Versatile Error-Control Coding Systems

$NC research reported in this thesis is in the field of error-correcting codes, which has evolved as a very important branch of information theory. The main use of error-correcting codes is to increase the reliability of digital data transmitted through a noisy environment. There are, sometimes, alternative ways of increasing the reliability of data transmission, but coding methods are now competitive in cost and complexity in many cases because of recent advances in technology. The first two chapters of this thesis introduce the subject of error-correcting codes, review some of the published literature in this field and discuss the advan­tages of various coding techniques. After presenting linear block codes attention is from then on concentrated on cyclic codes, which is the subject of Chapter 3. The first part of Chapter 3 presents the mathemati­cal background necessary for the study of cyclic codes and examines existing methods of encoding and their practical implementation. In the second part of Chapter 3 various ways of decoding cyclic codes are studied and from these considerations, a general decoder for cyclic codes is devised and is presented in Chapter 4. Also, a review of the principal classes of cyclic codes is presented. Chapter 4 describes an experimental system constructed for measuring the performance of cyclic codes initially RC5GI5SCD by random errors and then by bursts of errors. Simulated channels are used both for random and burst errors. A computer simulation of the whole system was made in order to verify the accuracy of the experimental results obtained. Chapter 5 presents the various results obtained with the experimental system and by computer simulation, which allow a comparison of the efficiency of various cyclic codes to be made. Finally, Chapter 6 summarises and dis­cusses the main results of the research and suggests interesting points for future investigation in the area. The main objective of this research is to contribute towards the solution of a fairly wide range of problems arising in the design of efficient coding schemes for practical applications; i.e. a study of coding from an engineering point of view.