With the rapid expansion of communication networks, there has been an increasing demand for efficient and reliable digital data transmission and storage systems. Many efficient codes have been developed. The LDPC code is one of them. In this thesis, the sum-product algorithm is used in the decoding of LDPC codes. Some schemes for encoding LDPC codes have been studied. In particular, two methods of producing regular H matrices have been attempted that include short cycles of length four with code rates of 0.5, and we present three schemes of finding regular H matrices which do not include short cycles of length four with code rate being 0.5. The effect of short cycles in the bipartite graph of regular LDPC codes has been considered. The simulation results show that the BER performances of regular H matrices that do not include short cycles of length four based on BPSK or 8PSK on AWGN channel is better than those of regular H matrices that include short cycles of length four. In conclusion, in order to obtain good performance with LDPC code, one should design H matrix related to bipartite graph without short cycles.

This book discusses both the theory and practical applications of self-correcting data, commonly known as error-correcting codes. The applications included demonstrate the importance of these codes in a wide range of everyday technologies, from smartphones to secure communications and transactions. Written in a readily understandable style, the book presents the authors’ twenty-five years of research organized into five parts: Part I is concerned with the theoretical performance attainable by using error correcting codes to achieve communications efficiency in digital communications systems. Part II explores the construction of error-correcting codes and explains the different families of codes and how they are designed. Techniques are described for producing the very best codes. Part III addresses the analysis of low-density parity-check (LDPC) codes, primarily to calculate their stopping sets and low-weight codeword spectrum which determines the performance of th ese codes. Part IV deals with decoders designed to realize optimum performance. Part V describes applications which include combined error correction and detection, public key cryptography using Goppa codes, correcting errors in passwords and watermarking. This book is a valuable resource for anyone interested in error-correcting codes and their applications, ranging from non-experts to professionals at the forefront of research in their field. This book is open access under a CC BY 4.0 license.

This book is devoted to one of the essential functions of modern telecommunications systems: channel coding or error correction coding. Its main topic is iteratively decoded algebraic codes, convolutional codes and concatenated codes.

Presents all of the key ideas needed to understand, design, implement and analyse iterative-based error correction schemes.

Mobile multimedia broadcasting compasses a broad range of topics including radio propagation, modulation and demodulation, error control, signal compression and coding, transport and time slicing, system on chip real-time implementation in ha- ware, software and system levels. The major goal of this technology is to bring multimedia enriched contents to handheld devices such as mobile phones, portable digital assistants, and media players through radio transmission or internet pro- col (IP) based broadband networks. Research and development of mobile multi- dia broadcasting technologies are now explosively growing and regarded as new killer applications. A number of mobile multimedia broadcasting standards related to transmission, compression and multiplexing now coexist and are being ext- sively further developed. The development and implementation of mobile multi- dia broadcasting systems are very challenging tasks and require the huge efforts of the related industry, research and regulatory authorities so as to bring the success. From an implementation design and engineering practice point of view, this book aims to be the ?rst single volume to provide a comprehensive and highly coherent treatment for multiple standards of mobile multimedia broadcasting by covering basic principles, algorithms, design trade-off, and well-compared implementation system examples. This book is organized into 4 parts with 22 chapters.