WAVELET BASED IMAGE COMPRESSION INTEGRATING ERROR PROTECTION via ARITHMETIC CODING with FORBIDDEN SYMBOL and MAP METRIC SEQUENTIAL DECODING with ARQ RETRANSMISSION By Veruschia Mahomed BSc. (Electronic Engineering) Submitted in fulfilment of the requirements for the Degree of Master of Science in Electronic Engineering in the School of Electrical, Electronic and Computer Engineering at the University of KwaZulu-Natal, Durban December 2009 Preface The research described in this dissertation was performed at the University of KwaZulu-Natal (Howard College Campus), Durban, over the period July 2005 until January 2007 as a full time dissertation and February 2007 until July 2009 as a part time dissertation by Miss. Veruschia Mahomed under the supervision of Professor Stanley Mneney. This work has been generously sponsored by Armscor and Morwadi. I hereby declare that all the material incorporated in this dissertation is my own original unaided work except where specific acknowledgment is made by name or in the form of a reference. The work contained herein has not been submitted in whole or part for a degree at any other university. Signed : ________________________ Name : Miss. Veruschia Mahomed Date : 30 December 2009 As the candidate’s supervisor I have approved this thesis for submission. Signed : ________________________ Name : Prof. S.H. Mneney Date : ii Acknowledgements First and foremost, I wish to thank my supervisor, Professor Stanley Mneney, for his supervision, encouragement and deep insight during the course of this research and for allowing me to pursue a dissertation in a field of research that I most enjoy. His comments throughout were invaluable, constructive and insightful and his willingness to set aside his time to assist me is most appreciated. I would also like to express my sincere thanks to my dear family for their continued support, encouragement and invaluable assistance throughout this dissertation. To my parents, Si and Romona, thank you for providing me with undying support and believing in me when I myself didn’t. Thanks to my dearest sister Katy, for constantly encouraging me and forcing me to complete. Furthermore, I express my appreciation to all staff and fellow post-graduate students who have assisted me in any way and for the exciting non-work related discussions and activities. Finally, special thanks go out to the sponsor’s Armscor and Morwadi and its representatives Ms. Franzette Vorster and Mr. Peter Handley for the funding of my research and for the regular visits and discussions. iii Publications The following publications are based on the work presented in this dissertation. V. Mahomed and S.H. Mneney, “ Wavelet Based Compression: The New Still Image Compression Technique ,” Pattern Recognition Association of South Africa (PRASA), Cape Town, South Africa, Nov. 2005. V. Mahomed and S.H. Mneney, “ Wavelet Based Image Compression and Transmission over Error-Prone Channels ,” South African Telecommunications and Networking Applications Conference (SATNAC), Cape Town, South Africa, Sept. 2006. V. Mahomed and S.H. Mneney, “ Robust EZW and SPIHT via Arithmetic Coding with Forbidden Symbol and MAP Decoding ,” Pattern Recognition Association of South Africa (PRASA), Parys, South Africa, Nov. 2006. V. Mahomed and S.H. Mneney, “ Robust SPIHT via Serially Concatenated Arithmetic Coding with Convolutional Coding and Sequential Decoding ,” Military Information and Communications Symposium of South Africa (MICSSA), CSIR, Pretoria, South Africa, July 2007. iv Abstract The phenomenal growth of digital multimedia applications has forced the communications industry to re-look at the manner in which multimedia is transmitted and stored. Multimedia technology will in the future produce such high excessive volumes of data traffic that it will exceed its network capacity, thereby prompting greater focus on higher compression techniques coupled with error protection mechanisms. These techniques and mechanisms will provide an efficient multimedia transmission infrastructure needed to sustain the growth whist minimising the impact of network capacity. This dissertation describes a myriad of compression techniques for image and videos used currently, with particular focus on the industry progression towards wavelet compression. The dissertation then commences through a review of wavelets and wavelet theory fundamentals for the use of compression before proceeding to outline the advanced wavelet coding algorithms developed for efficient image and video compression. Thereafter, evaluations of the wavelet coders are assessed with recommendations of two coders, EZW and SPIHT, for use in the proposed codec as low-bitrate compression coders. The dissertation reviews and examines the wireless transmission