Introduction to Error Control Codes

This textbook provides a firm foundation to the field of error control codes, leading the student step by step through this complex topic, beginning with single parity code checks and repetition codes. Through these basic error-control mechanisms the fundamental principles of error detection and correction, minimum distance and error-control limits are considered. The reader is guided from basic error-control codes through to linear codes, cyclic codes, linear feedback shift registers, vector fields, Galois fields, BCH codes and convolutional codes. Complex mathematical proofs are omitted where possible to keep the text concise and easy-to-follow. Additional notes on the contents: *Chapter 2 the treatment of linear codes in this chapter avoids reference to vector spaces, enabling the reader to gain an understanding of linear codes sufficient to move onto cyclic codes without the distraction of the complexity of vector spaces. *Chapter 5 considers vector spaces and revisits linear codes in the context of vector spaces. *Chapter 6 starts with the ordinary concepts of sets and gently leads the reader through the principles of groups and fields, the end goal being an understanding of Galois fields that will enable the reader to understand the BCH codes considered in Chapter 7.