Error Correction Coding, 2nd Edition

Chapter 13Trellis‐Coded Modulation

13.1 Adding Redundancy by Adding Signals

The error‐correction codes studied up to this point in the book have added redundancy by increasing the number of coded symbols. If the channel is bandlimited so that the transmitted symbol rate is fixed, this results in a lower information transmission rate. In the very common case that the high transmission rate is of interest (in contrast to minimizing transmission power), this reduction in effective information rate is unfortunate. Up until the early 1970s it was believed that coding would not greatly benefit channels needing a spectral efficiency — the number of bits transmitted per channel use — exceeding 1.

In 1976, a new method of coding was introduced by Ungerboeck which adds redundancy to the coded signal by increasing the number of symbols in the signal constellation employed in the modulation. If the average signal energy is fixed, having more signals in the signal constellation would tend to decrease the distance between points in the signal constellation. The key, therefore, is to combine the coding and modulation into a single unit which transmits only constrained sequences of symbols, and to employ a sequence detector (i.e., Viterbi algorithm) to detect the sequence. The combination of constrained symbol sequences and larger signal constellation gives rise to what is known as trellis coded modulation, or TCM.

13.2 Background on Signal Constellations

Because TCM is built upon signal ...