Algorithms for Communications Systems and their Applications, 2nd Edition

Chapter 12Trellis coded modulation

During the 1980s, an evolution in the methods to transmit data over channels with limited bandwidth took place, giving origin to techniques for joint coding and modulation that are generally known with the name of trellis coded modulation (TCM). The main characteristic of TCM lies in joint design of modulation mapping and coding. The first article on TCM appeared in 1976 by Ungerboeck; later, a more detailed publication by the same author on the principles of TCM [1] spurred considerable interest in this topic [2–8], leading to a full development of the theory of TCM.

TCM techniques use multilevel modulation with a set of signals from a one, two, or multi‐dimensional space. The choice of the signals that generate a code sequence is determined by a finite‐state encoder. In TCM, the set of modulation signals is expanded with respect to the set used by an uncoded, i.e. without redundancy, system; in this manner, it is possible to introduce redundancy in the transmitted signal without widening the bandwidth. At the receiver, the signals in the presence of additive noise and channel distortion are decoded by a maximum‐likelihood sequence decoder. By simple TCM techniques using a four‐state encoder, it is possible to obtain a coding gain of 3 dB with respect to conventional uncoded modulation; with more sophisticated TCM techniques, coding gains of 6 dB or more can be achieved (see Chapter 6).

Errors in the decoding of the received signal sequence ...