Error‐Correcting Codes

Systems for information processing and transmission constitute a major field of application for signal‐processing techniques. Error‐detection and correction techniques are also widely used in these systems and, therefore, they coexist and even interact with signal processing in communication equipment. This chapter provides an introduction to some important error‐correcting codes from a signal‐processing perspective, allowing readers to gain an understanding of these codes and assess their strengths and weaknesses. Reed–Solomon codes exploit predictable signals generated by line errors to identify these errors and subtract them from the received signal so as to recover the transmitted signal. Convolutional coding of a sequence of symbols consists of introducing redundancy into the sequence and correlation between symbols. An approach to cope with error packets consists of cascading the convolutional decoder with an interleaver and a Reed–Solomon decoder. Turbo codes combine recursive filtering, interleaving, and an iterative procedure.