Error Correction Coding, 2nd Edition

Chapter 1A Context for Error Correction Coding

I will make weak things become strong unto them

—Ether 12:27

he denies that any error in the machine is responsible for the so‐called errors in the answers. He claims that the Machines are self correcting and that it would violate the fundamental laws of nature for an error to exist in the circuits of relays.

—Isaac Asimov I, Robot

1.1 Purpose of This Book

Error control coding in the context of digital communication has a history dating back to the middle of the twentieth century. In recent years, the field has been revolutionized by codes which are capable of approaching the theoretical limits of performance, the channel capacity. This has been impelled by a trend away from purely combinatoric and discrete approaches to coding theory toward codes which are more closely tied to a physical channel and soft decoding techniques. The purpose of this book is to present error correction and detection coding covering both traditional concepts thoroughly as well as modern developments in soft‐decision and iteratively decoded codes and recent decoding algorithms for algebraic codes. An attempt has been made to maintain some degree of balance between the mathematics and their engineering implications by presenting both the mathematical ...