Coding Theory - Menezes, Alfred J.; van Oorschot, Paul C.; Joyner, David; Shaska, Tony; Shier, Douglas R.; Goddard, Wayne (Handbook of Discrete and Combinatorial Mathematics, 2018)
This chapter deals with techniques for the efficient and reliable transmission of data over communications channels that may be subject to non-malicious errors. The general topic areas related to these techniques are information theory and coding theory. Information theory is concerned with the mathematical theory of communication, and includes the study of redundancy and the underlying limits of communications channels. Coding theory deals with the translation between source data representations and the corresponding representative symbols used to transmit source data over a communications channel, or store this data. Error-correcting coding is the part of coding theory that adds systematic redundancy to messages to allow transmission errors not only to be detected, but also to be corrected. Coding theory is the subject devoted to the theory of error-correcting codes. With digital communications and digital storage media ubiquitous in the modern world, error-correcting codes have grown in importance.