Polar coding — The code used for control, not data

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Bits into a codeword

Where it sits

Sits atLevel 7 of the hierarchy · Bits into a codeword · explained
Also writtenPolar code · Polar
Learn firstCRC — 7 concepts in the full chain, see the paths
UnlocksPDCCH · PBCH
Primary clauseTS 38.212 §5.3.1, §7.3.3
Used inref-modulation 6 · index 1 · nr-pdsch 1
Scanned from the notes at page load and joined with terms.json; nothing on this card is typed by hand.

What it is

What it is. The channel code used for control information — DCI on PDCCH, the PBCH payload, and uplink control on PUCCH — while data uses LDPC. TS 38.212 clause 5.3.1, invoked for DCI by clause 7.3.3.

Why control does not use LDPC. The two codes are good at different lengths.

LDPC is an asymptotic code. Its performance comes from many short cycles averaging out over a long block; at a few hundred bits there is not enough block for that to happen. A DCI payload is about 44 bits (PDSCH §8.1) — three orders of magnitude shorter than the 770 000-bit transport block in PDSCH §9.2.

Polar codes are exact at any length. Arıkan's construction splits a channel into synthetic sub-channels of graded reliability and puts information on the good ones, frozen zeros on the bad. The construction is provably capacity-achieving and, unlike LDPC, behaves well when the block is small.

And control has a different job. A DCI must be found before it can be decoded — a device blind- decodes many candidates (nr-pdcch.md, still to be written). List decoding of a polar code with a CRC check is what makes "is this candidate mine?" a reliable question.

The RNTI is hidden in the CRC, and the mechanism is worth seeing. TS 38.212 clause 7.3.2 attaches a 24-bit CRC using $g_{\text{CRC24C}}$, then scrambles the last 16 parity bits with the RNTI:

$$ c_k = b_k \;\; (k \le A+7), \qquad c_k = \bigl(b_k + x_{\text{RNTI},\,k-A-8}\bigr) \bmod 2 \;\; (A+8 \le k \le A+23) \tag{1} $$
Equation 1: RNTI masking of the DCI CRC, TS 38.212 clause 7.3.2. Only the final sixteen parity bits are scrambled; the first eight are left alone. A device descrambles with an RNTI it owns and checks the CRC - if it passes, the message was addressed to it. There is no address field anywhere in the DCI.

So the CRC does three jobs at once: it detects errors, it identifies the recipient, and — because a wrong RNTI produces a random syndrome — it tells a device that a candidate it blind-decoded was never meant for it. That is why NR needs no address field on the control channel, and it is the counterpart of the PDSCH scrambling argument in PDSCH §6.1.

Read on

This concept was first written up in ref-modulation, which reads the whole group as one argument.

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Before this concept, the hierarchy says to learn the following — the full chain, in order:

To understand Polar coding (level 7) you first need 7 other concepts. Read them in this order — everything on one line can be read in any order, but no line before the one above it:
Level Learn these
0 Subcarrier
1 OFDM
2 OFDM symbol
3 Resource element
4 Physical layer
5 Transport block
6 CRC
Immediately before Polar coding: CRC.
Keep going — where this sits on the route
◀Code blockstep 74 · level 7
Step 75 of 118level 7 · Bits into a codeword
CSIstep 76 · level 7▶
Level 7 → 8 · this unlocks
PDCCH · PBCH
↳ all 8 concepts at level 8 · level 7 in full · the whole route
The route is every concept in the folder ordered by level, so nothing here needs anything after it. Computed at page load from terms.json; the same numbering as the route page.
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