References & Further Reading

References

  1. S. ten Brink, Convergence behavior of iteratively decoded parallel concatenated codes, 2001

    The foundational EXIT-chart paper. Introduces the J-function, the extrinsic/a priori mutual-information axes, and the convergence- tunnel picture that organise essentially every iterative-decoder analysis since. Most of s02 and s03 follow this paper's framework.

  2. X. Li and J. A. Ritcey, Bit-interleaved coded modulation with iterative decoding, 1997

    The original BICM-ID paper. Shows experimentally that with iterative feedback between a soft-input/soft-output demapper and a SISO decoder, set-partition labelling outperforms Gray on Rayleigh fading — flipping the one-shot BICM conclusion of Ch. 6.

  3. X. Li and J. A. Ritcey, Trellis-coded modulation with bit interleaving and iterative decoding, 1999

    Extends the BICM-ID idea to trellis-coded outer codes and provides the first systematic error-floor analysis. The SP labelling for 8-PSK analysed here sets the benchmark that most later work compares against.

  4. A. Chindapol and J. A. Ritcey, Design, analysis, and performance evaluation for BICM-ID with square QAM constellations in Rayleigh fading channels, 2001

    Systematic labelling design for 16-QAM, 64-QAM, and 256-QAM under BICM-ID. The M16a, M16r, and modified SP labellings proposed here remain the reference benchmarks for BICM-ID receiver papers today.

  5. S. ten Brink, G. Kramer, and A. Ashikhmin, Design of low-density parity-check codes for modulation and detection, 2004

    The canonical EXIT-matching code-design paper. Casts LDPC degree- profile optimisation for BICM-ID as a linear program that fits the inverted decoder curve below a given demapper curve. This is the backbone of s05's matched-code-design algorithm.

  6. A. Ashikhmin, G. Kramer, and S. ten Brink, Extrinsic information transfer functions: model and erasure channel properties, 2004

    Rigorous information-theoretic foundation of EXIT functions for the binary erasure channel, where the Gaussian-LLR assumption is replaced by an exact calculation. Clarifies when the intuitive ten-Brink picture is provably correct versus merely approximate.

  7. T. Richardson and R. Urbanke, Modern Coding Theory, Cambridge University Press, 2008

    Chapters 3–4 develop density evolution as the non-Gaussian counterpart to EXIT charts. Chapter 4 has the degree-distribution optimisation via linear programming that underlies the matched-code design of s05.

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

    The foundational BICM paper (Ch. 5–6). Forward-referenced here as the "one-shot" limit that BICM-ID seeks to exceed; the gap to CM capacity identified in §IV of this paper is what iterative decoding closes.

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

    Monograph-length treatment of BICM. Chapter 7 surveys BICM-ID and explicitly discusses the Gaussian-LLR assumption, the role of labelling, and the convergence-threshold picture we use here.

  10. D. Divsalar, H. Jin, and R. J. McEliece, Coding theorems for turbo-like codes, 1998

    Establishes the turbo-code iterative-decoder analysis framework that EXIT charts were designed to visualise. The "tunnel" between component decoders reappears here as the tunnel between demapper and decoder.

  11. S. ten Brink, J. Speidel, and R.-H. Yan, Iterative demapping and decoding for multilevel modulation, 1998

    Parallel to Li–Ritcey 1997: independently introduces iterative demapping for multilevel modulation and argues for set-partition labelling when iteration is available. Together with Li–Ritcey the intellectual origin of BICM-ID.

  12. M. Tüchler, R. Koetter, and A. C. Singer, Turbo equalization: principles and new results, 2002

    Shows that the extrinsic/a-priori decomposition of BICM-ID extends unchanged to turbo equalisation — the demapper box is replaced by an equaliser box, and everything else (EXIT chart, convergence tunnel, matched-code design) remains the same. The generality of the framework.

  13. E. Sharon, A. Ashikhmin, and S. Litsyn, EXIT functions for binary input memoryless symmetric channels, 2006

    Tightens the Gaussian-LLR assumption by deriving EXIT curves directly from mutual-information functionals, bypassing the J-function approximation. Useful when the Gaussian-LLR picture fails (low SNR, short block length).

  14. 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; Part 2: DVB-S2 Extensions (DVB-S2X), 2021. [Link]

    Satellite BICM with LDPC outer code. The optional "iterative APSK demapping" mode in the very-low-SNR MODCODs (QPSK 2/9 down to VL-SNR) is an explicit instantiation of BICM-ID — the engineering realisation of this chapter.

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

    5G NR LDPC and bit-interleaver specification. The standard does not mandate iterative demapping, but the LDPC-plus-QAM receiver architecture in practical chipsets uses a small number (typically 1–3) of demapper/decoder passes when the first pass fails CRC — a lightweight BICM-ID.

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

    Standard reference. Chapter 8 (iterative decoding) covers turbo codes and the BCJR algorithm that produces the soft extrinsic outputs fed back by the BICM-ID demapper.

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

    Chapter 9 treats BICM-ID with clean numerical examples for 8-PSK and 16-QAM. Complements our EXIT-chart treatment with direct BER simulations at several iterations.

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

    The SISO-decoder paper that supplies the "soft-in, soft-out" component used on the BICM-ID decoder side. The extrinsic- information concept that the EXIT chart tracks is defined here in full generality.

Further Reading

For readers who want to dig deeper into EXIT charts, density evolution, and matched code design for BICM-ID and its relatives.

  • Density evolution as the non-Gaussian upgrade of EXIT charts

    T. Richardson, M. A. Shokrollahi, and R. Urbanke, "Design of capacity-approaching irregular low-density parity-check codes," IEEE Trans. Inform. Theory, vol. 47, no. 2, pp. 619–637, Feb. 2001

    Tracks the full LLR density through the iteration rather than its mutual-information summary. More accurate than EXIT charts, and indispensable when the Gaussian-LLR approximation visibly breaks (short blocks, very low SNR).

  • Labelling design for BICM-ID beyond set partitioning

    N. H. Tran and H. H. Nguyen, "Signal mappings of 8-ary constellations for bit interleaved coded modulation with iterative decoding," IEEE Trans. Broadcasting, vol. 52, no. 1, pp. 92–99, Mar. 2006

    Exhaustive-search results for 8-PSK and 8-QAM labelings under BICM-ID. Confirms that SP is not globally optimal for all constellations — the M8 family beats SP in certain SNR ranges.

  • Matched-code design via linear programming

    A. Ashikhmin, G. Kramer, and S. ten Brink, "Extrinsic information transfer functions: a model and two properties," Proc. Conf. Inf. Sci. Syst. (CISS), 2002

    The original LP formulation of LDPC degree-distribution optimisation from the demapper EXIT curve. Our algorithm in s05 is a direct adaptation.

  • BICM-ID with finite-length codes and short-packet regimes

    A. G. Fàbregas and A. Martinez, "Bit-interleaved coded modulation with shaping," Proc. IEEE ITW 2010, pp. 1–5

    Studies how the Gaussian-LLR assumption breaks for short blocks (< 1000 bits) and what replaces the EXIT-chart convergence threshold in the finite-blocklength regime.

  • Generalisation to turbo equalisation and ISI channels

    M. Tüchler and A. C. Singer, "Turbo equalization: an overview," IEEE Trans. Inform. Theory, vol. 57, no. 2, pp. 920–952, Feb. 2011

    Extends the BICM-ID framework to ISI channels by replacing the memoryless demapper with a soft equaliser. The EXIT-chart machinery, the convergence tunnel, and the matched-code design all carry over unchanged — evidence that BICM-ID's architecture is the tip of a much larger iceberg.