An unparalleled learning tool and guide to error correction coding Error correction coding techniques allow the detection and correction of errors occurring during the transmission of data in digital communication systems. These techniques are nearly universally employed in modern communication systems, and are thus an important component of the modern information economy. Error Correction Coding: Mathematical Methods and Algorithms provides a comprehensive introduction to both the theoretical and practical aspects of error correction coding, with a presentation suitable for a wide variety of audiences, including graduate students in electrical engineering, mathematics, or computer science. The pedagogy is arranged so that the mathematical concepts are presented incrementally, followed immediately by applications to coding. A large number of exercises expand and deepen students' understanding. A unique feature of the book is a set of programming laboratories, supplemented with over 250 programs and functions on an associated Web site, which provides hands-on experience and a better understanding of the material. These laboratories lead students through the implementation and evaluation of Hamming codes, CRC codes, BCH and R-S codes, convolutional codes, turbo codes, and LDPC codes. This text offers both "classical" coding theory-such as Hamming, BCH, Reed-Solomon, Reed-Muller, and convolutional codes-as well as modern codes and decoding methods, including turbo codes, LDPC codes, repeat-accumulate codes, space time codes, factor graphs, soft-decision decoding, Guruswami-Sudan decoding, EXIT charts, and iterative decoding. Theoretical complements on performance and bounds are presented. Coding is also put into its communications and information theoretic context and connections are drawn to public key cryptosystems. Ideal as a classroom resource and a professional reference, this thorough guide will benefit electrical and computer engineers, mathematicians, students, researchers, and scientists. An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.
This book is open access under a CC BY 4.0 license. This book discusses both the theory and practical applications of self-correcting data, commonly known as error-correcting codes.
Among these are the elimination of intersymbol interference caused by filtering and multipath and the improved demodulation of certain frequency modulated signals by taking advantage of the "natural" coding provided by a continuous phase.
Fundamentals of Error Correcting Codes is an in-depth introduction to coding theory from both an engineering and mathematical viewpoint.
Exercises are placed within the main body of the text to encourage active participation by the reader, with comprehensive solutions provided.Error Correcting Codes will appeal to undergraduate students in pure and applied mathematical ...
An accessible textbook that uses step-by-step explanations, relatively easy mathematics and numerous examples to aid student understanding.
5. 2 Rings and Ideals 148 5. 3 Ideals and Cyclic Subspaces 152 5. 4 Generator Matrices and Parity-Check Matrices 159 5. 5 Encoding Cyclic Codest 163 5. 6 Syndromes and Simple Decoding Procedures 168 5. 7 Burst Error Correcting 175 5. 8 ...
This book starts by establishing the basic linear network error correction (LNEC) model and then characterizes two equivalent descriptions.
Error-correcting Coding Theory
This text offers an introduction to error-correcting linear codes for researchers and graduate students in mathematics, computer science and engineering.
Building on the success of the first edition, which offered a practical introductory approach to the techniques of error concealment, this book, now fully revised and updated, provides a comprehensive treatment of the subject and includes a ...