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CM4SOC Computational Mathematical Modelling for advanced System-On-Chip Design with special Emphasis on Channel Decoding Algorithms and Statistical Design.

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Präsentation zum Thema: "CM4SOC Computational Mathematical Modelling for advanced System-On-Chip Design with special Emphasis on Channel Decoding Algorithms and Statistical Design."—  Präsentation transkript:

1 CM4SOC Computational Mathematical Modelling for advanced System-On-Chip Design with special Emphasis on Channel Decoding Algorithms and Statistical Design

2 2 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) CM4SOC 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 3 Norbert Wehn Horst W. Hamacher Team Decoding of Blockcodes Frank Kienle (Akad. Rat) Mayur Punekar (PhD) Akin Tanatmis (PhD) Stefan Ruzika (Jun-Prof.) Sebastian Heupel (Diplomand) Michael Helmling (HiWI) Jie Liang (Studienarbeit)

4 4 Noisy Channel coding Channel Decoding Noisy Channel Channel Coding

5 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 ML Decoding  If p( ) is uniform - this is the case for the majority of communication systems 5

6 Goals 6 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

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

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

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, 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,  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

12 Progress 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 „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 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 „New Valid Inequalities for the LP-Decoding of Binary Linear Block Codes“, submitted to IEEE International Symposium on Information Theory New cut generation algorithm and calculation of Minimum Distance property of codes MISP seminar 12

13 Roadmap Dissertation Akin Tanatmis Dissertation Mayur Punekar Paper on LP decoding of Turbo codes Toolkit for AG Wehn Minimum Distance and ILP decoding framework Overview paper for LP decoding 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 DFG Initiative - Einzelantrag ? - SFB ? - Excellence Initiative

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

15  Worst Case / Corner Case Design  Statistical Design Motivation 30 nm 20 nm 10 nm Extreme device variations (L eff,T ox ) Wider 15

16 Leakage current of a SoC: sum of log-normal random variables Mathematical Approach 16 L i, L j, T i, T j 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

17 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 Mathematical Approach 17

18 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  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” Current Status and Next Steps 18

19 AWGN Channel Simulation Hardwareaccelerator ImplementationArchitectureThroughput Standard C code with custom random number generator 0.5 Mbps Optimized random generator using Intel SSE2 SIMD instruction set, GNU scientific library Intel Core 2 Duo PC 2.0 GHz, 3 GB RAM 6 Mbps Cell processor optimized using IBM Monte Carlo Llibrary Cell 3.2 GHz 256 MB RAM 72 Mbps FPGA Virtex 5Dedicted HW solution150 Mbps  FPGA based coprocessor for hardware supported Monte-Carlo based price finding 19

20 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: €  Zukünftiger Mittelbedarf aus (CM) 2 : ein WiMi + Softwarelizenzen AG Wehn 20

21 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: €  Zukünftiger Mittelbedarf aus (CM) 2 : ein WiMi + Softwarelizensen AG Hamacher 21

22 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 AG Korn 22

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