CM4SOC Computational Mathematical Modelling for advanced SystemOnChip Design with special Emphasis o

1
CM4SOC Computational 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 Modelli
erung und statistische Berechnung des Delays und
des Energieverbrauchs in Nanometer CMOS
Technologien (Hardwarebeschleuniger für
finanzmathematische Anwendungen)
3
Team
Decoding of Blockcodes
4
Channel Coding
5
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
State-of-the-art model
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
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
Statistical SoC Design

• Advanced Statistical Methods for Probabilistic
  Chip Design
• Finance mathematics

14
15
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
23
(No Transcript)