Are Polar Codes Practical?

Transcription

1 Are Polar Codes Practical? Prof. Warren J. Gross McGill University, Montreal, QC. Coding: from Practice to Theory Berkeley, CA. Feb. 10 th, 2015.

2 Achieving the Channel Capacity Successive cancellation Ñ low throughput. Mediocre performance at moderate code-length. Becomes excellent for N Polar Codes db using SC as n Ñ8 2/36

3 Channel Polarization u 0 W y 0 u 1 W y 1 I 0 IpW q I 1 1/26

4 Channel Polarization u 0 W y 0 u 1 W y 1 I 0 IpW q I 1 u 0 ` W y 0 u 1 W y 1 I 0 ă IpW q ă I 1 1/26

5 Channel Polarization u 0 W y 0 u 1 W y 1 I 0 IpW q I 1 u 0 ` W y 0 u 1 W y 1 u 0 ` ` ` y 0 u 1 ` ` y 1 u 2 ` ` y 2 u 3 ` y 3 u 4 ` ` y 4 u 5 ` y 5 u 6 ` y 6 u 7 y 7 Proportion of reliable bits Ñ IpW q. I 0 ă IpW q ă I 1 1/26

6 Successive Cancellation Decoding S 0 S 1 S 2 û 0 ` ` ` y 0 û 1 ` ` y 1 û 0 û 2 ` ` y 2 û 0 û 1 û 3 ` y 3 û 2 û 1 û 4 ` ` y 4 û 0 û 1 û 2 û 3 û 5 ` y 5 û 4 û 1 û 3 û 6 ` y 6 û 4 û 5 û 2 û 3 û 7 y 7 û 6 û 5 û 3 2/26

7 Successive Cancellation Decoding S 0 S 1 S 2 û 0 ` ` ` y 0 û 1 ` ` y 1 û 0 û 2 ` ` y 2 û 0 û 1 û 3 ` y 3 û 2 û 1 û 4 ` ` y 4 û 0 û 1 û 2 û 3 û 5 ` y 5 û 4 û 1 û 3 F û 6 ` y 6 û 4 û 5 û 2 û 3 û 7 y 7 û 6 û 5 û 3 2/26

8 Successive Cancellation Decoding S 0 S 1 S 2 û 0 ` ` ` y 0 û 1 ` ` y 1 û 0 û 2 ` ` y 2 û 0 û 1 û 3 ` y 3 û 2 û 1 û 4 ` ` y 4 û 0 û 1 û 2 û 3 û 5 ` y 5 û 4 û 1 û 3 û 6 ` y 6 û 4 û 5 û 2 û 3 G û 7 y 7 û 6 û 5 û 3 2/26

9 Semi-Parallel SC Decoder Implementation # PEs Speed, N 2 10 Utilization, N 2 10 ą 95% speed with 64 PEs. First polar decoder ASIC. Code (1024, 512) Technology 180 nm Area 1.72 mm 2 Frequency 150 MHz Info. T/P 49 Mbps Power 67 mw Mishra et al., A Successive Cancellation Decoder ASIC for a 1024-bit Polar Code in 180nm CMOS, A-SSCC /26

10 FPGA Implementation N LUT FF RAM (bits) f (MHz) T/P (Mbps) ,263 1, , R ,414 1, , R ,548 1,349 3, 278, R ,956 1,366 13, 109, R 4/26

11 Throughput of SC Decoders TP-SC Pamuk, ISIT SC-ASIC Mishra, A-SSCC SP-SC Raymond, TSP Info. T/P for R 0.9 (Mbps) 5/26

12 Improving Throughput 1000ˆ 100 Mbps SC 100 Gbps Unrolled

13 Successive Cancellation Tree View the SC decoder graph as a tree. û 0 ` ` ` y 0 û 1 ` ` y 1 û 2 ` ` y 2 û 3 ` y 3 û 4 ` ` y 4 û 5 ` y 5 û 6 ` y 6 û 7 y 7 6/26

14 Successive Cancellation Tree View the SC decoder graph as a tree. û 0 ` ` ` y 0 û 1 ` ` y 1 û 2 ` ` y 2 û 3 ` y 3 û 4 ` ` y 4 û 5 ` y 5 û 6 ` y 6 û 7 y 7 6/26

15 Successive Cancellation Tree View the SC decoder graph as a tree. û 0 ` ` ` y 0 û 1 ` ` y 1 û 2 ` ` y 2 û 3 ` y 3 û 4 ` ` y 4 û 5 ` y 5 û 6 ` y 6 û 7 y 7 6/26

16 Successive Cancellation Tree View the SC decoder graph as a tree. û 0 ` ` ` y 0 û 1 ` ` y 1 û 2 ` ` y 2 û 3 ` y 3 û 4 ` ` y 4 û 5 ` y 5 û 6 ` y 6 û 7 y 7 6/26

