Modulation, and the code that carries control

5G Systems Notes · Reference · Modulation Concept map · PDSCH · Hub

Modulation was the single largest debt on the concept map — named more than ninety times across the other notes and derived in none of them. This note pays it. It is a group note: it reads these concepts as one argument, and each of them also has a page of its own.

In one line. A modulation order $Q_m$ is a promise about how finely a receiver can tell two voltages apart. Every extra bit per symbol halves the distance between constellation points, and the whole of the rest of the radio — amplifier linearity, phase noise, reference-signal density — exists to make that promise keepable.

Concepts defined here. Modulation and the modulation mapper · Gray mapping · Constellation normalisation · What each order costs · EVM · Polar coding


The concepts this note covers

Each concept now has a page of its own. This note is the narrative — the group read as one argument, with the connective tissue that a page-per-concept cannot carry. The pages are the definitions, and each one shows what to learn before it.

ConceptWhat it isNeedsPrimary clause
EVMError vector magnitude — the transmitter's own noise floor1TS 38.101-1 §6.4.2
ModulationQPSK to 1024QAM — bits per resource element1TS 38.211 §5.1, Table 7.3.1.2-1
Polar codingThe code used for control, not data1TS 38.212 §5.3.1, §7.3.3

Which to read. Come here to see how these ideas hang together; go to a term page when you want one definition, its prerequisites, and everything that depends on it. The concept map indexes all 118, and its hierarchy puts them in learning order.


Sources

DocumentClauseWhat it gives
TS 38.2115.1Modulation mapper — the equations for π/2-BPSK, BPSK, QPSK, 16/64/256/1024QAM
7.3.1.2Table 7.3.1.2-1, which of them PDSCH may use
TS 38.2125.3.1Polar coding — interleaving, encoding, the frozen-bit construction
7.3.2DCI CRC attachment and RNTI scrambling of the parity bits
7.3.3–7.3.4DCI channel coding and rate matching, with the polar parameters
TS 38.2145.1.3.1The MCS tables that select $Q_m$ and $R$ together
TS 38.101-16.4.2Table 6.4.2.1-1 — the EVM requirements of Table 1
Table 1: The clauses this reference note stands on. All are in the archive folder Courses (RAW)/5G Topics, at the versions given in the folder's CLAUDE.md.

On polar codes, the original is Arıkan, Channel polarization: a method for constructing capacity-achieving codes for symmetric binary-input memoryless channels (IEEE Transactions on Information Theory, vol. 55, no. 7, 2009), and the decoder NR actually relies on is Tal and Vardy, List decoding of polar codes (IEEE Trans. Inf. Theory, vol. 61, no. 5, 2015). Neither checked against a copy here.

On constellations and Gray mapping, any of the standard texts: Proakis and Salehi, Digital Communications, or Tse and Viswanath, Fundamentals of Wireless Communication (Cambridge, 2005; free PDF), which the other notes already use. Not checked against a copy here.

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