medium as the preferred medium for error protection of the compressed bitstream. The two wireless mediums selected are the additive white Gaussian noise channel, and the Rayleigh multipath fading channel. The channels are modelled to induce errors in the compressed bitstreams whereby the proposed codec can in turn offer protection of the bitstream for successful transmission. This dissertation presents a codec offering low-bitrate compression via the use of the wavelet coding algorithms of EZW and SPIHT, combined with error protection incorporating error detection and correction to determine and process errors induced by the wireless channels. Error protection is segmented into error detection and error correction, with error detection involving integer arithmetic coding with forbidden symbol and convolutional coding, and error correction using automatic repeat request (ARQ) retransmission and maximum a posteriori (MAP) metric sequential decoding. Error detection via arithmetic coding with forbidden symbol, is able to identify errors that have been produced by noisy channel impairments and interferences during the transmission. Error correction is designed to correct, resolve and rectify the identified errors. The MAP metric sequential decoding concept is multifaceted, as it involves sequential decoding that exploits the optimal stack algorithm that uses a greedy tree search and the MAP decoding metric, which is in turn computed using a complex set of a priori and a posteriori statistical v probabilities. ARQ retransmission is used as a double error correction mechanism in the event that the MAP decoding fails; it is invoked and requests a retransmission of the erroneous bitstream. The proposed codec is then compared to current three systems arithmetic coding and decoding, convolutional coding with MAP decoding and arithmetic coding, convolutional coding with MAP decoding and arithmetic decoding, through multiple simulations focusing on image quality and erasure performances. Results show that the proposed codec is competitive and its performance surpasses three systems used in the evaluation. The proposed ARQ-MAP scheme proved better and showed greater improvement in error-free decoding than the three systems. The highly successful coupling of error detection, using the forbidden symbol and error correction using MAP metric sequential decoding showed immense potential and ability for error-free compression and transmission of images and video. vi Table of Contents Preface ii Acknowledgements iii Publications iv Abstract v Table of Contents vii List of Figures xi List of Tables xvi List of Acronyms xvii CHAPTER 1 - INTRODUCTION 20 1.1 COMPRESSION 21 1.1.1 Lossless Compression 21 1.1.2 Lossy Compression 22 1.2 WAVELETS 23 1.3 ERROR RESILIENCE 23 1.4 LAYOUT of DISSERTATION 25 1.5 EXECUTIVE SUMMARY 27 CHAPTER 2 - CURRENT COMPRESSION STANDARDS 29 2.1 STILL IMAGE COMPRESSION 29 2.1.1 JPEG 29 2.1.2 JPEG 2000 32 2.2 VIDEO COMPRESSION 34 2.2.1 MPEG 34 2.2.2 MPEG4 36 2.2.3 H.263+ 39 2.2.4 H.264 / MPEG4 part 10 AVC 40 2.3 PERFORMANCE METRICS 41 2.4 PERFORMANCE 43 2.4.1 Still Image Compression Standards 43 2.4.2 Video compression Standards 46 2.5 SUMMARY 47 CHAPTER 3 - WAVELET COMPRESSION 48 3.1 WAVELET THEORY 48 3.1.1 Fourier Transform 48 vii 3.1.2 Wavelet Transform 49 3.1.3 Discrete Wavelet Transform 51 3.1.4 Filter Banks 52 3.1.5 Subband Coding 54 3.1.6 Multi-resolution Analysis 54 3.1.7 Fast Wavelet Transform 57 3.2 WAVELET FAMILIES 62 3.2.1 Haar Wavelet 64 3.2.2 Daubechies Wavelet 64 3.2.3 Coiflet Wavelet 65 3.2.4 Symlet Wavelet 66 3.2.5 Meyer Wavelet 66 3.2.6 Morlet Wavelet 67 3.2.7 Mexican Hat Wavelet 67 3.2.8 Wavelet Family Properties 68 3.3 WAVELET IMAGE CODING 70 3.3.1 Embedded Zerotree Wavelet 70 3.3.2 Set Partitioning in Hierarchical Trees 74 3.3.3 Space Frequency Quantisation 76 3.3.4 Stack-Run Image Coding 77 3.3.5 Embedded Conditional Entropy Coding of Wavelet Coefficients 78 3.4 PERFORMANCE 80 3.4.1 Various Wavelet Coding Schemes 80 3.4.2 EZW and SPIHT 81 3.5 SUMMARY 85 CHAPTER 4 - WIRELESS CHANNELS 87 4.1 ADDITIVE WHITE GAUSSIAN NOISE CHANNEL MODEL 87 4.2 MULTIPATH FADING CHANNELS 89 4.3 PATH LOSS 90 4.4 SHADOWING 90 4.5 FADING CHANNELS 91 4.5.1 Large Scale Fading Channels 91 4.5.2 Small Scale Fading Channels 92 4.5.3 Flat Fading Channels 92 4.5.4 Frequency-Selective Fading Channels 93 4.5.5 Fast Fading Channels 94 4.5.6 Slow Fading Channels 94 viii 4.6 RAYLEIGH MULTIPATH FADING CHANNEL MODEL 95 4.7 PERFORMANCE 96 4.7.1 Theoretical AWGN Channel 98 4.7.2 Theoretical Rayleigh Multipath Fading Channel 99 4.7.3 EZW and SPIHT over AWGN Channel 99 4.7.4 EZW and SPIHT over Rayleigh Multipath Fading Channel 102 4.8 SUMMARY 105 CHAPTER 5 - ERROR PROTECTION 106 5.1 ERROR DETECTION USING ARITHMETIC CODING WITH FORBIDDEN