References & Further Reading

References

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

    The foundational BICM paper — the central CommIT contribution of this chapter. Introduces the parallel-bit-channel model, derives $C_{\rm BICM} = \sum_\ell I(Y; B_\ell)$ with a mismatched-decoding converse, proves Gray labelling is near-optimal on AWGN (numerical tables in §V.B), and analyses the diversity order on fading channels in §IV. Required reading.

  2. E. Zehavi, 8-PSK trellis codes for a Rayleigh channel, 1992

    The BICM precursor. Zehavi proposed bit-interleaving a binary code before 8-PSK mapping to break up the trellis structure of TCM on fading channels. No capacity analysis; six years later Caire-Taricco-Biglieri provided the theoretical foundation.

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

    Book-length expansion of the 1998 paper. Chapters 3 and 4 rework the BICM capacity formula rigorously via mismatched decoding and the generalised mutual information (GMI). Chapter 5 treats error exponents, Chapter 6 iterative decoding. Essential companion to the 1998 paper; our Chapter 7 of this book follows its GMI treatment.

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

    The set-partitioning principle used throughout this chapter (Definition <a href="#def-sp-labelling" class="ferkans-ref" title="Definition: Set-Partition (Ungerboeck) Labelling" data-ref-type="definition"><span class="ferkans-ref-badge">D</span>Set-Partition (Ungerboeck) Labelling</a>). Ungerboeck's TCM is the monolithic alternative BICM replaces.

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

    Definitive survey of coded modulation for the Gaussian channel. §IV.D discusses BICM and its capacity, with a careful comparison to MLC. Excellent companion reading to this chapter.

  6. T. J. Richardson and R. L. Urbanke, Modern Coding Theory, Cambridge University Press, 2008

    The standard reference on capacity-approaching binary codes (LDPC, turbo, polar). §4 covers density evolution; §6 applies LDPC to BICM on memoryless channels. The specific design recipe we assume for the binary code in the chapter's examples.

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

    Standard textbook. Chapter 8 covers trellis-coded and BICM modulation. Our constellation energy normalisations follow this book.

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

    Comprehensive textbook on coded modulation for wireless by one of the three BICM authors. Chapter on BICM complements our treatment with additional design examples and union-bound analysis.

  9. 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 BICM capacity gap formula of §3. Also standard reference for KL divergence, Fano's inequality, and the mismatched-decoding GMI machinery of §7.

  10. A. Martinez, A. Guillén i Fàbregas, and G. Caire, Bit-interleaved coded modulation revisited: a mismatched decoding perspective, 2009

    The paper that rigorously recasts BICM as a mismatched-decoding problem and identifies the BICM capacity formula with the GMI under product bit metric. Central to the treatment of Chapter 7.

  11. 3GPP, NR; Multiplexing and channel coding, 2022. [Link]

    5G NR channel-coding specification. Single LDPC base graph (BG1/BG2) handles all modulations from QPSK to 1024-QAM via rate matching — the pure industrial form of BICM. Cited in engineering note <a href="#eng-5g-nr-bicm" class="ferkans-ref" title="engineering_note: 5G NR: One LDPC Base Graph, Every Modulation" data-ref-type="engineering_note"><span class="ferkans-ref-badge">E</span>5G NR: One LDPC Base Graph, Every Modulation</a>.

  12. IEEE 802.11 Working Group, IEEE Std 802.11ax-2021: Enhancements for high-efficiency WLAN, 2021. [Link]

    Wi-Fi 6 / 6E standard with BICM + LDPC + up to 1024-QAM. Wi-Fi 7 (802.11be, 2023) extends to 4096-QAM with the same BICM architecture. Cited in <a href="#eng-wifi7-4096qam" class="ferkans-ref" title="engineering_note: Wi-Fi 7: BICM Pushes to 4096-QAM" data-ref-type="engineering_note"><span class="ferkans-ref-badge">E</span>Wi-Fi 7: BICM Pushes to 4096-QAM</a>.

  13. 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 2003-era standard that consolidated BICM's industrial dominance over TCM and MLC. LDPC + BICM + quasi-Gray APSK across 28 MODCOD points. DVB-S2X (2014) extends to 256-APSK. Cited in <a href="#eng-dvbs2-apsk" class="ferkans-ref" title="engineering_note: DVB-S2 / S2X: BICM with APSK for Satellite" data-ref-type="engineering_note"><span class="ferkans-ref-badge">E</span>DVB-S2 / S2X: BICM with APSK for Satellite</a>.

  14. A. Alvarado, F. Brännström, and E. Agrell, High SNR bounds for the BICM capacity, 2015

    Sharper analytical bounds on the BICM capacity gap at high SNR, refining the Caire-Taricco-Biglieri 1998 numerical tables. Useful for asymptotic analysis.

  15. S. Lin and D. J. Costello, Error Control Coding, Prentice Hall, 2nd ed., 2004

    Classical textbook on binary codes. Background reference for the free-distance concept used in the forward-to-Ch.-6 diversity exercise.

Further Reading

For readers interested in deeper aspects of BICM — error-exponent analysis, iterative decoding, and labelling design.

  • BICM error exponents and cutoff rate

    A. Martinez, A. Guillén i Fàbregas, and G. Caire, "Error probability of bit-interleaved coded modulation," IEEE Trans. Inform. Theory, vol. 52, no. 1, pp. 262–271, Jan. 2006 (preparation for Ch. 7 of this book).

    Rigorous treatment of the error exponent of BICM under the product bit metric, including the GMI-based cutoff rate. Key for the Chapter 7 development.

  • BICM with iterative decoding (BICM-ID)

    X. Li and J. A. Ritcey, "Bit-interleaved coded modulation with iterative decoding," IEEE Communications Letters, vol. 1, no. 6, pp. 169–171, Nov. 1997.

    The original BICM-ID paper. Shows how to feed decoder output back to the demapper to recover the MLC capacity benefit. Background for Chapter 8.

  • Labelling design optimisation

    F. Schreckenbach, N. Görtz, J. Hagenauer, and G. Bauch, "Optimized symbol mappings for bit-interleaved coded modulation with iterative decoding," IEEE GLOBECOM, 2003.

    How to search for labellings beyond Gray and SP for BICM-ID systems. Useful background for Chapter 8.

  • Probabilistic amplitude shaping for BICM

    G. Böcherer, F. Steiner, and P. Schulte, "Bandwidth-efficient and rate-matched low-density parity-check coded modulation," IEEE Trans. Comm., vol. 63, no. 12, pp. 4651–4665, Dec. 2015.

    Modern approach to closing the BICM-to-Shannon gap by shaping the input distribution. Preview of Chapter 9.

  • BICM for MIMO and multi-user channels

    B. M. Hochwald and S. ten Brink, "Achieving near-capacity on a multiple-antenna channel," IEEE Trans. Comm., vol. 51, no. 3, pp. 389–399, Mar. 2003.

    Shows how to extend the per-bit demapper of Algorithm <a href="#alg-llr-computation" class="ferkans-ref" title="Algorithm: Max-Log Per-Bit LLR Computation at the BICM Demapper" data-ref-type="algorithm"><span class="ferkans-ref-badge">A</span>Max-Log Per-Bit LLR Computation at the BICM Demapper</a> to MIMO spatial-multiplexing channels — another setting where BICM's modularity pays off. Forward to Book MIMO Chapter 4.

ExercisesCh 6 →