A profusion and variety of communication systems, which carry massive amounts of digital data between terminals and data users of many kinds, exist today. Alongside these communication systems are many different magnetic tape storage systems, and magnetic and optical disk storage systems. The received signal in any communication or recording system is always contaminated by thermal noise and, in practice, may also be contaminated by various kinds of defects, nongaussian noise, burst noise, interference, fading, dispersion, cross talk, and packet loss. The communication system or storage system must transmit its data with very high reliability in the presence of these channel impairments. Bit error rates as small as one bit error in 1012 bits (or even smaller) are routinely specified.

Primitive communication and storage systems may seek to keep bit error rates small by the simple expedient of transmitting high signal power or by repeating the message. These simplistic techniques may be adequate if the required bit error rate is not too stringent, or if the data rate is low, and if errors are caused by noise rather than by defects or interference. Such systems, however, buy performance with the least expendable resources: Power and bandwidth.

In contrast, modern communication and storage systems obtain high performance via the use of elaborate message structures with complex cross-checks built into the waveform. The advantage of these modern communication waveforms is that high data rates can be reliably transmitted while keeping the transmitted power and spectral bandwidth small.