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Efficient Decoders for Polar Codes in 5G: Can Machine Learning Help? Seyyed Ali Hashemi Stanford University SystemX Conference November 19, 2019 S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 1 / 20 5th Gen. of

  1. Efficient Decoders for Polar Codes in 5G: Can Machine Learning Help? Seyyed Ali Hashemi Stanford University SystemX Conference November 19, 2019 S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 1 / 20

  2. 5th Gen. of Cellular Mobile Communications (5G) Stringent requirements: Peak (20 Gb/s) and user experienced (1 Gb/s) data rate End-to-end latency (1 ms) Scenarios: eMBB, mMTC, URLLC Data channel: actual information Control channel: system parameters → Polar Codes S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 2 / 20

  3. Polar Code Challenges in 5G Simple polar decoding algorithms do not perform well with moderate code lengths Effective algorithms are slow and complex to implement S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 3 / 20

  4. Outline Polar Codes 1 Fast Decoding 2 Memory-Efficient Decoding 3 Can Machine Learning Help? 4 Conclusion 5 S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 4 / 20

  5. Polar Codes Forward Error Correction (FEC) Transmitter Channel Receiver Improves transmission reliability Repetition code: 0 Channel 1 S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 5 / 20

  6. Polar Codes Forward Error Correction (FEC) Transmitter Channel Receiver Improves transmission reliability Repetition code: Encoder 000 0 Channel 010 0 Decoder S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 5 / 20

  7. Polar Codes Polar Codes Channel Capacity Maximum rate at which information can be reliably transmitted Polar Codes Provably achieve channel capacity at infinite code length Selected for 5G eMBB control channel: short codes S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 6 / 20

  8. Polar Codes Polar Encoding layer 0 1 u 0 x 0 u 1 x 1 S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 7 / 20

  9. Polar Codes Polar Encoding layer 0 1 u 0 x 0 u 1 x 1 S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 7 / 20

  10. Polar Codes Polar Encoding layer 0 1 2 u 0 x 0 u 1 x 1 u 2 x 2 u 3 x 3 S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 7 / 20

  11. Polar Codes Polar Encoding layer 0 1 2 3 u 0 x 0 u 1 x 1 u 2 x 2 u 3 x 3 u 4 x 4 u 5 x 5 u 6 x 6 u 7 x 7 S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 7 / 20

  12. Polar Codes Polar Encoding layer 0 1 2 3 x 0 0 F x 1 F 0 x 2 0 F u 3 x 3 I x 4 0 F u 5 x 5 I u 6 x 6 I u 7 x 7 I Input bits are divided into information ( I ) and frozen ( F ) bits S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 7 / 20

  13. Polar Codes Polar Decoding layer 0 1 2 3 x 0 0 F x 1 F 0 x 2 0 F u 3 x 3 I x 4 0 F u 5 x 5 I u 6 x 6 I u 7 x 7 I S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 8 / 20

  14. Polar Codes Polar Decoding layer 0 1 2 3 x 0 0 F x 1 F 0 x 2 0 F u 3 x 3 I x 4 0 F u 5 x 5 I u 6 x 6 I u 7 x 7 I S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 8 / 20

  15. Polar Codes Successive-Cancellation (SC) Decoding layer 3 α β 2 β r α l α r β l 1 0 S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 9 / 20

  16. Polar Codes SC List (SCL) Decoding layer 3 2 1 0 List size L = 4 S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 10 / 20

  17. Polar Codes SC List (SCL) Decoding layer 3 2 1 0 Bits are decoded one by one → High latency! S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 10 / 20

  18. Polar Codes SC List (SCL) Decoding layer 3 2 1 0 Bits are decoded one by one → High latency! S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 10 / 20

  19. Polar Codes SC List (SCL) Decoding layer 3 2 1 0 Bits are decoded one by one → High latency! S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 10 / 20

  20. Polar Codes SC List (SCL) Decoding layer 3 2 1 0 Bits are decoded one by one → High latency! S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 10 / 20

  21. Polar Codes SC List (SCL) Decoding layer 3 2 1 0 Bits are decoded one by one → High latency! S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 10 / 20

  22. Polar Codes SC List (SCL) Decoding layer 3 2 1 0 Bits are decoded one by one → High latency! S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 10 / 20

  23. Polar Codes SC List (SCL) Decoding layer 3 2 1 0 Bits are decoded one by one → High latency! S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 10 / 20

  24. Polar Codes SC List (SCL) Decoding layer 3 2 1 0 Bits are decoded one by one → High latency! S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 10 / 20

