Chapter 5: BICM — The Caire-Taricco-Biglieri Framework

Learning Objectives

• State the BICM encoder/decoder paradigm — one binary code, one bit interleaver, one higher-order mapper — and explain why it decouples channel coding from modulation
• Derive the BICM capacity formula $C_{\rm BICM}(\mu) = \sum_{\ell=0}^{L-1} I(Y; B_\ell)$ from the independent-parallel-channels model and prove that it is tight only when the demapper uses the ideal bit metric
• Prove the capacity ordering $C_{\rm CM} \ge C_{\rm BICM}(\mu)$ and quantify the gap as a sum of conditional mutual informations
• State and prove the Gray-labelling near-optimality result: for square QAM and AWGN, the Gray-BICM gap to CM capacity is below a few tenths of a bit over the whole practical SNR range
• Contrast Gray and set-partition labellings operationally: why Gray wins on the non-iterative AWGN channel and why SP can win with iterative decoding (forward reference to Ch. 8) or on fading channels (Ch. 6)
• Identify where BICM lives in every modern wireless standard (5G NR, Wi-Fi 6/7, DVB-S2) and explain why its modularity and rate-adaptability defeated MLC in the standards war