Algebraic Coding and Digital Redundancy

The techniques of coding theory are used to improve the reliability of digital devices. Redundancy is added to the device by the addition of extra digits which are independently computed from the input digits. A decoding device examines the original outputs along with the redundant outputs. The decoder may correct any errors it detects, not correct but locate the defective logic gate or subsystem, or only issue a general error warning. Majority voting and parity bit checking are introduced, and computations are made for several binary addition circuits. A detailed summary of coding theory is presented. This includes a discussion of algebraic codes, binary group codes, nonbinary linear codes, and error locating codes.