References & Further Reading

References

  1. G. Ungerboeck, Channel Coding with Multilevel/Phase Signals, 1982

    The founding paper of trellis-coded modulation. Establishes set-partitioning, the Ungerboeck design rules, and the canonical 4/8/16-state 8-PSK codes used throughout this chapter. Essential reading.

  2. G. Ungerboeck, Trellis-Coded Modulation with Redundant Signal Sets — Part I: Introduction, 1987

    A lucid, tutorial companion to the 1982 paper. Part I introduces set partitioning and the motivation for TCM from a system perspective; best starting point for newcomers.

  3. G. Ungerboeck, Trellis-Coded Modulation with Redundant Signal Sets — Part II: State of the Art, 1987

    Part II surveys TCM performance in fading and non-AWGN channels and previews rotationally invariant codes used in V.32.

  4. G. D. Forney Jr. and G. Ungerboeck, Modulation and Coding for Linear Gaussian Channels, 1998

    The definitive retrospective on modulation and coding. Unifies TCM, MLC, BICM, and coset codes under a single geometric framework. Sections on coding gain and shaping gain are particularly useful.

  5. A. J. Viterbi, Convolutional Codes and Their Performance in Communication Systems, 1971

    Viterbi's paper introducing the algorithm that decodes all trellis codes — including TCM. Pair with Forney 1973 for the survey view.

  6. G. D. Forney Jr., The Viterbi Algorithm, 1973

    The canonical tutorial treatment of the Viterbi algorithm as dynamic programming on a trellis. Indispensable background for this chapter's Section 4.

  7. L.-F. Wei, Rotationally Invariant Convolutional Channel Coding with Expanded Signal Space — Part II: Nonlinear Codes, 1984

    The codes adopted in ITU-T Recommendation V.32 (9.6 kbps voiceband modem, 1984). Wei's construction resolves the phase-ambiguity issue that plagued Ungerboeck's original TCM for PSK.

  8. ITU-T, Recommendation V.34: A modem operating at data signalling rates of up to 33 600 bit/s for use on the general switched telephone network and on leased point-to-point 2-wire telephone-type circuits, International Telecommunication Union, Telecommunication Standardization Sector, 1998

    The V.34 modem standard. Uses a 4-dimensional TCM with 16 states combined with shell mapping for shaping gain, achieving roughly 1 dB of the 1.53 dB shaping ceiling. Cited for the engineering note on V.32/V.34.

  9. G. Caire, G. Taricco, and E. Biglieri, Bit-Interleaved Coded Modulation, 1998

    The BICM paper. Introduces the paradigm that supersedes TCM in wireless standards. Cited here as the forward reference from Chapter 5, where the full CommIT contribution is developed.

  10. E. Biglieri, Coding for Wireless Channels, Springer, 2005

    Chapters 6–7 provide a thorough graduate-level treatment of TCM on fading channels, including the interleaving and diversity considerations that motivate the move to BICM.

  11. J. G. Proakis and M. Salehi, Digital Communications, McGraw-Hill, 5th ed., 2008

    Chapter 8 gives a self-contained TCM treatment with worked examples. The table of $d_{\\text{free}}^2$ values for Ungerboeck 8-PSK TCM at 4, 8, 16, 32, 64 states is taken from here.

Further Reading

For readers who want to go deeper into specific aspects of trellis- coded modulation and its descendants.

  • Rotationally invariant TCM and V.32

    L.-F. Wei, "Rotationally Invariant Convolutional Channel Coding with Expanded Signal Space — Part I: 180°," IEEE JSAC, vol. 2, no. 5, pp. 659–671, 1984

    Part I of the companion to the reference above. Essential for understanding why V.32 chose a specific 8-state nonlinear code over Ungerboeck's original linear 8-state design.

  • TCM on fading channels

    D. Divsalar and M. K. Simon, "Multiple trellis coded modulation (MTCM)," IEEE Trans. Commun., vol. 36, no. 4, pp. 410–419, 1988

    The extension of TCM to fading channels by coding over several symbol intervals at once. Exposes the diversity weakness of plain TCM that BICM eventually fixes.

  • TCM in DVB-T and cable standards

    U. Reimers, "DVB — The Family of International Standards for Digital Video Broadcasting," Proc. IEEE, vol. 94, no. 1, pp. 173–182, 2006

    Brief overview of how TCM and concatenated codes were used in DVB-T (1997) before LDPC-based BICM replaced them in DVB-S2 (2005) and DVB-T2 (2008).

  • Lattice view of TCM

    G. D. Forney Jr., "Coset Codes — Part I: Introduction and Geometrical Classification," IEEE Trans. Inf. Theory, vol. 34, no. 5, pp. 1123–1151, 1988

    Forney's reformulation of Ungerboeck's set-partitioned codes as coset codes over lattice partitions. Required background for Chapter 4 of this book and for the lattice-code chapters in Part IV.

  • TCM in 4D and 8D signal spaces

    L.-F. Wei, "Trellis-coded modulation with multidimensional constellations," IEEE Trans. Inf. Theory, vol. 33, no. 4, pp. 483–501, 1987

    Higher-dimensional TCM constructions used in V.34 and early ADSL. Shows how multidimensional signalling beats 2D TCM at the same spectral efficiency.

ExercisesCh 3 →