One significant contribution of this dissertation is a study of some major performance factors that intensely contribute in the performance of both turbo codes and LDPC codes. These include Bit Error Rate, latency, code rate and computational resources. Simulation results show the performance of turbo codes and LDPC codes under different performance factors. i University of Southern Queensland Faculty of Engineering and Surveying ENG411 & ENG4112 Research Project Limitations of Use The Council of the University of Southern Queensland, its Faculty of Engineering and Surveying, and the staff of the University of Southern Queensland, do not accept any responsibility for the truth, accuracy or completeness of material contained within or associated with this dissertation. Persons using all or any part of this material do so at their own risk, and not at the risk of the Council of the University of Southern Queensland, its Faculty of Engineering and Surveying or the staff of the University of Southern Queensland. This dissertation reports an educational exercise and has no purpose or validity beyond this exercise. The sole purpose of the course pair entitled "Research Project" is to contribute to the overall education within the student’s chosen degree program. This document, the associated hardware, software, drawings, and other material set out in the associated appendices should not be used for any other purpose: if they are so used, it is entirely at the risk of the user. Prof G Baker Dean Faculty of Engineering and Surveying ii Certification I certify that the ideas, designs and experimental work, results and analyses and conclusions set out in this dissertation are entirely my own effort, except where otherwise indicated and acknowledged. I further certify that the work is original and has not been previously submitted for assessment in any other course or institution, except where specifically stated. Tawfiqul Hasan Khan Student Number: D1231090 ________________________________ Signature ________________________________ Date iii Acknowledgements I wish to extend my gratitude to Dr. Wei Xiang of the Faculty of Engineering and Surveying, University of Southern Queensland, as my supervisor and for his timely and dedicated assistance throughout the conduct of this project and dissertation. Without his knowledge, experience and supervision, completion of this task would have been much more difficult. Special thanks are also due to my father Mazharul Hasan Khan and my mother Yasmeen Ahmed for their moral support. iv Contents Page Abstract............................................................................................................................... i Certification...................................................................................................................... iii Acknowledgements........................................................................................................... iv Contents ..............................................................................................................................v List of Figures................................................................................................................. viii List of Tables ......................................................................................................................x List of Appendices........................................................................................................... xii Chapter 1 Introduction.....................................................................................................1 1.1 Wireless communications ....................................................................................2 1.1.1 Cellular communication systems .............................................................3 1.1.2 Paging systems.........................................................................................6 1.1.3 Wireless data networks ............................................................................7 1.1.4 Cordless telephony...................................................................................8 1.1.5 Satellite telephony....................................................................................9 1.1.6 Third generation systems .......................................................................10 1.2 Other applications of error control coding.........................................................10 1.2.1 Hamming codes......................................................................................11 1.2.2 The binary Golay code...........................................................................12 1.2.3 Binary cyclic codes ................................................................................12 1.3 Purpose and structure of thesis...........................................................................13 v Chapter 2 Error correction coding................................................................................15 2.1 History................................................................................................................16 2.2 Basic concepts of error correcting coding..........................................................17 2.3 Shannon capacity limit.......................................................................................19 2.4 Block codes ........................................................................................................20 2.5 Convolution codes..............................................................................................21 2.6 Concatenated codes............................................................................................23 2.7 Iterative decoding for soft decision codes..........................................................23 2.7.1 Turbo codes............................................................................................24 2.7.2 LDPC codes ...........................................................................................26 2.8 Chapter summary ...............................................................................................28 Chapter 3 Turbo codes: Encoder and decoder construction ......................................29 3.1 Constituent block codes .....................................................................................29 3.1.1 Encoding of block codes ........................................................................30 3.1.2 Systematic codes ....................................................................................31 3.2 Constituent convolution codes ...........................................................................32 3.2.1 Encoding of convolution codes..............................................................32 3.2.2 State diagram..........................................................................................33 3.2.3 Generator matrix ....................................................................................34 3.2.4 Trellis diagram .......................................................................................35 3.2.5 Punctured convolution codes .................................................................36 3.2.6 Recursive systematic codes....................................................................38 3.3 Classes of soft-input, soft- output decoding algorithms ....................................41 3.3.1 Viterbi algorithm....................................................................................41 3.3.2 Soft-output Viterbi algorithm (SOVA) ..................................................43 3.3.3 Maximum- a – Posteriori ( MAP ) algorithm.........................................45 3.3.4 Max –Log- MAP and Log- MAP algorithms.........................................49 3.4 Encoding of turbo codes.....................................................................................53 3.5 Overview of turbo decoding ..............................................................................56 3.5.1 Soft-input, soft- output decoding ...........................................................56 3.5.2 Turbo decoder schematic .......................................................................58 vi 3.5.3 Example of turbo decoding ....................................................................60 3.6 Chapter summary ...............................................................................................61 Chapter
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