CODING AND MODULATION FOR BANDWIDTH COMPRESSION OF TELEVISION AND FACSIMILE SIGNALS. A thesis submitted for the degree of Doctor of Philosophy by PIOTR WLADYSLAW JOZta BYLANSKI Imperial College, University of London. 1966. 2. ABSTRACT Two aspects relevant to the coding of picture signals with a view to compression of signal bandwidth are considered. Firstly: the problem of combining the information associated with the run length representation of the picture signal, for transmission over a practical channel, is studied. A solution is proposed in terms of combined amplitude and phase modulation and an analysis is presented which demonstrates the feasibility of the technique. Secondly, several aspects of the digram representation of the picture signal are studied. The second order redundancy is experimentally determined using a digital technique. The results obtained lead to the design of several simple and efficient digram -based codes for black and white facsimile pictures, result- ing in useful reduction of signal bandwidth. These codes are implemented and assessed experimentally. An adaptive encoding technique is proposed whereby errors produced by a non-uniquely decodable code may be minimised in a controlled way by the use of predictive feedback at the encoder. 3. CONTENTS. Item Page ABSTRACT 2 CONTENTS 3 LIST OF SYMBOLS AND ABBREVIATIONS 6 ACKNOWLEDGEMENTS 9 CHAPTER. 1. INTRODUCTION 10 141 The Trend of Modern Communications. 10 1.2 Visual Redundancy. 11 1.3 Signal Compression. 13 1.4 Television and Facsimile Communication. 16 1,5 The Organisation of the Material of this Work. 18 1.6 Summaries of Individual Chapters. 19 CHAPTER 2. THE PROBLEM OF CHANNEL UTILISATION. 21 2.1 Bandwidth Compression. 21 2.2 The Run Length Coding System. 24 2.3 The Channel Utilisation Problem. 29 2.4 On Efficiency of Communication, 32 2.5 Possible Modulation and Coding Systems. 36 2.6 Digram Encoding, Error Rates and Channel Distortion. 45 2.7 Combined Amplitude and Phase Modulation. 50 2.8 Conclusions. 52 CHAPTER 3. ANALYSIS OF COMBINED AMPLITUDE AND PHASE MODULATION OF THE PIMEt SIGNAL. 56 3.1 Objectives. 56 Page 3.2 On the Spectra of Angle Modulated Processes. 58 3.3 The Method of Analysis due to N. Abramson. 60 3.4 Spectral Computations. 64 3.5 Effects of Band Limiting. 70 3,6 Precoding of the Position Signal. 73 3,7 Compatibility with Known Requirements. 79 3.8 Summary and Conclusions. 81 CHAPTER 4, MEASUREMENT OF DIGRAM STATISTICS OF PICTURE SIGNALS. 83 4.1 Statistical Redundancy: 83 4.2 Calculation of Redundancy from Limited Statistics, 87 4.3 The Experiment. 92 4.4 Apparatus. 99 4.5 Results. 105 4.6 Conclusions and Discussion. 112 CHAPTER 5, INVESTIGATIONS INTO DIGRAM CODES. 116 5.1 Encoding of Black and White Signals. 116 5.2 Coding Theory Implications. 124 5.3 Experiments with Restriction of the Digram Alphabet. 130 5.4 A Restricted Alphabet Digram Code. 143 CHAPTER 6•. ADAPTIVE ENCODING. 145 6.1 A Specific Example. 145 6.2 An Adaptive Encoding Technique. 147 Page 6.3 Transmission Considerations. 151 6.4 A Proposed Adaptive Code. 159 SUMMARY OF CONCLUSIONS 3.65 REFERENCES 3.68 APPENDICES 172 Error Probability of Quantised Signal in Gaussian Noise. 172 The Decodability of Combined Amplitude and Phase Modulation. 171+ Autocorrelation Fianction of Combined Amplitude and Phase Modulation, 176 Table of Spectral Functions of Sec. 3.4. 180 Circuit Details of Digram Encoder. 181 6. LIST OF SYMBOLS AND ABBREVIATIONS AN Amplitude modulation. B - Message bandwidth. Sanders' efficiency index. C - Channel capacity, bits or bits/sec. cps cycles per second. db decibels, d,c. direct current, 8 Quantal amplitude step. 8(x) Impulse function, 80 Quantal phase step. aT Sampling interval. D(t) = R(t) R(o) G(N) Gaussian density function of variance N. Kc Kilocycles per second, L - Average code word length. M - Number of message states or signal levels.. Mc Megacycles per second. N - Mean noise energy. nsec Nanosecond, 10-9 sec. P Mean signal energy. P Peak signal energy. pps Pulses per second, p(e) Probability of error. PM Phase modulation. 7. PCM Pulse code modulation. P-signal Position signal. R(t) Autocorrelation function. r(t) Normalised autocorrelation function. r Data compression factor. Information rate bits/sec. R, First order redundancy, bits. R 2 Second order redundancy, bits. S/N Signal to noise ratio, general term. s(t) Channel signal. SSB Single sideband. a r.m.s. noise. )( Characteristic function. VSB Vestigial sideband. Vsignal - Compressed video signal. W - Channel bandwidth. W(f) Power density spectrum. w(f) Normalised power density spectrum. Denotes convolution. Notation used for ensembles [X) - the set of symbols tx,,x2 xk..xm] P(X) the set of simple (first order) probabilities associated with the set X. P(X/Y) - the set of conditional probabilities associated with the sets X and Y. H(X) the entropy measure associated with the set X; arbitrary units. Hr(X) entropy expressed in units to the base r. H(XN) entropy associated with the N-th extension of X. E(X) expectation of X. Summation convention: i=M :Ef(X) - f(xi) X i=1 and i=M f()(4Y f(xi XY i=1 Boolean Logic Notation Denoting the binary input symbols by a and b the notation is as follows: a + b = a OR b , signifying Boolean addition, a.b a AND b, signifying Boolean multiplication. a = NOT a , signifying Boolean negation. In block diagrams logic gates are shown as triangles, the OR and AND functions being denoted by a plus sign and a dot respectively, in the centre of the triangle. A slanting line inside the triangle adjacent to any input denotes negation of that input. 