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 these 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 work was published by saint philip street press pursuant to a creative commons license permitting commercial use. all rights not granted by the work's license are retained by the author or authors.