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Trellis-Coded Modulation (TCM) is a technique which combines channel coding and modulation for the transmission of digital signals over bandlimited channels. The basic idea is to use signal-set expansion to provide redundancy for coding, and to design coding and signal-mapping functions jointly so as to maximize directly the minimum Euclidean distance between coded signal sequences. The coding gain is achieved without sacrificing data rate or expanding bandwidth at the expense of increasing decoder complexity. Simple TCM schemes with 2 to 8 states can provide asymptotic coding gains of 3 dB compared to uncoded modulation. With more complex schemes, asymptotic coding gains of 6 dB can be realized. This paper describes the general principle and performance of conventional TCM schemes and the methods for maximizing such performance. Additional 1 to 2 dB gain can be obtained by introducing asymmetry to signal constellation or by transmitting multiple symbols per state transition. Performance improvement and drawbacks of these schemes are also discussed. The important effects of carrier-phase offset are presented. Problems arise when a carrier-modulated TCM signal is demodulated with a phase offset which could be caused by the inability of the phase-tracking scheme of the receiver to track phase disturbances instantly. Several concepts relating to the application of soft-decision maximum-likelihood Viterbi decoder are discussed. An example of soft-decision decoding of M-ary signals is also presented.