Efficient Decoders for Polar Codes in 5G: Can Machine Learning Help? - - PowerPoint PPT Presentation

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Efficient Decoders for Polar Codes in 5G: Can Machine Learning Help? - - PowerPoint PPT Presentation

Mar 22, 2023 117 likes •703 views

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

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SLIDE 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

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SLIDE 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

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SLIDE 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

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SLIDE 4

Outline

1

Polar Codes

2

Fast Decoding

3

Memory-Efficient Decoding

4

Can Machine Learning Help?

5

Conclusion

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 4 / 20

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SLIDE 5

Polar Codes

Forward Error Correction (FEC)

Transmitter Channel Receiver Improves transmission reliability Repetition code: Channel 1

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 5 / 20

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SLIDE 6

Polar Codes

Forward Error Correction (FEC)

Transmitter Channel Receiver Improves transmission reliability Repetition code:

Encoder 000

Channel

Decoder

010

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 5 / 20

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SLIDE 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

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SLIDE 8

Polar Codes

Polar Encoding

u0 u1 x0 x1 layer 1

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 7 / 20

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SLIDE 9

Polar Codes

Polar Encoding

u0 u1 x0 x1 layer 1

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 7 / 20

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SLIDE 10

Polar Codes

Polar Encoding

u0 u1 u2 u3 x0 x1 x2 x3 layer 1 2

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 7 / 20

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SLIDE 11

Polar Codes

Polar Encoding

u0 u1 u2 u3 u4 u5 u6 u7 x0 x1 x2 x3 x4 x5 x6 x7 layer 1 2 3

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 7 / 20

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SLIDE 12

Polar Codes

Polar Encoding

u3 u5 u6 u7 F F F I F I I I x0 x1 x2 x3 x4 x5 x6 x7 layer 1 2 3 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

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SLIDE 13

Polar Codes

Polar Decoding

u3 u5 u6 u7 F F F I F I I I x0 x1 x2 x3 x4 x5 x6 x7 layer 1 2 3

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 8 / 20

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SLIDE 14

Polar Codes

Polar Decoding

u3 u5 u6 u7 F F F I F I I I x0 x1 x2 x3 x4 x5 x6 x7 layer 1 2 3

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 8 / 20

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SLIDE 15

Polar Codes

Successive-Cancellation (SC) Decoding

layer 3 2 1 α β αl βl βr αr

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 9 / 20

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SLIDE 16

Polar Codes

SC List (SCL) Decoding

layer 3 2 1 List size L = 4

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 10 / 20

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SLIDE 17

Polar Codes

SC List (SCL) Decoding

layer 3 2 1 Bits are decoded one by one → High latency!

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 10 / 20

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SLIDE 18

Polar Codes

SC List (SCL) Decoding

layer 3 2 1 Bits are decoded one by one → High latency!

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 10 / 20

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SLIDE 19

Polar Codes

SC List (SCL) Decoding

layer 3 2 1 Bits are decoded one by one → High latency!

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 10 / 20

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SLIDE 20

Polar Codes

SC List (SCL) Decoding

layer 3 2 1 Bits are decoded one by one → High latency!

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 10 / 20

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SLIDE 21

Polar Codes

SC List (SCL) Decoding

layer 3 2 1 Bits are decoded one by one → High latency!

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 10 / 20

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SLIDE 22

Polar Codes

SC List (SCL) Decoding

layer 3 2 1 Bits are decoded one by one → High latency!

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 10 / 20

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SLIDE 23

Polar Codes

SC List (SCL) Decoding

layer 3 2 1 Bits are decoded one by one → High latency!

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 10 / 20

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SLIDE 24

Polar Codes

SC List (SCL) Decoding

layer 3 2 1 Bits are decoded one by one → High latency!

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 10 / 20

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SLIDE 25

Polar Codes

SC List (SCL) Decoding

layer 3 2 1 Roughly L times the memory usage of SC → High area!

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 10 / 20

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SLIDE 26

Fast Decoding

Fast-SSCL Decoding

layer 3 2 1 Conventional SCL

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 11 / 20

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SLIDE 27

Fast Decoding

Fast-SSCL Decoding

layer 3 2 1 Rate-0 Fast-SSCL: Exact reformulation of Rate-0 nodes

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 11 / 20

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SLIDE 28

Fast Decoding

Fast-SSCL Decoding

layer 3 2 1 Rep Fast-SSCL: Exact reformulation of repetition (Rep) nodes

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 11 / 20

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SLIDE 29

Fast Decoding

Fast-SSCL Decoding

layer 3 2 1 Rep Rate-1 Fast-SSCL: Exact reformulation of Rate-1 nodes

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 11 / 20

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SLIDE 30

Fast Decoding

Fast-SSCL Decoding

layer 3 2 1 Rep SPC 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

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SLIDE 31

Fast Decoding

Performance for P(1024, 512)

L: 2 4 8 16 32 Fast-SSCL: Fast-SSCL-SPC:

