Coding Theory

• Published in: Handbook of Discrete and Combinatorial Mathematics pp. 1023 - 1068
• Main Authors: Menezes, Alfred J., van Oorschot, Paul C., Joyner, David, Shaska, Tony, Shier, Douglas R., Goddard, Wayne
• Format: Book Chapter
• Language: English
• Published: United Kingdom CRC Press 2018; CRC Press LLC
• Edition: 2
• Subjects: Discrete mathematics; Prefix Code; Parity Check Matrix; RS Code; Reed Muller Code; Coset Leader; Received Word; BSC; Finite Field GF; Generator Matrix; Symbol Error Probability; Maximum Likelihood Decoding; Generator Polynomial; Decoding Algorithm; Nordstrom Robinson Code; Linear Code; Reed Solomon Codes; ECC; BCH Code; Convolutional Codes; Hamming Code; Golay Code; MDS Code; Cyclic Code; Turbo Codes; Block Codes
• ISBN: 158488780X; 9781584887805
• DOI: 10.1201/9781315156484-14

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.