Design of Energy-Efficient LDPC Codes and Decoders Elsa Dupraz - PowerPoint PPT Presentation

Design of Energy-Efficient LDPC Codes and Decoders Elsa Dupraz 16/04/2019

Section 1: Introduction 2 OUTLINE Introduction LDPC codes and decoders Perf. analysis of faulty decoders Effect of faults in the decoders Conclusion 1. Introduction 2. LDPC codes and decoders 3. Perf. analysis of faulty decoders 4. Effect of faults in the decoders 5. Conclusion D ESIGN OF E NERGY -E FFICIENT LDPC C ODES AND D ECODERS Elsa Dupraz 16/04/2019

Section 1: Introduction 3 Acknowledgments Introduction LDPC codes and decoders Perf. analysis of faulty decoders Effect of faults in the decoders Conclusion ◮ ANR JCJC project EF-FECtive (January 2018 - December 2020) ◮ Fangping Ye, Mohamed Yaoumi, Zeina Mheich ◮ Franc ¸ois Leduc-Primeau, David Declercq, Valentin Savin, Bane Vasic, Lav Varshney, Emanuel Popovici, Frederic Guilloud ... D ESIGN OF E NERGY -E FFICIENT LDPC C ODES AND D ECODERS Elsa Dupraz 16/04/2019

Section 1: Introduction 4 Moore’s Law Introduction LDPC codes and decoders Perf. analysis of faulty decoders Effect of faults in the decoders Conclusion ◮ In 1965, Moore predicted that the number of transistors on processors was going to double every 2 years 1e+12 1e+10 Number of transistors Core i7 Core 2 Duo 1e+08 Pentium 4 Pentium 1e+06 80386DX 8088 1e+04 4004 Moore Actual Intel 1e+02 1970 1980 1990 2000 2010 2020 Year ◮ What about energy consumption? D ESIGN OF E NERGY -E FFICIENT LDPC C ODES AND D ECODERS Elsa Dupraz 16/04/2019

Section 1: Introduction 5 5G Introduction LDPC codes and decoders Perf. analysis of faulty decoders Effect of faults in the decoders Conclusion In the 5G standardization process ◮ Huge increase of number of users, terminals, etc. ◮ Need to improve environmental footprint, battery lifetime D ESIGN OF E NERGY -E FFICIENT LDPC C ODES AND D ECODERS Elsa Dupraz 16/04/2019

Section 1: Introduction 6 Faulty computation operations Introduction LDPC codes and decoders Perf. analysis of faulty decoders Effect of faults in the decoders Conclusion ◮ Hardware energy consumption has become a major issue ◮ Energy consumption can be reduced by • Aggressive voltage scaling • Increased sampling frequency ◮ Problem : this may introduce faults in the computation operations V V dd faulty Value 1 p xor = P (˜ Value 0 c � = a ⊕ b ) t t d D ESIGN OF E NERGY -E FFICIENT LDPC C ODES AND D ECODERS Elsa Dupraz 16/04/2019

Section 1: Introduction 7 Energy-efficient LDPC codes Introduction LDPC codes and decoders Perf. analysis of faulty decoders Effect of faults in the decoders Conclusion ◮ In this talk, focus on channel coding E D Channel faulty faulty ◮ Noisy vs Faulty ◮ Family of error-correction codes : LDPC codes D ESIGN OF E NERGY -E FFICIENT LDPC C ODES AND D ECODERS Elsa Dupraz 16/04/2019

Section 1: Introduction 7 Energy-efficient LDPC codes Introduction LDPC codes and decoders Perf. analysis of faulty decoders Effect of faults in the decoders Conclusion ◮ In this talk, focus on channel coding E D Channel faulty faulty ◮ Noisy vs Faulty ◮ Family of error-correction codes : LDPC codes ◮ Objectives • Study the effect of faults in LDPC decoders • Design fault-tolerant LDPC decoders D ESIGN OF E NERGY -E FFICIENT LDPC C ODES AND D ECODERS Elsa Dupraz 16/04/2019

