Chapter Summary

Chapter Summary

Key Points

• 1.

  BICM is a paradigm, not a specification. Every modern wireless standard — 5G NR, Wi-Fi 6/7, DVB-S2/S2X — implements BICM by customising the three ingredients (code, interleaver, mapper) to its own constraints. 5G picks LDPC BG1/BG2 + Gray QAM; Wi-Fi picks the legacy 802.11n LDPC code + high-QAM; DVB picks LDPC-plus-BCH with APSK to match the non-linear TWT satellite amplifier. The common skeleton is the Caire-Taricco-Biglieri structure of Chapter 5.

• 2.

  5G NR BICM uses a single LDPC family with full rate matching. Two base graphs BG1 (46x68, long codewords, high rates) and BG2 (42x52, short codewords, low rates) lifted by $Z \in \{2, \ldots, 384\}$ drive every QAM from QPSK to 1024-QAM. The MCS index selects $(Q_m, R)$ from one of four tables in 3GPP TS 38.214: Table 1 (legacy 64-QAM), Table 2 (256-QAM), Table 3 (URLLC, $R$ as low as 0.03), Table 4 (1024-QAM in Release 17). HARQ-IR with 4 redundancy versions provides incremental-redundancy retransmission.

• 3.

  Wi-Fi 6/7 BICM uses legacy 802.11n LDPC + high-order QAM. Wi-Fi 7 adds 4096-QAM ($Q_m = 12$) — the highest modulation order ever in mass-market wireless. The 4096-QAM 5/6 SNR threshold is $\sim 32.5$ dB, achievable only in short-range, clean-spectrum environments. In residential settings, MCS 7-9 (256-QAM or 1024-QAM) is the operational reality. Wi-Fi has no HARQ — adaptation is frame-level via MCS re-selection.

• 4.

  DVB-S2/S2X uses LDPC + BCH + APSK. APSK places constellation points on concentric rings (typically 3-6 rings for $M = 32$-256), reducing PAPR for travelling-wave-tube amplifier operation. Ring radii are rate-dependent design parameters tabulated in ETSI Annex A. The BCH outer code cleans any LDPC error floor to deliver quasi-error-free (BER $\le 10^{-11}$) broadcast quality.

• 5.

  AMC is throughput-optimal via pointwise MCS selection. On a block-fading channel, the throughput-optimal AMC policy picks the highest-rate MCS that meets the BLER target at each instantaneous SNR. No cross-bin coupling constraint forces the optimality of the pointwise-greedy policy. As the MCS set becomes denser, the throughput envelope approaches Shannon to within 1 dB (NR) or 2 dB (Wi-Fi 6). CQI feedback provides the SNR measurement; OLLA corrects long-run BLER drift.

• 6.

  HARQ-IR composes with AMC to smooth the staircase. A first-try MCS $i$ at effective spectral efficiency $\eta_i$ that fails, then succeeds after one retransmission, achieves effective rate $\eta_i / \mathbb{E}[K]$ where $\mathbb{E}[K]$ is the expected number of transmissions. The HARQ-IR throughput formula gives the optimality condition $\mathbb{E}[K] \approx 1.1$ at BLER target 10%. Feedback delay in fast-fading channels requires conservative MCS choice — a 1-2 step margin below CQI-indicated optimum.

• 7.

  Probabilistic shaping closes the 1.53 dB gap to Shannon. The Maxwell-Boltzmann distribution $p_\lambda(x) \propto \exp(-\lambda |x|^2)$ maximises entropy at fixed second moment on any finite constellation — a direct Lagrangian. Böcherer-Steiner-Schulte's PAS architecture (2015) implements MB-shaped QAM within BICM using a CCDM distribution matcher + systematic LDPC encoder. The asymptotic shaping gain is $\pi e / 6 \approx 1.53$ dB, approached within 0.1 dB at $M = 256$-QAM. PAS is now mandatory in 400G optical (OIF 400ZR) and proposed for 6G.

• 8.

  The Shannon-to-standards gap closes by $\sim 2$ dB per decade. LTE ($\sim 2$ dB gap in 2008) to 5G NR ($\sim 1$ dB gap in 2018) to 6G + PAS (projected $\sim 0.3$ dB gap by 2030). Each step comes from a specific BICM innovation: first LDPC (NR), then higher-QAM with denser MCS set (Wi-Fi 6/7), then probabilistic shaping (PAS). The remaining gap is dominated by finite-blocklength penalty and implementation loss, not by coding theory.