1. Polar Codes for 5G Bin Li， Senior Technical Expert Huawei Technologies
NASIT, San Diego, August 13th, 2015
Bin Li， Senior Technical Expert
Huawei Technologies

2. Contents Polar Codes for 5G Performance Comparisons
Low-Complexity Parallel SC-List Decoder
Latency and Power Reduction

3. Polar Codes for 5G Encoder: Polar concatenated with CRC
Decoder: Adaptive SC-List decoder

4. Polar Codes for 5G Polar concatenated with CRC
Increase minimum distance of Polar codes
Adaptive SC-List decoder
SC-List provides ML-approaching decoding
Adaptive SC-List provides latency/power reduction

5. Flexible Coding Rate and Block Size
Flexible coding rate K/N
arbitrarily increase/decrease K for any given N
Flexible block size N
perform bit-reversal puncturing to obtain a polar code with any arbitrary block size

6. Puncturing of Polar Codes
Bit-reversal puncture of Polar code
It is extremely difficult to find a “good” puncture pattern to obtain a punctured polar code
Alternatively we propose a simple solution:
Puncture Polar codes first ;
Select the frozen and information bits.

7. Puncturing of Polar Codes
Bit-reversal puncture:
For example, N=16, 4 bits to be punctured, (X0000,X1000,X0100,X1100)
Compute reliabilities of (U0,U1,…,U N-1)
Select K most reliable bits as information bits.

8. Puncturing of Polar Codes
Rate Matching
Puncture
Frozen bit
000
000
Frozen bit X1
001
100
Frozen bit X2
010
010
Good bit U1 X3
011
110
Frozen bit
100
001
Good bit U2 X4
101
101
Good bit U3 X5
110
011
Good bit U4 X6
111
111
N=6, K=4, R=2/3
Bit Reversal Order

9. Capacity-Achieving Polar HARQ
HARQ: Incremental Freezing
After m transmissions, the reliabilities of all information bits are computed based on all received data.
The most unreliable information bits are encoded and sent at the next transmission.

10. Polar HARQ: Incremental Freezing
Polar code (16,12) with 4 transmissions

11. Polar HARQ: Incremental Freezing
2nd Polar (16,6): If it is decoded correctly, after feedback, the 1st Polar (16,12) becomes a (16,6) code
3rd Polar (16,4): if it is decoded correctly, after feedback, the 2nd (16,12) becomes a (16,4) code, after the decoding and feedback, 1st (16,12) becomes a (16,4) code

12. Polar HARQ: Capacity-Achieving
1st (N,RN) is a capacity-achieving code of rate R
2nd Polar (N,RN/2) is a capacity-achieving code of rate R/2,
3rd Polar (N,RN/3) is a capacity-achieving code of rate R/3
4th Polar (N,RN/4) is a capacity-achieving code of rate R/4

13. Polar HARQ: Incremental Freezing
Same bit ordering at all encoders for soft combining

14. Polar HARQ: Joint Decoding
Soft combining at decoder

15. Contents Polar Codes for 5G Performance Comparisons
Low-Complexity Parallel SC-List Decoder
Latency and Power Reduction

16. Polar and Binary LDPC, N=256, R=1/2
0.8dB gain when L=32768

17. RM-Polar and Non-Binary LDPC,N=128,R=1/2
[1] Baldi-Bianchi-Chiaraluce…, “Advanced channel coding for space mission telecommand links”, IEEE VTC 2013 Fall

18. Polar and Theoretical Limit
N=2048, R=1/2, 0.25dB from theoretical limit

19. Polar Replaces LTE-turbo
Polar can use the 24-bit CRC at SC-List decoder “for free”

20. Polar and LTE-turbo, N=256, K=88
Polar uses 24-bit CRC in LTE standard

21. Polar and LTE-turbo, N=2048, K=1024
Polar uses 24-bit CRC in LTE standard

22. Contents Polar Codes for 5G Performance Comparisons
Low-Complexity Parallel-List Decoder
Latency and Power Reduction

23. Parallel SC-List Decoder
In order to increase decoding throughput
Parallel decoder observes multiple bits at each decoding time

24. Sorting Problem of Parallel SC-List Decoder
List Size L=32
2 bits per decoding time, 4*L=128
4 bits per decoding time, 16*L=512
The sorting of 512 paths to obtain the top 32 is very complex

25. Decision-Aided Algorithm
According to Polar principle, all information bits have different reliabilities;
Divide the information bits into two sets;
Good bits having higher reliabilities;
Bad bits having lower reliabilities.

26. Decision-Aided Algorithm
If both U2k-1 and U2k are good bits, each survival path only output one path:
max{Pr(0,0), Pr(0,1), Pr(1,0), Pr(1,1)};
If both U2k-1 is a bad bit and U2k is a good bits, each survival path outputs two paths:
max{Pr(0,0), Pr(0,1)};
max{Pr(1,0), Pr(1,1)};

27. Decision-Aided Algorithm
(2048, 1040) + 16-bit CRC, R=1/2, 4 bits per decoding time
75% and 80% of 1040 information bits are selected as good bits

28. Decision-Aided Algorithm
Bit patterns of Polar code (2048, 1040)
Good-bit patterns for each bit pattern

29. Decision-Aided Algorithm
Complexity
(M*M)
(M*log2(M))
No Decision
57640
14836
Decision-Aided (75%)
2664=4.6%*57640
1140=7.7%*14836
Decision-Aided (80%)
1352=2.4%*57640
660=4.5%*14836
Complexity is M*M and M*log2(M), M is sorting number
Decision-aided has 20 times lower complexity

30. Contents Polar Codes for 5G Performance Comparisons
Low-Complexity Parallel-List Decoder
Latency and Power Reduction

31. Power Reduction by Adaptive LIST
Adaptive list increases list size L until CRC passes
L increases, L={1,2,4,8,16,32},
90% can be decoded with L=1
The average list size is very small
This average complexity reduction saves power

32. Power Reduction by Adaptive LIST
Before
After
Complexity:
8192/2.47=3316
Adaptive list reduces average power significantly

33. A Simple Architecture of Adaptive List
L=1 (SC) can decode 90% of frames
SC is much faster than L=32
When CRC passes at SC, L=32 is stopped
Computation power can be greatly reduced

34. Performance ~ Block Size, R=1/32x 4x
Polar needs 1/4~1/2 block sizes of turbo

35. Performance ~ Block Size, R=1/22x 2x 8x 4x
Polar needs 1/8~1/2 block sizes of turbo

36. Performance ~ Block Size, R=3/44x 2x 2x 8x 8x 4x
Polar needs 1/8~1/4 block sizes of turbo