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Anwendung von fortgeschrittenen mathematischen Modellierungs- und Optimierungstechniken auf den Entwurf von mikroelektro

CM4SOC C omputational M athematical Modelling for advanced S ystem- O n- C hip Design with special Emphasis on Channel Decoding Algorithms and Statistical Design. CM4SOC.

JasminFlorian
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Anwendung von fortgeschrittenen mathematischen Modellierungs- und Optimierungstechniken auf den Entwurf von mikroelektro

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  1. CM4SOCComputational Mathematical Modelling for advanced System-On-Chip Design with special Emphasis on Channel Decoding Algorithms and Statistical Design

  2. CM4SOC Anwendung von fortgeschrittenen mathematischen Modellierungs- und Optimierungstechniken auf den Entwurf von mikroelektronischen Systemen (System-on-Chip) • Techniken der ganzzahligen, kombinatorischen Optimierung (AG Hamacher) • Risikomaße, Abhängigkeitsmodellierung und stochastische Modelle aus der Finanzmathematik (AG Korn) Effiziente Dekodieralgorithmen für lineare Blockcodes in der drahtlosen Kommunikation Modellierung und statistische Berechnung des Delays und des Energieverbrauchs in Nanometer CMOS Technologien (Hardwarebeschleuniger für finanzmathematische Anwendungen)

  3. Jie Liang (Studienarbeit) Mayur Punekar (PhD) Frank Kienle (Akad. Rat) Norbert Wehn Michael Helmling (HiWI) Akin Tanatmis (PhD) Stefan Ruzika (Jun-Prof.) Horst W. Hamacher Sebastian Heupel (Diplomand) Decoding of Blockcodes Team

  4. Noisy Channel Channel coding Channel Decoding Noisy Channel Channel Coding

  5. If p( ) is uniform - this is the case for the majority of communication systems ML Decoding Let be the transmitted datablock and be the received noisy data block Optimal decoder (Maximum Likelihood Decoder) • Decodes the output as the input that has the maximum a posteriori probability 5

  6. Goals ML decoding as integer linear programming problem (NP complete) • Exact algorithms & heuristics Importance for information theory • New bounds, code quality e.g. minimum distance • Decoding algorithms Mathematical approach • Investigation of polyhedral structures, binary matroids • Algorithms e.g. cutting planes Algorithmic tool box • Code analysis, code design, decoding algorithm evaluation 6

  7. Solution ILP model State-of-the-art model LP relaxation Techniques

  8. Results Irregular Low-Density Parity-Check Code (64,32) 8

  9. Activities • MISP SS 07 “Optimization and Digital Communications” • Discussion on possible interdisciplinary research topics • ILP/ LP based algorithms for decoding • Seminar/Proseminar topics on LP/IP decoding • SS 08, WS 08/09, SS 09 • Diploma Theses (MAT, EIT) • S. Heupel: “Cycle Polytopes and their Application in Coding Theory” • B. Thome: “Linear Programming Based Approaches in Coding Theory” • J. Liang: “Deoding of Linear Blocks by Ant Algorithms” • Regular meetings 9

  10. Talks, Cooperations • Plenary Presentation • A Separation Algorithm for Improved LP-Decoding of Linear Block • Codes, 5th Int. Symp. on Turbo Codes and Related Topics, • Lausanne, 2008. • Talk at TU Kaiserslautern • Rüdiger Stephan and Akin Tanatmis: Polyhedral Components • for LP-Decoding / TU Berlin - AG Grötschel • Cooperations • Yair Beery: School of Electrical Engineering, Tel Aviv University • Pascal Vontobel: Information Theory Research Group, Information and Quantum Systems Laborator Hewlett-Packard Laboratories Palo Alto 10

  11. Interdisciplinary Publications • New Algorithm for improved LP decoding • A. Tanatmis, S. Ruzika, H.W. Hamacher, M. Punekar, F. Kienle, and N. Wehn „A separation algorithm for improved LP-decoding of linear block codes“, Proc. 5th International Symposium on Turbo Codes and Related Topics, Lausanne Switzerland, Sept. 1-5, 2008. • A. Tanatmis, S. Ruzika, H.W. Hamacher, M. Punekar, F. Kienle, and N. Wehn „A separation algorithm for improved LP-decoding of linear block codes“, submitted to IEEE Transactions on Information Theory. • New cut generation algorithm and computation of minimum distance property of codes • A. Tanatmis, S. Ruzika, H.W. Hamacher, M. Punekar, F. Kienle, and N. Wehn „New Valid Inequalities for the LP Decoding of Binary Linear Block Codes“, submitted to IEEE International Symposium on Information Theory 2009. 11