1 2 3 10−6 10−5 10−4 10−3 10−2 10−1 100

Eb/N0 [dB] FER

1 2 3 10−7 10−6 10−5 10−4 10−3 10−2 10−1

Eb/N0 [dB] BER

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 12 / 20

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SLIDE 32

Fast Decoding

Hardware Implementation

TSMC 65 nm Implementation Results for P(1024, 512)

Decoder Area [mm2] 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

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SLIDE 33

Memory-Efficient Decoding

Memory-Efficient SCL

layer 3 2 1 memory 23 4 × 22 4 × 21 4 × 20 36 Conventional SCL

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 14 / 20

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SLIDE 34

Memory-Efficient Decoding

Memory-Efficient SCL

layer 3 2 1 memory 23 1 × 22 1 × 21 4 × 20 18 Partitioned SCL (PSCL)

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 14 / 20

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SLIDE 35

Memory-Efficient Decoding

Memory-Efficient SCL

layer 3 2 1 memory 23 2 × 22 2 × 21 4 × 20 24 Generalized PSCL (GPSCL)

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 14 / 20

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SLIDE 36

Memory-Efficient Decoding

Memory-Efficient SCL

layer 3 2 1 memory 23 1 × 22 2 × 21 4 × 20 20 Layered PSCL (LPSCL)

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 14 / 20

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SLIDE 37

Memory-Efficient Decoding

Performance for P(1024, 512): GPSCL and LPSCL

1 2 3 10−6 10−5 10−4 10−3 10−2 10−1 100

Eb/N0 [dB] FER

GPSCL(8,8,8) SCL(8)

8 8 8 8 8 8 8 8 8 8 8 8 8 8 10 9 8 7

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 15 / 20

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SLIDE 38

Memory-Efficient Decoding

Performance for P(1024, 512): GPSCL and LPSCL

1 2 3 10−6 10−5 10−4 10−3 10−2 10−1 100

Eb/N0 [dB] FER

GPSCL(8,8,8) SCL(8) GPSCL(8,8,1) PSCL(8,8)

8 8 8 8 8 8 8 8 8 8 8 8 8 8 10 9 8 7 1 1 1 1 1 1 1 1 1 1 1 1 1 1 10 9 8 7

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 15 / 20

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SLIDE 39

Memory-Efficient Decoding

Performance for P(1024, 512): GPSCL and LPSCL

1 2 3 10−6 10−5 10−4 10−3 10−2 10−1 100

Eb/N0 [dB] FER

GPSCL(8,8,8) SCL(8) GPSCL(8,8,1) PSCL(8,8) GPSCL(8,8,2)

8 8 8 8 8 8 8 8 8 8 8 8 8 8 10 9 8 7 1 1 1 1 1 1 1 1 1 1 1 1 1 1 10 9 8 7 2 2 2 2 2 2 2 2 2 2 2 2 2 2 10 9 8 7

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 15 / 20

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SLIDE 40

Memory-Efficient Decoding

Performance for P(1024, 512): GPSCL and LPSCL

1 2 3 10−6 10−5 10−4 10−3 10−2 10−1 100

Eb/N0 [dB] FER

GPSCL(8,8,8) SCL(8) GPSCL(8,8,1) PSCL(8,8) GPSCL(8,8,2) GPSCL(8,8,4)

8 8 8 8 8 8 8 8 8 8 8 8 8 8 10 9 8 7 1 1 1 1 1 1 1 1 1 1 1 1 1 1 10 9 8 7 2 2 2 2 2 2 2 2 2 2 2 2 2 2 10 9 8 7 4 4 4 4 4 4 4 4 4 4 4 4 4 4 10 9 8 7

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 15 / 20

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SLIDE 41

Memory-Efficient Decoding

Performance for P(1024, 512): GPSCL and LPSCL

1 2 3 10−6 10−5 10−4 10−3 10−2 10−1 100

Eb/N0 [dB] FER

LPSCL(8,8,{8, 8, 8}) SCL(8) LPSCL(8,8,{2, 2, 2}) GPSCL(8,8,2)

8 8 8 8 8 8 8 8 8 8 8 8 8 8 10 9 8 7 2 2 2 2 2 2 2 2 2 2 2 2 2 2 10 9 8 7

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 15 / 20

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SLIDE 42

Memory-Efficient Decoding

Performance for P(1024, 512): GPSCL and LPSCL

1 2 3 10−6 10−5 10−4 10−3 10−2 10−1 100

Eb/N0 [dB] FER

LPSCL(8,8,{8, 8, 8}) SCL(8) LPSCL(8,8,{2, 2, 2}) GPSCL(8,8,2) LPSCL(8,8,{2, 2, 4})

8 8 8 8 8 8 8 8 8 8 8 8 8 8 10 9 8 7 2 2 2 2 2 2 2 2 2 2 2 2 2 2 10 9 8 7 2 2 2 2 2 2 4 4 4 4 4 4 4 4 10 9 8 7

