## Trellis-Coded Modulation

Trellis-coded modulation (TCM) is a baseband modulation technique in which the message modulates the phase of a constant amplitude signal. The transmitted signal is created by convolutionally encoding the binary input signal and mapping the result to a signal constellation. At the receiver, the modulated signal uses the Viterbi algorithm to decode TCM modulated signals.

For a k/n convolutional code, n bits map to a signal constellation. k is the number of input bits and n is the number of output bits from the convolutional encoder, with M = 2n being the modulation order for the constellation type used.

Communications Toolbox™ software includes these modulation and demodulation System objects and blocks to model general TCM, M-PSK TCM, and rectangular QAM TCM.

FunctionsSystem objectsBlocks
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### General QAM TCM

The general TCM method convolutionally encodes the binary input signal and maps the result to an arbitrary signal constellation. You define the signal constellation points as an ordered set partition with an M-element vector of complex values. The modulation order, M=2n, where n is the number of output bits from the convolutional encoder.

### PSK TCM

The PSK TCM method convolutionally encodes the binary input signal and maps the result to an M-PSK signal constellation. The PSK modulation order (or M-ary number), M = 2n, where n is the number of output bits from the convolutional encoder.

### Rectangular QAM TCM

The rectangular QAM TCM method convolutionally encodes the binary input signal and maps the result to a QAM signal constellation. The QAM modulation order (or M-ary number), M = 2n, where n is the number of output bits from the convolutional encoder.

## References

[1] Biglieri, E., D. Divsalar, P.J. McLane, and M.K. Simon, Introduction to Trellis-Coded Modulation with Applications, New York, Macmillan, 1991.

[2] Proakis, John G. Digital Communications. 5th ed. New York: McGraw Hill, 2007.

[3] Ungerboeck, G. “Channel Coding with Multilevel/Phase Signals,” IEEE Transactions on Information Theory, Vol. IT28, Jan. 1982, pp. 55–67.