17 Successive Cancellation Tree View the SC decoder graph as a tree. û 0 ` ` ` y 0 û 1 ` ` y 1 û 2 ` ` y 2 û 3 ` y 3 û 4 ` ` y 4 û 5 ` y 5 û 6 ` y 6 û 7 y 7 6/26

18 Successive Cancellation Tree View the SC decoder graph as a tree. û 0 ` ` ` y 0 û 1 ` ` y 1 û 2 ` ` y 2 û 3 ` y 3 û 4 ` ` y 4 û 5 ` y 5 û 6 ` y 6 û 7 y 7 6/26

19 Simplified Successive-Cancellation Decoding Alamdar-Yazdi and Kschischang., A Simplified Successive-Cancellation Decoder for Polar Codes, Comm. Lett., /26

20 Simplified Successive-Cancellation Decoding Rate-0 Alamdar-Yazdi and Kschischang., A Simplified Successive-Cancellation Decoder for Polar Codes, Comm. Lett., /26

21 Simplified Successive-Cancellation Decoding Alamdar-Yazdi and Kschischang., A Simplified Successive-Cancellation Decoder for Polar Codes, Comm. Lett., /26

22 Simplified Successive-Cancellation Decoding Rate-1 Alamdar-Yazdi and Kschischang., A Simplified Successive-Cancellation Decoder for Polar Codes, Comm. Lett., /26

23 Simplified Successive-Cancellation Decoding Alamdar-Yazdi and Kschischang., A Simplified Successive-Cancellation Decoder for Polar Codes, Comm. Lett., /26

24 Fast-SSC Decoding Sarkis et al., Fast Polar Decoders: Algorithm and Implementation, IEEE JSAC, /26

25 Fast-SSC Decoding Repetition Sarkis et al., Fast Polar Decoders: Algorithm and Implementation, IEEE JSAC, /26

26 Fast-SSC Decoding Sarkis et al., Fast Polar Decoders: Algorithm and Implementation, IEEE JSAC, /26

27 Fast-SSC Decoding Single Parity Check Sarkis et al., Fast Polar Decoders: Algorithm and Implementation, IEEE JSAC, /26

28 Fast-SSC Decoding Sarkis et al., Fast Polar Decoders: Algorithm and Implementation, IEEE JSAC, /26

29 Fast-SSC Decoding New Nodes N 8 Repetition Rep-SPC N 4 SPC ML /26

30 SC Tree (256, 230) 10/26

31 SSC and Fast-SSC Trees (256, 230) Developed a compiler to convert the graph to instructions. 11/26

32 SSC and Fast-SSC Trees (256, 230) Developed a compiler to convert the graph to instructions. 11/26

33 Fast-SSC Decoder Implementation R LUT FF RAM (bits) f (MHz) T/P (Mbps) Fast-SSC ,866 7, , ,081 SSC For any code of length = 32,768. Sarkis et al. Fast polar decoders: algorithm and implementation, IEEE JSAC, /26

34 Throughput of Hardware Decoders BP Park, Sym. VLSI 2014 ASIC, 300 MHz (1024, 512) 2,338 Fast-SSC Sarkis, JSAC 2014 FPGA, 108 MHz (32678, 29492) 1,081 TP-SC Pamuk, ISIT 2013 FPGA, 230 MHz (16384, 14746) ,000 1,500 2,000 2,500 3,000 Info. T/P (Mbps) 13/26

35 The Unrolled Decoder (8, 4) polar code: 14/26

36 The Unrolled Decoder (8, 4) polar code: Unroll and pipeline all operations. F Rep G SPC 14/26

37 The Unrolled Decoder (8, 4) polar code: C 0 Unroll and pipeline all operations. C 0 F Rep G SPC 14/26

38 The Unrolled Decoder (8, 4) polar code: C 1 C 0 Unroll and pipeline all operations. C 1 C 0 F Rep G SPC 14/26

39 The Unrolled Decoder (8, 4) polar code: C 2 C 1C0 Unroll and pipeline all operations. F Rep G SPC C 2 C 1 C 0 14/26

40 The Unrolled Decoder (8, 4) polar code: C 3 C 2C1 C 0 Unroll and pipeline all operations. F Rep G SPC C 3 C 2 C 1 C 0 14/26

41 The Unrolled Decoder (8, 4) polar code: C 4 C 3C2 C 1 C 0 Unroll and pipeline all operations. F Rep G SPC C 4 C 3 C 2 C 1 C 0 14/26

42 The Unrolled Decoder (8, 4) polar code: C 5 C 0 C 4C3 C 2 C 1 Unroll and pipeline all operations. F Rep G SPC C 5 C 4 C 3 C 2 C 1 C 0 14/26

43 The Unrolled Decoder Implementation LUT FF RAM (bits) f (MHz) Info. T/P (Gbps) SP-SC 4,130 1,388 11, Unrolled 155, , , BP (ASIC) For a (1024, 512) polar code. Giard et al. A 237 Gbps unrolled hardware polar decoder, submitted to IET Letters and arxiv, Dec /26

