Successive Cancellation Decoding of Single Parity-Check Product - - PowerPoint PPT Presentation

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Successive Cancellation Decoding of Single Parity-Check Product - - PowerPoint PPT Presentation

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Institute for Communications Engineering Technische Universit at M unchen Successive Cancellation Decoding of Single Parity-Check Product Codes: Analysis and Improved Decoding Algorithms skun 1 , 2 Mustafa Cemil Co Joint work with

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SLIDE 1

Institute for Communications Engineering Technische Universit¨ at M¨ unchen

Successive Cancellation Decoding of Single Parity-Check Product Codes: Analysis and Improved Decoding Algorithms

Mustafa Cemil Co¸ skun1,2 Joint work with Gianluigi Liva2, Alexandre Graell i Amat3, Michael Lentmaier4 and Thomas Jerkovits2

1Institute for Communications Engineering, Technical University of Munich, Munich, Germany

2Institute for Communication and Navigation, German Aerospace Center, Weßling, Germany 3Department of Signals and Systems, Chalmers University of Technology, Gothenburg, Sweden 4Department of Electrical and Information Technology, Lund University, Lund, Sweden

LAWCI, Campinas - July, 2018

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SLIDE 2

Institute for Communications Engineering Technische Universit¨ at M¨ unchen

Basics on Product Codes1

The first deterministic code construction allowing vanishing bit error probability at a non-zero rate Very popular:

IEEE 802.16 (Wimax) ITU-G975 (Optical) Storage

  • 1P. Elias, “Error-free coding,” IRE T-IT, Sep. 1954.

Mustafa Cemil Co¸ skun — SC Decoding of Single Parity-Check Product Codes: Analysis and Improved Decoding Algorithms 1/5

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SLIDE 3

Institute for Communications Engineering Technische Universit¨ at M¨ unchen

Basics on Product Codes

u0 u1 u2 u3 u4 u5 u6 u7 u8 u9 u10 u11

Mustafa Cemil Co¸ skun — SC Decoding of Single Parity-Check Product Codes: Analysis and Improved Decoding Algorithms 2/5

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SLIDE 4

Institute for Communications Engineering Technische Universit¨ at M¨ unchen

Basics on Product Codes

u0 u1 u2 u3 u4 u5 u6 u7 u8 u9 u10 u11

Row Encoding: (n1, k1) code C1

p0 p1 p2

Mustafa Cemil Co¸ skun — SC Decoding of Single Parity-Check Product Codes: Analysis and Improved Decoding Algorithms 2/5

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SLIDE 5

Institute for Communications Engineering Technische Universit¨ at M¨ unchen

Basics on Product Codes

u0 u1 u2 u3 u4 u5 u6 u7 u8 u9 u10 u11

Row Encoding: (n1, k1) code C1

p0 p1 p2 p3 p4 p5

Mustafa Cemil Co¸ skun — SC Decoding of Single Parity-Check Product Codes: Analysis and Improved Decoding Algorithms 2/5

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SLIDE 6

Institute for Communications Engineering Technische Universit¨ at M¨ unchen

Basics on Product Codes

u0 u1 u2 u3 u4 u5 u6 u7 u8 u9 u10 u11

Row Encoding: (n1, k1) code C1

p0 p1 p2 p3 p4 p5 p6 p7 p8

Mustafa Cemil Co¸ skun — SC Decoding of Single Parity-Check Product Codes: Analysis and Improved Decoding Algorithms 2/5

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SLIDE 7

Institute for Communications Engineering Technische Universit¨ at M¨ unchen

Basics on Product Codes

u0 u1 u2 u3 u4 u5 u6 u7 u8 u9 u10 u11

Row Encoding: (n1, k1) code C1

p0 p1 p2 p3 p4 p5 p6 p7 p8

Column Encoding (n2, k2) code C2

p9 p10 p11 p12

Mustafa Cemil Co¸ skun — SC Decoding of Single Parity-Check Product Codes: Analysis and Improved Decoding Algorithms 2/5

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SLIDE 8

Institute for Communications Engineering Technische Universit¨ at M¨ unchen

Basics on Product Codes

u0 u1 u2 u3 u4 u5 u6 u7 u8 u9 u10 u11

Row Encoding: (n1, k1) code C1

p0 p1 p2 p3 p4 p5 p6 p7 p8

Column Encoding (n2, k2) code C2

p9 p10 p11 p12 p13 p14 p15 p16

Mustafa Cemil Co¸ skun — SC Decoding of Single Parity-Check Product Codes: Analysis and Improved Decoding Algorithms 2/5

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SLIDE 9

Institute for Communications Engineering Technische Universit¨ at M¨ unchen

Basics on Product Codes

u0 u1 u2 u3 u4 u5 u6 u7 u8 u9 u10 u11

Row Encoding: (n1, k1) code C1

p0 p1 p2 p3 p4 p5 p6 p7 p8

Column Encoding (n2, k2) code C2

p9 p10 p11 p12 p13 p14 p15 p16 p17 p18 p19 p20

Mustafa Cemil Co¸ skun — SC Decoding of Single Parity-Check Product Codes: Analysis and Improved Decoding Algorithms 2/5