Section 1: Introduction 8 Outline Introduction LDPC codes and decoders Perf. analysis of faulty decoders Effect of faults in the decoders Conclusion 1. Introduction 2. LDPC codes and decoders 3. Perf. analysis of faulty decoders 4. Effect of faults in the decoders 5. Conclusion D ESIGN OF E NERGY -E FFICIENT LDPC C ODES AND D ECODERS Elsa Dupraz 16/04/2019

Section 2: LDPC codes and decoders 9 OUTLINE Introduction LDPC codes and decoders Perf. analysis of faulty decoders Effect of faults in the decoders Conclusion 1. Introduction 2. LDPC codes and decoders 3. Perf. analysis of faulty decoders 4. Effect of faults in the decoders 5. Conclusion D ESIGN OF E NERGY -E FFICIENT LDPC C ODES AND D ECODERS Elsa Dupraz 16/04/2019

Section 2: LDPC codes and decoders 10 Block channel codes Introduction LDPC codes and decoders Perf. analysis of faulty decoders Effect of faults in the decoders Conclusion E D Channel ◮ Channel : P ( Y | X ) D ESIGN OF E NERGY -E FFICIENT LDPC C ODES AND D ECODERS Elsa Dupraz 16/04/2019

Section 2: LDPC codes and decoders 10 Block channel codes Introduction LDPC codes and decoders Perf. analysis of faulty decoders Effect of faults in the decoders Conclusion E D Channel ◮ Channel : P ( Y | X ) Encoding Decoding u k : information sequence ( k ) x n : codeword ( n ) H ( n × m ) : parity check matrix G : generator matrix ( n × k ) H T x n = 0 x n = G u k LDPC codes : H sparse, optimized for good perf. D ESIGN OF E NERGY -E FFICIENT LDPC C ODES AND D ECODERS Elsa Dupraz 16/04/2019

Section 2: LDPC codes and decoders 11 Code construction Introduction LDPC codes and decoders Perf. analysis of faulty decoders Effect of faults in the decoders Conclusion ◮ H is a sparse parity check matrix, H T x n = 0.   1 0 1 1 0 0 H T = 0 1 0 0 1 1   0 1 0 1 1 0 ◮ v 1 , v 2 , · · · , v n : Variable Nodes (VN), degrees d v i c 1 , c 2 , · · · , c m : Check Nodes (CN), degrees d c j ◮ Regular codes : constant degrees d v , d c R = k n = 1 − d v d c D ESIGN OF E NERGY -E FFICIENT LDPC C ODES AND D ECODERS Elsa Dupraz 16/04/2019

Section 2: LDPC codes and decoders 12 LDPC code construction Introduction LDPC codes and decoders Perf. analysis of faulty decoders Effect of faults in the decoders Conclusion ◮ H is a sparse parity check matrix, H T x 6 = 0 3   1 0 1 1 0 0 H T = 0 1 0 0 1 1   0 1 0 1 1 0 ◮ v 1 , v 2 , · · · , v n : Variable Nodes (VN), degrees d v i c 1 , c 2 , · · · , c m : Check Nodes (CN), degrees d c j ◮ Regular codes : constant degrees d v , d c R = k n = 1 − d v d c D ESIGN OF E NERGY -E FFICIENT LDPC C ODES AND D ECODERS Elsa Dupraz 16/04/2019

Section 2: LDPC codes and decoders 13 LDPC decoders Introduction LDPC codes and decoders Perf. analysis of faulty decoders Effect of faults in the decoders Conclusion Ex : Gallager decoder, hard-decision decoder CN c 1 VN v 1 1 1 0 0 D ESIGN OF E NERGY -E FFICIENT LDPC C ODES AND D ECODERS Elsa Dupraz 16/04/2019

