References & Further Reading

References

  1. H. Imai and S. Hirasawa, A new multilevel coding method using error-correcting codes, 1977

    The original MLC paper. Introduces the idea of using separate binary codes per partition level combined by a partition-based labelling. Predates Ungerboeck's TCM by five years but received less industrial attention until Wachsmann et al. reconnected it to modern coding theory.

  2. U. Wachsmann, R. F. H. Fischer, and J. B. Huber, Multilevel codes: theoretical concepts and practical design rules, 1999

    The definitive modern reference for MLC/MSD. Proves the capacity rule from the chain rule of mutual information, gives quantitative design tables, analyses error propagation, and compares MLC against BICM. Every serious study of coded modulation should read this.

  3. G. Ungerboeck, Channel coding with multilevel/phase signals, 1982

    Ungerboeck's foundational TCM paper. Establishes the set-partitioning principle that MLC (this chapter) and TCM (Chapter 2) both rely on.

  4. G. D. Forney Jr. and G. Ungerboeck, Modulation and coding for linear Gaussian channels, 1998

    A sweeping survey of coded modulation for the Gaussian channel, with a careful treatment of the capacity rule and the relationships between TCM, MLC, and BICM. Essential reading.

  5. G. Caire, G. Taricco, and E. Biglieri, Bit-interleaved coded modulation, 1998

    The foundational BICM paper. Introduces the independent-parallel- channels model, proves the BICM capacity formula, and establishes Gray-labelling + powerful binary code as the design rule for modern wireless modems. CommIT contribution — featured centrally in Chapter 5.

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

    Comprehensive textbook on coded modulation for wireless, with dedicated chapters on TCM, MLC, and BICM. Chapter on MLC complements our treatment with additional examples and design tables.

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

    Standard textbook reference. Chapter on coded modulation covers TCM; MLC is treated more briefly but our numerical examples follow this book's normalisations.

  8. T. M. Cover and J. A. Thomas, Elements of Information Theory, Wiley-Interscience, 2nd ed., 2006

    Source for the chain rule of mutual information (Thm. 2.5.1) that drives the capacity rule of this chapter. Also the standard reference for Fano's inequality used in the converse.

  9. ETSI, Digital Video Broadcasting (DVB); Second generation framing structure, channel coding and modulation systems for Broadcasting, Interactive Services, News Gathering and other broadband satellite applications (DVB-S2), 2014. [Link]

    The standard that consolidated BICM's industrial dominance over MLC. Uses 28 MODCOD points (QPSK/8-PSK/16-APSK/32-APSK × 11 LDPC rates) — all single-code BICM. Referenced in the engineering notes of s02 and s05.

  10. R. F. H. Fischer, Precoding and Signal Shaping for Digital Transmission, Wiley-IEEE Press, 2002

    Extended treatment of MLC with signal shaping. Chapter on shell mapping relevant for Ch. 4 of this book. Authored by one of the co-authors of the Wachsmann–Fischer–Huber capacity-rule paper.

  11. J. Hou, P. H. Siegel, and L. B. Milstein, Performance analysis and code optimization of low-density parity-check codes on Rayleigh fading channels, 2001

    LDPC design for multilevel-coded modulation, including the density-evolution analysis per-level. Shows that capacity-approaching LDPC codes at each level recover the MLC/MSD-capacity promise in practice.

  12. J. Hagenauer, E. Offer, and L. Papke, Iterative decoding of binary block and convolutional codes, 1996

    Introduces the iterative demapper–decoder loop that became BICM-ID. Referenced in the wireless-connection block on turbo-MSD.

  13. G. D. Forney Jr. and M. D. Trott, The dynamics of group codes: state spaces, trellis diagrams, and canonical encoders, 1993

    Foundational framework for coset/lattice codes. Relevant to the "MLC still wins on lattices" argument in s05 and forward reference to Ch. 4.

  14. A. Guillén i Fàbregas, A. Martinez, and G. Caire, Bit-interleaved coded modulation, 2008

    Book-length treatment of BICM that expands the 1998 paper by Caire, Taricco, and Biglieri. Self-contained introduction to all the comparison material in s04.

  15. 3GPP, NR; Multiplexing and channel coding, 2022. [Link]

    5G NR channel-coding specification. Single LDPC base graph handles every modulation from QPSK to 256-QAM via rate matching — a BICM-style single-code design that ruled out MLC. Cited in s05's engineering notes.

Further Reading

For readers who want to go deeper into the information-theoretic structure, the design details, or the historical arc of multilevel coding.

  • Capacity-approaching LDPC codes for multilevel modulation

    J. Hou, P. H. Siegel, L. B. Milstein, and H. D. Pfister, "Capacity- approaching bandwidth-efficient coded modulation schemes based on low-density parity-check codes," IEEE Trans. Inform. Theory, vol. 49, no. 9, pp. 2141–2155, Sep. 2003

    Shows how to design rate-matched LDPC codes per level that approach the MLC/MSD capacity rule in simulation, with gains of a few dB over a matched-rate BICM comparator for 8-PSK.

  • Alternative capacity rules and the uniform-rate MLC approximation

    R. F. H. Fischer, J. B. Huber, and U. Wachsmann, "On the capacity-approaching code design for multilevel coded modulation," ISIT 1998, pp. 444

    Discusses when using a uniform rate across levels (easier to deploy) loses appreciable capacity, and when it does not. Practical middle ground between pure MLC and pure BICM.

  • The BICM framework and its extensions

    A. Guillén i Fàbregas, A. Martinez, and G. Caire, *Bit-Interleaved Coded Modulation*, Foundations and Trends in Communications and Information Theory, Now Publishers, 2008

    Book-length reference for the BICM side of the comparison. Reading it alongside Wachsmann et al. is the ideal preparation for Ch. 5.

  • MLC for lattice coded modulation

    G. D. Forney Jr., "Coset codes — part I: introduction and geometrical classification," IEEE Trans. Inform. Theory, vol. 34, no. 5, pp. 1123–1151, Sep. 1988

    Forney's coset-code framework is the mathematical setting in which MLC is most naturally formulated. Required reading before Ch. 4 (lattice coded modulation).

  • Shaping and non-uniform MLC

    R. F. H. Fischer, *Precoding and Signal Shaping for Digital Transmission*, Wiley-IEEE Press, 2002, Chs. 6–8

    Combines MLC with signal shaping for approaches that close both the modulation-capacity gap and the shaping-gain gap ($1.53$ dB). Sets up the material of Ch. 4.

ExercisesCh 4 →