Error Correction Coding and Decoding : Bounds Codes Decoders Analysis and Applications Part I: Theoretical Performance of Error Correcting Codes Bounds on Error Correction Coding Performance Soft and Hard Decision Decoding Performance Soft Decision and Quantised Soft Decision Decoding Part II: Code Construction Cyclotomic Cosets The Mattson Solomon Polynomial Idempotents and Cyclic Codes Good Binary Linear Codes Lagrange Codes Extended BCH Reed Solomon Codes Algebraic Geometry Codes Algebraic Quasi Cyclic Codes Convolutional Codes: A Historical Perspective Aalogue BCH Codes LDPC Codes Part III: Analysis of Codes True Search for Stopping Sets for LDPC Codes Part IV: Decoders Erasures and Error Correcting Codes The Modified Dorsch Decoder A Concatenated Error Correction System Using the |u|u+v| Code Construction Part V: Applications Combined Error Detection and Error Correction Password Correction and Confidential Information Access System Variations on the McEliece Public Key Encryption System Error Correcting Codes and Dirty Paper Coding 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 book is open access under a CC BY 4.0 license