Section 2: LDPC codes and decoders 14 LDPC decoders Introduction LDPC codes and decoders Perf. analysis of faulty decoders Effect of faults in the decoders Conclusion Ex : Gallager decoder, hard-decision decoder CN c 1 VN v 1 1 1 1 0 0 0 0 D ESIGN OF E NERGY -E FFICIENT LDPC C ODES AND D ECODERS Elsa Dupraz 16/04/2019

Section 2: LDPC codes and decoders 15 LDPC decoders Introduction LDPC codes and decoders Perf. analysis of faulty decoders Effect of faults in the decoders Conclusion Ex : Gallager decoder, hard-decision decoder CN c 1 VN v 1 1 1 1 0 0 0 0 0 0 D ESIGN OF E NERGY -E FFICIENT LDPC C ODES AND D ECODERS Elsa Dupraz 16/04/2019

Section 2: LDPC codes and decoders 16 LDPC decoders Introduction LDPC codes and decoders Perf. analysis of faulty decoders Effect of faults in the decoders Conclusion Ex : Gallager decoder, hard-decision decoder CN c 1 VN v 1 1 1 1 0 0 0 0 0 0 0 D ESIGN OF E NERGY -E FFICIENT LDPC C ODES AND D ECODERS Elsa Dupraz 16/04/2019

Section 2: LDPC codes and decoders 17 LDPC decoders Introduction LDPC codes and decoders Perf. analysis of faulty decoders Effect of faults in the decoders Conclusion Ex : Gallager decoder, hard-decision decoder CN c 1 VN v 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 D ESIGN OF E NERGY -E FFICIENT LDPC C ODES AND D ECODERS Elsa Dupraz 16/04/2019

Section 2: LDPC codes and decoders 18 LDPC decoders Introduction LDPC codes and decoders Perf. analysis of faulty decoders Effect of faults in the decoders Conclusion Ex : Gallager decoder, hard-decision decoder CN c 1 VN v 1 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 D ESIGN OF E NERGY -E FFICIENT LDPC C ODES AND D ECODERS Elsa Dupraz 16/04/2019

Section 2: LDPC codes and decoders 18 LDPC decoders Introduction LDPC codes and decoders Perf. analysis of faulty decoders Effect of faults in the decoders Conclusion Ex : Gallager decoder, hard-decision decoder CN c 1 VN v 1 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 ◮ Hard-decision decoders : binary messages ◮ Soft-decision decoders : LLR messages, e.g. , log P ( X = 0 | y ) P ( X = 1 | y ) D ESIGN OF E NERGY -E FFICIENT LDPC C ODES AND D ECODERS Elsa Dupraz 16/04/2019

Section 2: LDPC codes and decoders 19 LDPC decoders Introduction LDPC codes and decoders Perf. analysis of faulty decoders Effect of faults in the decoders Conclusion ◮ VN update function : γ ( ℓ ) = Φ v ( µ ( ℓ ) 0 , µ ( ℓ ) 1 , · · · , µ ( ℓ ) d v − 1 ) ... ◮ CN update function : µ ( ℓ + 1 ) = Φ c ( γ ( ℓ ) 1 , · · · , γ ( ℓ ) d c − 1 ) ... D ESIGN OF E NERGY -E FFICIENT LDPC C ODES AND D ECODERS Elsa Dupraz 16/04/2019

Section 2: LDPC codes and decoders 20 LDPC decoders Introduction LDPC codes and decoders Perf. analysis of faulty decoders Effect of faults in the decoders Conclusion ◮ VN update function : γ ( ℓ ) = Φ v ( µ ( ℓ ) 0 , µ ( ℓ ) 1 , · · · , µ ( ℓ ) d v − 1 ) ◮ CN update function : µ ( ℓ + 1 ) = Φ c ( γ ( ℓ ) 1 , · · · , γ ( ℓ ) d c − 1 ) D ESIGN OF E NERGY -E FFICIENT LDPC C ODES AND D ECODERS Elsa Dupraz 16/04/2019