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SLIDE 10

Institute for Communications Engineering Technische Universit¨ at M¨ unchen

Basics on Product Codes

u0 u1 u2 u3 u4 u5 u6 u7 u8 u9 u10 u11

Row Encoding: (n1, k1) code C1

p0 p1 p2 p3 p4 p5 p6 p7 p8

Column Encoding (n2, k2) code C2

p9 p10 p11 p12 p13 p14 p15 p16 p17 p18 p19 p20 p21 p22 p23 p24

Mustafa Cemil Co¸ skun — SC Decoding of Single Parity-Check Product Codes: Analysis and Improved Decoding Algorithms 2/5

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SLIDE 11

Institute for Communications Engineering Technische Universit¨ at M¨ unchen

Basics on Product Codes

u0 u1 u2 u3 u4 u5 u6 u7 u8 u9 u10 u11

Row Encoding: (n1, k1) code C1

p0 p1 p2 p3 p4 p5 p6 p7 p8

Column Encoding (n2, k2) code C2

p9 p10 p11 p12 p13 p14 p15 p16 p17 p18 p19 p20 p21 p22 p23 p24 p25 p26 p27 p28

Mustafa Cemil Co¸ skun — SC Decoding of Single Parity-Check Product Codes: Analysis and Improved Decoding Algorithms 2/5

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SLIDE 12

Institute for Communications Engineering Technische Universit¨ at M¨ unchen

Basics on Product Codes

u0 u1 u2 u3 u4 u5 u6 u7 u8 u9 u10 u11

Row Encoding: (n1, k1) code C1

p0 p1 p2 p3 p4 p5 p6 p7 p8

Column Encoding (n2, k2) code C2

p9 p10 p11 p12 p13 p14 p15 p16 p17 p18 p19 p20 p21 p22 p23 p24 p25 p26 p27 p28 p29 p30 p31 p32

Mustafa Cemil Co¸ skun — SC Decoding of Single Parity-Check Product Codes: Analysis and Improved Decoding Algorithms 2/5

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SLIDE 13

Institute for Communications Engineering Technische Universit¨ at M¨ unchen

Basics on Product Codes

u0 u1 u2 u3 u4 u5 u6 u7 u8 u9 u10 u11

Row Encoding: (n1, k1) code C1

p0 p1 p2 p3 p4 p5 p6 p7 p8

Column Encoding (n2, k2) code C2

p9 p10 p11 p12 p13 p14 p15 p16 p17 p18 p19 p20 p21 p22 p23 p24 p25 p26 p27 p28 p29 p30 p31 p32 p33 p34 p35 p36

Mustafa Cemil Co¸ skun — SC Decoding of Single Parity-Check Product Codes: Analysis and Improved Decoding Algorithms 2/5

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SLIDE 14

Institute for Communications Engineering Technische Universit¨ at M¨ unchen

Basics on Product Codes

u0 u1 u2 u3 u4 u5 u6 u7 u8 u9 u10 u11

Row Encoding: (n1, k1) code C1

p0 p1 p2 p3 p4 p5 p6 p7 p8

Column Encoding (n2, k2) code C2

p9 p10 p11 p12 p13 p14 p15 p16 p17 p18 p19 p20 p21 p22 p23 p24 p25 p26 p27 p28 p29 p30 p31 p32 p33 p34 p35 p36

Mustafa Cemil Co¸ skun — SC Decoding of Single Parity-Check Product Codes: Analysis and Improved Decoding Algorithms 2/5

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Institute for Communications Engineering Technische Universit¨ at M¨ unchen

Last year in ISIT2...

Applied successive cancellation decoding (SCD) to product codes with single parity check component codes (SPC-PCs) Theoretical bounds on PB under both SCD and Elias’ decoding over the binary erasure channel (BEC) Showed that PB under SCD is upper bounded by the one under Elias’ decoding over the BEC

  • 2M. C. Coskun, G. Liva, A. G. i Amat, M. Lentmaier, “Successive

Cancellation Decoding of Single Parity-Check Product Codes,” IEEE ISIT, June 2017.

Mustafa Cemil Co¸ skun — SC Decoding of Single Parity-Check Product Codes: Analysis and Improved Decoding Algorithms 3/5

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Institute for Communications Engineering Technische Universit¨ at M¨ unchen

As an extension...

Provide some asymptotic constructions with a positive rate and vanishing error probability over the BEC Show that they can be seen as a ”polar code” with larger kernels and different selection of frozen bits Introduce successive cancellation list decoding+outer CRC3 Comments on open problems...

  • 3I. Tal and A. Vardy, “List decoding of polar codes,” Proc. ISIT, 2011.

Mustafa Cemil Co¸ skun — SC Decoding of Single Parity-Check Product Codes: Analysis and Improved Decoding Algorithms 4/5

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Institute for Communications Engineering Technische Universit¨ at M¨ unchen

THANKS!

Mustafa Cemil Co¸ skun — SC Decoding of Single Parity-Check Product Codes: Analysis and Improved Decoding Algorithms 5/5