11 - Error correction

Summary

This chapter is concerned with a remarkable type of code, whose purpose is to ensure that any errors occurring during the transmission of data can be identified and automatically corrected. These codes are referred to as error-correcting codes (ECC). The field of error-correcting codes is rather involved and diverse; therefore, this chapter will only constitute a first exposure and a basic introduction of the key principles and algorithms. The two main families of ECC, linear block codes and cyclic codes, will be considered. I will then describe in further detail some specifics concerning the most popular ECC types used in both telecommunications and information technology. The last section concerns the evaluation of corrected bit-error-rates (BER), or BER improvement, after information reception and ECC decoding.

Communication channel

The communication of information through a message sequence is made over what we shall now call a communication channel or, in Shannon's terminology, a channel. This channel first comprises a source, which generates the message symbols from some alphabet. Next to the source comes an encoder, which transforms the symbols or symbol arrangements into codewords, using one of the many possible coding algorithms reviewed in Chapters 9 and 10, whose purpose is to compress the information into the smallest number of bits. Next is a transmitter, which converts the codewords into physical waveforms or signals. These signals are then propagated through a physical transmission pipe, which can be made of vacuum, air, copper wire, coaxial wire, or optical fiber.