Performance of Error-Correcting Channel Codes for Reliable Digital Communication

Abstract

A digital communication link carries information over a channel that corruptsit with noise, so that some of the bits received differ from those sent, anderror-correcting channel codes combat this by adding carefully structuredredundancy that lets the receiver detect and correct errors, allowing reliablecommunication at a lower signal-to-noise ratio than would otherwise beneeded. This study examines the performance of error-correcting channelcodes for reliable digital communication, by the reduction in errors theyachieve. The bit error rate was determined as a function of the signal-to-noise ratio for transmission without coding and with error-correcting codes of differing strength, and the coding gain, the reduction in the signal-to-noise ratio required to reach a given error rate, was assessed. Without coding the bit error rate fell only gradually as the signal-to-noise ratio rose, so that a high ratio was needed for reliable communication, whereas with coding the error rate fell far more steeply, reaching the same low error rate at a much lower signal-to-noise ratio, and the stronger code did so at a lower ratio still. The coding gain thus obtained means that a coded link can communicate reliably with less signal power, or over a noisier channel, than an uncoded one, at the cost of the redundancy the code adds and the processing the decoding requires. The study shows that error-correcting channel codes substantially improve the reliability of digital communication for a given signal-to-noise ratio, approaching the limit set by information theory, and it discusses the trade-off between coding gain, redundancy, and decoding complexity. KEYWORDS: Channel coding, Error-correcting codes, Bit error rate, Codinggain, Forward error correction, Convolutional codes, Digital communication,Signal-to-noise ratio, Shannon limit