Polar Codes

5G Uplink Control Information (UCI) Polar Codes

The following codes are derived from the respective 5G standardization document:

3GPP TS 38.212 V15.2.0: Multiplexing and channel coding, Jul. 2018.
The frozen bit set was selected according to the reliability sequence in Table 5.3.1.2-1. For the simulation results with successive cancellation (SC) decoding, no CRC was attached. For the simulation results with SC list (SCL) decoding, a CRC was attached according to Subclause 6.3.1.2.1 with the CRC-polynomials gCRC11(D) = D11 + D10 + D9 + D5 + 1 and gCRC6(D) = D6 + D5 + 1, respectively. No interleaving was performed.

Blocklength: n = 64 bits

Rate k n Simulation Results SC Simulation Results SCL, L=8 Simulation Results SCL, L=32
1/4 16 64
1/2 32 64
2/3 43 64
3/4 48 64
4/5 51 64
5/6 53 64

Blocklength: n = 128 bits

Rate k n Simulation Results SC Simulation Results SCL, L=8 Simulation Results SCL, L=32
1/4 32 128
1/2 64 128
2/3 85 128
3/4 96 128
4/5 102 128
5/6 107 128

Blocklength: n = 256 bits

Rate k n Simulation Results SC Simulation Results SCL, L=8 Simulation Results SCL, L=32
1/4 64 256
1/2 128 256
2/3 171 256
3/4 192 256
4/5 205 256
5/6 213 256

Blocklength: n = 512 bits

Rate k n Simulation Results SC Simulation Results SCL, L=8 Simulation Results SCL, L=32
1/4 128 512 SC SCL+CRC11 SCL+CRC11
1/2 256 512 SC SCL+CRC11 SCL+CRC11
2/3 341 512 SC SCL+CRC11 SCL+CRC11
3/4 384 512 SC SCL+CRC11 SCL+CRC11
4/5 410 512 SC SCL+CRC11 SCL+CRC11
5/6 427 512 SC SCL+CRC11 SCL+CRC11

Blocklength: n = 1024 bits

Rate k n Simulation Results SC Simulation Results SCL, L=8 Simulation Results SCL, L=32
1/4 256 1024 SC SCL+CRC11 SCL+CRC11
1/2 512 1024 SC SCL+CRC11 SCL+CRC11
2/3 683 1024 SC SCL+CRC11 SCL+CRC11
3/4 768 1024 SC SCL+CRC11 SCL+CRC11
4/5 819 1024 SC SCL+CRC11 SCL+CRC11
5/6 853 1024 SC SCL+CRC11 SCL+CRC11