1 / 28

101

Using Feedback in MANETs: a Control Perspective. 101. 111. Todd P. Coleman colemant@illinois.edu University of Illinois DARPA ITMANET. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A A A A A A. Current Uses of Feedback. Theory

vicky
Télécharger la présentation

101

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Using Feedback in MANETs: a Control Perspective 101 111 Todd P. Coleman colemant@illinois.edu University of Illinois DARPA ITMANET TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAA

  2. Current Uses of Feedback • Theory • Feedback modeled noiseless • Point-to-point: capacity unchanged • Significantly improved error exponents • Reduction in complexity • MANETs: Enlargement of capacity region

  3. Current Uses of Feedback • Practice • Feedback is noisy, used primarily for • Robustness to channel uncertainty • Estimation of channel parameters • ARQ-style communication w/ erasures

  4. Current Uses of Feedback • Practice • Feedback is noisy, used primarily for • Robustness to channel uncertainty • Estimation of channel parameters • ARQ-style communication w/ erasures • But: Burnashev-style “forward error correction+ARQ” schemes are extremely fragile w/ noisy feedback (Kim, Lapidoth, Weissman 07)

  5. Applicability of Feedback in MANETs 101 111 • Instantiate network feedback control algorithms for MANETs • Develop iterative practical schemes for noisy feedback? • Coding w/ feedback over statistically unknown channels? • Develop fundamental limits of error exponents with feedback w/ fixed block length

  6. Communication w/ Noiseless Feedback 0 0.25 0.50 0.75 1.00 00 01 10 11 0 1

  7. Communication w/ Noiseless Feedback 0 0.25 0.50 0.75 1.00 00 01 10 11 0 1 Given an encoder’s Tx strategy, decoding is almost trivial (Baye’s rule)

  8. Communication w/ Noiseless Feedback 0 0.25 0.50 0.75 1.00 00 01 10 11 0 1 Given an encoder’s Tx strategy, decoding is almost trivial (Baye’s rule) How do we select a (recursive) encoder strategy for an arbitrary memoryless channel?

  9. A Control Interpretation of the Dynamics of the Posterior Coleman ’09: “A Stochastic Control Approach to ‘Posterior Matching’-style Feedback Communication Schemes”

  10. A Control Interpretation of the Dynamics of the Posterior Coleman ’09: “A Stochastic Control Approach to ‘Posterior Matching’-style Feedback Communication Schemes”

  11. A Control Interpretation of the Dynamics of the Posterior Coleman ’09: “A Stochastic Control Viewpoint on ‘Posterior Matching’-style Feedback Communication Schemes” uk Fk P(Fk|Fk-1, uk) reference signal Controller Fk-1 Z-1 Fw*

  12. Stochastic Control: Reward Coleman ’09 Fw* Fk+1 D(Fw*||Fk+1) Reward at any stage k is the reduction in “distance” to target Xk Fk D(Fw*||Fk)

  13. Maximum Long-Term Average Reward Coleman ’09

  14. Maximum Long-Term Average Reward Coleman ’09 • (1),(2) hold w/ equality if: • a) Y’s all independent • b) Each Xi drawn according to P*(x)

  15. Maximum Long-Term Average Reward Coleman ’09 • (1),(2) hold w/ equality if: • a) Y’s all independent • b) Each Xi drawn according to P*(x) • Horstein ’63 (BSC) • Schalwijk-Kailath ’66 (AWGN) • Shayevitz-Feder ‘07, ‘08 (DMC)

  16. The Posterior Matching Scheme: an Optimal Solution Coleman ’09 • Next input indepof everything decoder has seen so far, withcapacity-achieving marginal distribution • No forward error correction. Adapt on the fly. Posterior matching scheme

  17. The Posterior Matching Scheme: an Optimal Solution Coleman ’09 • Next input indepof everything decoder has seen so far, withcapacity-achieving marginal distribution • No forward error correction. Adapt on the fly. Posterior matching scheme

  18. Implications for Demonstrating Achievable Rates Coleman ’09 0 1 0 1 1 0 1 0 1

  19. Coleman ’09 Lyapunov Function 0 1 Posterior matching scheme: 0 1

  20. Lyapunov Function (cont’d) Coleman ’09 0 1 1 0 1 0 1

  21. Information Theory Control Theory Symbiotic Relationship Coleman ’09: “A Stochastic Control Viewpoint on ‘Posterior Matching’-style Feedback Communication Schemes” Converse Thms Give Upper Bounds on Average Long-Term Rewards for Stochastic Control Problem

  22. Information Theory Control Theory Symbiotic Relationship Coleman ’09: “A Stochastic Control Viewpoint on ‘Posterior Matching’-style Feedback Communication Schemes” Converse Thms Give Upper Bounds on Average Long-Term Rewards for Stochastic Control Problem KL Divergence Lyapunov functions guarantee all rates achievable

  23. Research Results with This Methodology • Interpret feedback communication encoder design as stochastic control of posterior towards certainty • Converse theorems specify fundamental performance bounds on a stochastic control problem related to controlling posterior. • An optimal policy implies the existence of a Lyapunov function, which is in essence a KL divergence • Lyapunov function directly implies achievability for all R < C Coleman ’09

  24. Research Results with This Methodology • Interpret feedback communication encoder design as stochastic control of posterior towards certainty • Converse theorems specify fundamental performance bounds on a stochastic control problem related to controlling posterior. • An optimal policy implies the existence of a Lyapunov function, which is in essence a KL divergence • Lyapunov function directly implies achievability for all R < C Coleman ’09 Gorantla and Coleman ‘09: Encoders that achieve El Gamal 78: “Physically degraded broadcast channels w/ feedback“ capacity region in an iterative fashion w/ low complexity

  25. Information Theory Control Theory New Important Directions this Approach Enables 101 111 • Develop iterative low-complexity encoders/decoders for noisyfeedback? Partially Observed Markov Decision Process

  26. Information Theory Control Theory New Important Directions this Approach Enables 101 111 • Develop iterative low-complexity encoders/decoders for noisyfeedback? Partially Observed Markov Decision Process • Optimal coding w/ feedback over statistically unknown channels?Reinforcement learning from control literature

  27. Information Theory Control Theory New Important Directions this Approach Enables 101 111 • Develop iterative low-complexity encoders/decoders for noisyfeedback? Partially Observed Markov Decision Process • Optimal coding w/ feedback over statistically unknown channels?Reinforcement learning from control literature • Develop fundamental limits of error exponentswith feedback w/ fixed block length Lyapunov function enables a fundamental Martingale condition

  28. Information Theory Control Theory New Important Directions this Approach Enables 101 111 • Develop iterative low-complexity encoders/decoders for noisyfeedback? Partially Observed Markov Decision Process • Optimal coding w/ feedback over statistically unknown channels?Reinforcement learning from control literature • Develop fundamental limits of error exponents with feedback w/ fixed block length Lyapunov function enables a fundamental Martingale condition • Also:stochastic control approach provides a rubric to check tightness of converses via structure of optimal solution

More Related