Error Detection and Correction Codes

Diego L. Gonzalez

Abstract This article presents an elementary introduction to the encoding methods used for error detection and correction in communication processes. These methods have been developed following the pioneering work of Claude Shannon in the 1940s that founded Information Theory. Information theory studies in mathematical terms how to transmit messages in a reliable way using communication channels that necessarily introduce "noise" or errors in the messages. The key point for the implementation of error-free communication is the encoding of the information to be transmitted in such a way that: (a) some extent of redundancy is included in the encoded data, and (b) a method for efficient decoding at the receiver is available. These two requirements together usually imply that the data to be transmitted need to be mathematically organized, often following principles borrowed from discrete group theory. In this article a review of encoding methods so far developed for this end is given.

Just as it is clear that error-correcting coding methods represent a key feature for the development of successful practical communication technologies, it is also becoming ever more clear that living organisms need to resort to analogous strategies for optimizing the flux and integrity of biological information. In addition to the general theoretical constraints which every communication system needs to obey, the possible role of such error detection and correction codes in biological (genetic and neural) systems is briefly discussed here, and a new possibility for implementing error detection and correction based on generic properties of nonlinear dynamical systems and their associated symbolic dynamics is presented.

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