  12. Progress 2007 2008 2009 MISP seminar New cut generation algorithm and calculation of Minimum Distance property of codes New Integer Programming/ Linear Programming formulation of the ML decoding problem Publication: A. Tanatmis, S. Ruzika, H.W. Hamacher, M. Punekar, F. Kienle, and N. Wehn „New Valid Inequalities for the LP-Decoding of Binary Linear Block Codes“, submitted to IEEE International Symposium on Information Theory 2009. New Algorithm for improved LP decoding Publication: A. Tanatmis, S. Ruzika, H.W. Hamacher, M. Punekar, F. Kienle, and N. Wehn „A separation algorithm for improved LP-Decoding of linear block codes“ submitted to IEEE Transactions on Information Theory Publication: A. Tanatmis, S. Ruzika, H.W. Hamacher, M. Punekar, F. Kienle, and N. Wehn „A separation algorithm for improved LP-Decoding of linear block codes“ Proc. 5th International Symposium on Turbo Codes and Related Topics, Lausanne Switzerland, Sept. 1-5, 2008 12

  13. DFG Initiative • - Einzelantrag ? • SFB ? • - Excellence Initiative Roadmap 2009 2010 2011 Paper on LP decoding of Turbo codes Dissertation Akin Tanatmis Dissertation Mayur Punekar Overview paper for LP decoding Toolkit for AG Wehn Minimum Distance and ILP decoding framework • Research Goals • Polynomial time decoding algorithms based on LP • Library of „optimum decoding“ (Reference) curves • for codes used in current standards e.g. UMTS. • Low complexity LP decoding algorithms • Simulation framework 13

  14. Ralf Korn Nicole Tschauder Norbert Wehn Statistical SoC Design Advanced Statistical Methods for Probabilistic Chip Design • Finance mathematics 14

  15. Wider 30 nm 20 nm 10 nm Extreme device variations (Leff,Tox) Motivation • Worst Case / Corner Case Design  Statistical Design 15

  16. Mathematical Approach Leakage current of a SoC: sum of log-normal random variables Li, Lj, Ti, Tj are dependent on each other Total distribution = Marginal distribution + Dependency unknown Moment based approximation • Wilkinson Method, inverse Gamma Method Bounds • Frechet-Hoeffding Bounds Focus on critical regions e.g. high leakage currents • Tail dependencies • Gumbel-Copulas 16

  17. Mathematical Approach Risk measures Quantify the consequences of a distribution, i.e, the risk of a random variable X • Variance • Value-at-risk, Tail-Value-at-risk • Stop-Loss-Rate • Expected Shortfall Concept of Comonotonicity • Allows calculation of bounds for risk measures 17

  18. Current Status and Next Steps Investigated new mathematical approaches Open issue: performance evaluation with concrete technology data Set up cooperation with TU München (Prof. Dr. U. Schlichtmann) • Presentation at TU München 4.11.2009 • Scientific exchange and cooperation agreement • Decision on same technology platform Request for Infineon C12 technology data in progress Performance evaluation with IFX C12 technology Cooperation TU Munich DFG Initiative: Einzelantrag / SFB ? R. Korn: Seminar “Monte-Carlo für Elektroingenieure” 18

  19. Hardwareaccelerator AWGN Channel Simulation • FPGA based coprocessor for hardware supported Monte-Carlo based price finding 19

  20. AG Wehn Current projects • INFINEON Project “Channel coding in Software Defined Radio” • DFG Excellence Cluster UMIC RWTH Aachen “MIMO & Channel Coding” • BMBF Project “Autonome integrierte Systeme” DFG SPP Proposal submitted • Entwurf und Architekturen verlässlicher eingebetteter Systeme: Ein Grand Challenge im Nano-Zeitalter (TU Kaiserslautern,TU Karlsruhe, TU Mün-chen,Univ. Tübingen) Zugewiesene Mittel • Bisher: 30.000 € • Zukünftiger Mittelbedarf aus (CM)2: ein WiMi + Softwarelizenzen 20

  21. AG Hamacher Current projects • DFG-SPP 1126 “Algorithmik großer und komplexer Netze” • BMBF-Projekt “REPKA” (mit Siemens, Fraunhofer IIS) DFG Proposal • Combinatorial Properties of Multiple Criteria Integer Programming Problems • Joint Proposal “Discrete Optimization Methods in Digital Communications” with AG Wehn in discussion Zugewiesene Mittel: • Bisher: 30.000 € • Zukünftiger Mittelbedarf aus (CM)2: ein WiMi + Softwarelizensen 21

  22. AG Korn Current projects • DFG-Projekt “Anwendung und Entwicklung neuer Monte Carlo Methoden bei freien Randwertproblemen und Quasi-Variationsungleichungen in der Finanzmathematik” Zugewiesene Mittel • Bisher: 0 € - Finanzierung von N. Tschauder aus DFG Graduiertenkolleg Mathematik und Praxis • Zukünftiger Mittelbedarf aus (CM)2: ein WiMi + Softwarelizenzen 22

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