  25. Polar Codes SC List (SCL) Decoding layer 3 2 1 0 Roughly L times the memory usage of SC → High area! S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 10 / 20

  26. Fast Decoding Fast-SSCL Decoding layer 3 2 1 0 Conventional SCL S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 11 / 20

  27. Fast Decoding Fast-SSCL Decoding layer 3 2 1 Rate-0 0 Fast-SSCL: Exact reformulation of Rate-0 nodes S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 11 / 20

  28. Fast Decoding Fast-SSCL Decoding layer 3 2 Rep 1 0 Fast-SSCL: Exact reformulation of repetition (Rep) nodes S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 11 / 20

  29. Fast Decoding Fast-SSCL Decoding layer 3 2 Rep 1 Rate-1 0 Fast-SSCL: Exact reformulation of Rate-1 nodes S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 11 / 20

  30. Fast Decoding Fast-SSCL Decoding layer 3 2 Rep SPC 1 0 Fast-SSCL-SPC: Exact reformulation of single parity-check (SPC) nodes for L = 2 S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 11 / 20

  31. Fast Decoding Performance for P (1024 , 512) L : 2 4 8 16 32 Fast-SSCL: Fast-SSCL-SPC: 10 0 10 − 1 10 − 1 10 − 2 10 − 2 10 − 3 FER BER 10 − 3 10 − 4 10 − 4 10 − 5 10 − 5 10 − 6 10 − 6 10 − 7 1 2 3 1 2 3 E b / N 0 [dB] E b / N 0 [dB] S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 12 / 20

  32. Fast Decoding Hardware Implementation TSMC 65 nm Implementation Results for P (1024 , 512) Area [mm 2 ] Decoder Frequency [MHz] Throughput [Mb/s] SCL(8) 2 . 686 722 272 Fast-SSCL(8) 3 . 622 ( ↑ 36 %) 722 1053 ( ↑ 287 %) Fast-SSCL-SPC(8) 3 . 975 ( ↑ 48 %) 722 1198 ( ↑ 340 %) S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 13 / 20

  33. Memory-Efficient Decoding Memory-Efficient SCL memory layer 2 3 3 4 × 2 2 2 4 × 2 1 1 4 × 2 0 0 36 Conventional SCL S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 14 / 20

  34. Memory-Efficient Decoding Memory-Efficient SCL memory layer 2 3 3 1 × 2 2 2 1 × 2 1 1 4 × 2 0 0 18 Partitioned SCL (PSCL) S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 14 / 20

  35. Memory-Efficient Decoding Memory-Efficient SCL memory layer 2 3 3 2 × 2 2 2 2 × 2 1 1 4 × 2 0 0 24 Generalized PSCL (GPSCL) S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 14 / 20

  36. Memory-Efficient Decoding Memory-Efficient SCL memory layer 2 3 3 1 × 2 2 2 2 × 2 1 1 4 × 2 0 0 20 Layered PSCL (LPSCL) S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 14 / 20

  37. Memory-Efficient Decoding Performance for P (1024 , 512): GPSCL and LPSCL 10 8 8 10 0 9 8 8 8 8 8 10 − 1 8 8 8 8 8 8 8 8 7 10 − 2 FER 10 − 3 10 − 4 10 − 5 GPSCL(8,8,8) SCL(8) 10 − 6 1 2 3 E b / N 0 [dB] S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 15 / 20

  38. Memory-Efficient Decoding Performance for P (1024 , 512): GPSCL and LPSCL 10 8 8 10 0 9 8 8 8 8 8 10 − 1 8 8 8 8 8 8 8 8 7 10 1 1 10 − 2 9 1 1 1 1 FER 8 1 1 1 1 1 1 1 1 10 − 3 7 10 − 4 GPSCL(8,8,8) SCL(8) 10 − 5 GPSCL(8,8,1) PSCL(8,8) 10 − 6 1 2 3 E b / N 0 [dB] S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 15 / 20

  39. Memory-Efficient Decoding Performance for P (1024 , 512): GPSCL and LPSCL 10 8 8 10 0 9 8 8 8 8 8 10 − 1 8 8 8 8 8 8 8 8 7 10 1 1 10 − 2 9 1 1 1 1 FER 8 1 1 1 1 1 1 1 1 10 − 3 7 10 2 2 10 − 4 9 2 2 2 2 GPSCL(8,8,8) SCL(8) 8 2 2 2 2 2 2 2 2 GPSCL(8,8,1) 10 − 5 7 PSCL(8,8) GPSCL(8,8,2) 10 − 6 1 2 3 E b / N 0 [dB] S. A. Hashemi Efficient Decoders for Polar Codes in 5G SystemX Conference 15 / 20

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