9. ACKNOWLEDGEMENTS The author wishes to express his gratitude to his supervisor, Professor E. C. Cherry, for his guidance and encouragement and for the tedious task of ensuring funds for the research. Thanks are due to the following bodies for providing personal financial support: the Department of Scientific and Industrial Research in particular, for providing a research scholarship for most of the duration of the work; the Institution of Electrical Engineers for granting an Oliver Lodge scholarship,and the Racal Co. Ltd., for a bursary during the final difficult period. Help from the National Research Development Council in financing the project is also appreciated. I am deeply indebted to Mr. R. E. C. White for undertaking the laborious task of reading, correcting and criticising the manuscript. Thanks are also due to Mr. A. M. Maciejowski for reading part of the manuscript. The cooperation of my colleagues is also appreciated; much useful information was acquired in informal discussions, especially with Messrs. D. J. Goodman, L. S. Moye, D. E. Pearson, A. H. Robinson, R. Thomas, B. J. Vieri, R. E. C. White and A. A. White. Thanks are also due to Mrs. J. Dean for truly expert despatch of the manuscript and to Miss E. Krzysztoforska for much time devoted to this work. Finally I would like to thank my mother for constant encouragement. 10. CHAPTER 1 INTRODUCTION 1.1 THE TREND OF MODERN COMMUNICATIONS The development in recent years of the theory of communication based on statistical concepts has contributed to a changing approach in the treatment of communication systems. The pioneering work of Shannon (42) on information transfer, and Wiener (48) on the optimum filtering of signals, have enabled a new overall understanding of existing systems and provided basic theoretical criteria for the synthesis of new ones. Hitherto the communications engineer has been absorbed in the pursuit of systems which are at the same time both efficient and simple. The statistical theory of communication has brought to light the basic fact that, in general, increased efficiency can only be bought at the price of increased complexity. This fact emerges directly from the coding theorems of Information Theory and is all the harder since the pursuit of efficiency hass to a great extent, been urged by the new appreciation of the basic inefficiency of some existing systems, made possible only by the tools provided by the very same theory. The appreciation of the fundamental dicta of communication theory has led to significant changes in attitude to communication problems. No longer is there an ingrained fear of growing complexity, a fear 11. previously arising from an unknown but suspected law of diminishing returns; the situation is now one where the returns are fully under- stood in the light of Information Theory. Thus, bold and ingenious systems have evolved; significant examples are pulse code modulation, digital transmission systems, colour television, pseudo-noise radar and many other systems of a more specialised nature. 1.2 VISUAL REDUNDANCY The ability to define and measure information and the com- plementary quantity known as redundancy, have prompted the search for methods of optimising communication. This may be achieved by the exploitation of the natural redundancy which exists in many communication systems, especially those which have a human destina- tion. In such cases the information transferred is either visual or auditory and a great deal of redundancy is involved. Present day conventional monochrome television systems use a channel capable 6 of transmitting about 50.10 bits of information per second. Measure.. ments on human subjects (Pierce and Karlin, 31) indicate a human information transfer capacity of only about 50 bits per second. The discrepancy or mismatch involved is enormous, and a great deal of redundant information is thus transmitted over a costly commodity - the communication channel. Efforts to decrease this visual re- dundancy by more efficient encoding seem, therefore, to be well 12. justified. Visual redundancy may be divided into two classes; perceptual and statistical redundancy. The process of communicating a picture to a human viewer is exceedingly complex and insufficiently under- stood.