44 SDR and Modern Software ECC ECC Viterbi decoder Demodulation OFDM Instructions Demel et al. A LTE Receiver Framework Using GNU Radio, JSPS, /26

45 SDR and Modern Software ECC ECC Viterbi decoder Demodulation OFDM Instructions Demel et al. A LTE Receiver Framework Using GNU Radio, JSPS, Turbo Wu et al. Asilomar iterations LDPC Sarkis et al. GlobalSIP iterations Info. T/P (Mbps) per Core 16/26

46 SDR and Modern Software ECC ECC Viterbi decoder Demodulation OFDM Instructions Demel et al. A LTE Receiver Framework Using GNU Radio, JSPS, Turbo Wu et al. Asilomar iterations LDPC Sarkis et al. GlobalSIP iterations Info. T/P (Mbps) per Core Goal: 50Mbps! 16/26

47 Floating-Point Throughput Info. T/P (Mbps) ICASSP 2014 GlobalSIP 2014 SIMD. Branchless. Single core. 150 (2048, 1707) (16384, 14746) (32768, 29492) Giard et al. Fast Software Polar Decoders, ICASSP Sarkis et al. Autogenerating Software Polar Decoders, GlobalSIP /26

48 Fixed-Point Software Polar Decoders Decoder f pghzq Info. T/P (Mbps) Latency µs Le Gal et al , Fast-SSC-int , (32768, 29492) polar code. Le Gal et al. Multi-Gb/s Software decoding of Polar Codes, TSP Giard et al. Low-latency Software Polar Decoders, in preparation. 18/26

49 Improving Finite-Length Error-Correction Performance PC BER PC List-CRC LDPC E b {N 0 19/26

50 List Decoding For each information bit, continue decoding assuming both 0 and 1. û 0 û 1 û 2 û ˆ ˆ û 0 0 û û û Select paths according to reliability values. 20/26

51 List Decoding For each information bit, continue decoding assuming both 0 and 1. û 0 û 1 û 2 û ˆ ˆ û 0 0 û û û Select paths according to reliability values. 20/26

52 List Decoding For each information bit, continue decoding assuming both 0 and 1. û 0 û 1 û 2 û ˆ ˆ û 0 û 1 û 2 û Select paths according to reliability values. 20/26

53 List Decoding For each information bit, continue decoding assuming both 0 and 1. û 0 û 1 û 2 û ˆ ˆ û 0 û 1 û 2 û Select paths according to reliability values. 20/26

54 List Decoding For each information bit, continue decoding assuming both 0 and 1. û 0 û 1 û 2 û ˆ ˆ û 0 û 1 û 2 û Select paths according to reliability values. 20/26

55 List Decoding For each information bit, continue decoding assuming both 0 and 1. û 0 û 1 û 2 û ˆ ˆ û 0 û 1 û 2 û Select paths according to reliability values. Using a CRC to select the output yields a significant improvement. 20/26

56 ASIC Implementation Synthesis results for N 1024 using UMC 90nm: L Area (mm 2 ) f (MHz) T/P (Mbps) R R Balatsoukas-Stimming et al. Hardware Architecture for List Successive Cancellation Decoding of Polar Codes, TCAS II, /26

57 Two-Step SW List Decoder List decoders are slower than Fast-SSC decoders. List have better error-correction performance than Fast-SSC decoders. 22/26

58 Two-Step SW List Decoder List decoders are slower than Fast-SSC decoders. List have better error-correction performance than Fast-SSC decoders. Combine both: Fast- SSC Valid CRC? no List- CRC yes Done Sarkis et al. Increasing the Speed of Polar List Decoders, SiPS, /26

59 Two-Step SW List Decoder Fast-SSC FER SSC-List-CRC (2048, 1723) E b {N 0 23/26

60 Two-Step SW List Decoder Fast-SSC FER SSC-List-CRC (2048, 1723) T E b {N 0 k p1 FER F qlpfast-sscq`fer F LpListq bit/s 23/26

61 Two-Step SW List Decoder (2048, 1723) 10 3 FER E b {N 0 (db) LDPC, I max 30 SSC-List-CRC, L 32 SSC-List-CRC, L 64 24/26

62 Two-Step SW List Decoder 60 (2048, 1723) 50 Information T/P (Mbps) E b {N 0 (db) LDPC, I max 30 SSC-List-CRC, L 32 SSC-List-CRC, L 64 25/26

63 Conclusion Polar codes can have excellent error-correction performance. Polar codes can have throughput in the hundred-gbps range. Once throughput and performance improvements are combined, we believe that polar codes will be a viable option for multiple applications. 26/26

64 Conclusion Polar codes can have excellent error-correction performance. Polar codes can have throughput in the hundred-gbps range. Once throughput and performance improvements are combined, we believe that polar codes will be a viable option for multiple applications. Thank you! 26/26