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 15 / 20

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SLIDE 43

Memory-Efficient Decoding

Performance for P(1024, 512): GPSCL and LPSCL

1 2 3 10−6 10−5 10−4 10−3 10−2 10−1 100

Eb/N0 [dB] FER

LPSCL(8,8,{8, 8, 8}) SCL(8) LPSCL(8,8,{2, 2, 2}) GPSCL(8,8,2) LPSCL(8,8,{2, 2, 4}) LPSCL(8,8,{2, 4, 4})

8 8 8 8 8 8 8 8 8 8 8 8 8 8 10 9 8 7 2 2 2 2 2 2 2 2 2 2 2 2 2 2 10 9 8 7 2 2 2 2 2 2 4 4 4 4 4 4 4 4 10 9 8 7 2 2 4 4 4 4 4 4 4 4 4 4 4 4 10 9 8 7

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 15 / 20

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SLIDE 44

Memory-Efficient Decoding

Hardware Implementation

TSMC 65 nm implementation results for P(1024, 512)

Decoder Area [mm2] Eb/N0 [dB] @ FER = 10−4 SCL(8) 2.728 2.6803 GPSCL(2,8,2) 1.788 (↓ 34.5%) 2.6920 (↑ 0.0117 dB) GPSCL(4,8,2) 1.609 (↓ 41.1%) 2.7108 (↑ 0.0305 dB) GPSCL(4,8,4) 1.703 (↓ 37.6%) 2.6818 (↑ 0.0015 dB) GPSCL(8,8,4) 1.563 (↓ 42.8%) 2.6908 (↑ 0.0105 dB) LPSCL(8,8,{2, 2, 4}) 1.288 (↓ 52.8%) 2.7141 (↑ 0.0338 dB) LPSCL(8,8,{2, 4, 4}) 1.345 (↓ 50.7%) 2.7003 (↑ 0.0200 dB)

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 16 / 20

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SLIDE 45

Can Machine Learning Help?

Machine Learning

A data-driven approach to build mathematical models in order to make predictions or decisions Neural Networks:

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 17 / 20

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SLIDE 46

Can Machine Learning Help?

Off-the-Shelf Neural Decoding

Encoder

000 Channel

Decoder

010

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 18 / 20

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SLIDE 47

Can Machine Learning Help?

Off-the-Shelf Neural Decoding

Encoder

000 Channel 010

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 18 / 20

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SLIDE 48

Can Machine Learning Help?

Off-the-Shelf Neural Decoding

Encoder

000 Channel 010 They can be used for codes with a few information bits K

Output labels can be as large as 2K High-dimensional classification problem

Generating training data is difficult in a noisy environment

For each codeword, several training samples should be made

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 18 / 20

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SLIDE 49

Can Machine Learning Help?

Model-Based Neural Learning

Can we help existing decoders with machine learning? Belief propagation (BP) decoding u0 u1 u2 u3 x0 x1 x2 x3 1 2

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 19 / 20

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SLIDE 50

Can Machine Learning Help?

Model-Based Neural Learning

Can we help existing decoders with machine learning? Belief propagation (BP) decoding u0 u1 u2 u3 x0 x1 x2 x3 1 2

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 19 / 20

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SLIDE 51

Can Machine Learning Help?

Model-Based Neural Learning

Can we help existing decoders with machine learning? Belief propagation (BP) decoding u0 u1 u2 u3 x0 x1 x2 x3 1 2

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 19 / 20

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SLIDE 52

Can Machine Learning Help?

Model-Based Neural Learning

Can we help existing decoders with machine learning? Belief propagation (BP) decoding u0 u1 u2 u3 x0 x1 x2 x3 1 2

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 19 / 20

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SLIDE 53

Can Machine Learning Help?

Model-Based Neural Learning

Can we help existing decoders with machine learning? Belief propagation (BP) decoding u0 u1 u2 u3 x0 x1 x2 x3 1 2

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 19 / 20

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SLIDE 54

Can Machine Learning Help?

Model-Based Neural Learning

Can we help existing decoders with machine learning? Belief propagation (BP) decoding Deep unfolding: u0 u1 u2 u3 x0 x1 x2 x3 1 2 x0 x1 x2 x3 1 2 u0 u1 u2 u3 1 2 Assign trainable weights to each edge at each layer Performance can be significantly improved!

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 19 / 20

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SLIDE 55

Conclusion

Conclusion

We addressed two main obstacles in the deployment of polar codes in 5G:

Improved decoding speed by 4.4× Reduced decoder’s area occupation by up to 52.8%

We provided directions on using Machine Learning for channel coding in 5G:

Off-the-Shelf neural decoding Model-based neural decoding

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 20 / 20

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SLIDE 56

Conclusion

Thank you!

  • S. A. Hashemi

Efficient Decoders for Polar Codes in 5G SystemX Conference 20 / 20