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

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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)

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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)

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NoisyChannel

Channelcoding

ChannelDecoding

NoisyChannel

Channel Coding

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

)yx(Pmaxargx̂C x

y)yx(P

x

ML Decoding

If p( ) is uniform - this is the case for the majority of communication systems

)xy(Pmaxargx̂Cx

x

x

y

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Goals

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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

Solution

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State-of-the-art model ILP model

LP relaxation Techniques

Results

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

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

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Talks, Cooperations

Plenary Presentation A Separation Algorithm for Improved LP-Decoding of Linear BlockCodes, 5th Int. Symp. on Turbo Codes and Related Topics, Lausanne, 2008.

Talk at TU KaiserslauternRüdiger 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

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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.

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Progress

2007 2008 2009

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 2009.

New cut generation algorithm and calculation of Minimum Distance

property of codes

MISP seminar

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Roadmap

2009 2010 2011

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

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DFG Initiative- Einzelantrag ?- SFB ?- Excellence Initiative

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Nicole Tschauder Norbert WehnRalf Korn

Statistical SoC Design

Advanced Statistical Methods for Probabilistic Chip Design Finance mathematics

Worst Case / Corner Case Design Statistical Design

Motivation

30 nm 20 nm10 nm

Extreme device variations (Leff,Tox)

0

50

100

100 120 140 160 180 200Vt(mV)

Rel

ativ

e

Wider

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Leakage current of a SoC: sum of log-normal random variables

Mathematical Approach

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gN

1iiXgN

1iiRidiTiciLibiagN

1i igate,leakleak eeIILi, Lj, Ti, Tj are dependent on each other

Total distribution = Marginal distribution + Dependencyunknown

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

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

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Investigated new mathematical approachesOpen 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 MunichDFG Initiative: Einzelantrag / SFB ?

R. Korn: Seminar “Monte-Carlo für Elektroingenieure”

Current Status and Next Steps

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AWGN Channel Simulation

Hardwareaccelerator

Implementation Architecture Throughput 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 RAM72 Mbps

FPGA Virtex 5 Dedicted HW solution 150 Mbps

FPGA based coprocessor for hardware supported Monte-Carlo based price finding

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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

AG Wehn

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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

AG Hamacher

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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

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