1. Information Theory for Mobile Ad-Hoc Networks (ITMANET): The FLoWS Project Thrusts 0 and 1 Metrics and Upper Bounds Muriel Medard, Michelle Effros and Ralf Koetter

2. Capacity Delay Power Upper Bound Lower Bound Capacity and Fundamental Limits Capacity Delay Power Utility=U(C,D,E) Application and Network Optimization (C*,D*,E*) Constraints Degrees of Freedom Models and Dynamics Application Metrics and Network Performance Layerless Dynamic Networks New Paradigms for Upper Bounds MANET Metrics Fundamental Limits of Wireless Systems Application Metrics Models New MANET Theory Metrics

3. Metrics and Upper Bounds Objective: –Develop a framework for new fundamental performance metrics (in conjunction with 3) –Develop meaningful upper bounds based on our metrics, thereby establishing the boundaries of operation MANETs –Use these bounds to obtain constructive approaches to leverage in other thrusts Performance metrics: capacity regions, distortion, delay per packet, completion time… Meaningful upper bounds: –May reflect achievability in certain regimes or topologies –Provide insight into effect of side information –Connect information-theoretic notions with queueing notions in a fundamental fashion Provide fundamental limits of performance in a way that naturally connects with other thrusts

4. Thrust Areas 1.Metric design Define relevant metrics that reconcile capacity with network-centric views of throughput and delay 2.New bounding techniques Consider techniques that move away from a layered approach and that build upon the designed metrics Characterization of effect of side information on networks 3.Combinatorial approaches Isolate the combinatorial nature to separate combinatorial difficulty from statistical methods 4.Code construction and network information theory Create new approaches to constructing codes based on metrics and bounding techniques 5.Networking and optimization Use optimization techniques to create bounds using new techniques for the metrics we designed

5. Recent Thrust Achievements: Networks with Side Information New Inner and Outer Bounds for Networks with Side Information (Cohen, Avestimehr, Effros 08) –Current understanding of networks with side information is limited mostly to depth one networks –Canonical source coding problems can be used to derive bounds for more complex networks –Strategies intended for small problems, when combined with network coding, can tackle complex networks, even in non-multicast problems –New inner and outer bounds are tight for several families of network – Opens new connections between networking and successive refinement

6. Recent Thrust Achievements: New Relaying Results Relaying for Multiple Communicating Pairs (Maric, Dabora, Goldsmith 08) –Consider relaying pairs over interference channel –The relay forwards an unwanted message, thus increasing the interference at the receiver –This allows the receiver to decode and cancel the interference –Under strong interference conditions, forwarding messages and interference achieves capacity relay dest1 dest2 source 1 source 2

7. Recent Thrust Achievements: Strong Converses Capacity Region for Gelfand-Pinsker MAC Channels (Moulin 08) –Most approaches to converses rely on Fano’s lemma –For MACs, it may be more tractable to consider worst-case errors rather than average errors –Gelfand-Pinsker represents transmission in the presence of known interference –A sphere packing analysis is conducted to bound the number of codewords that can be packed based on the requirement that the error probability is small for exponentially many codewords

8. Recent Thrust Achievements: Use of Feedback in Networks Feedback-based Increase in Network Capacity (Bakshi, Effros 08) –Feedback does not help in general in point-to-point links inside networks –It does help in even simple networks, particularly when we consider it jointly with network coding –Applies to several fundamental examples such as: –Butterfly network –Source coding with coded side information –Multiterminal source coding

9. Recent Inter-Thrust Achievements: Time-Division Duplex Channel with Feedback Minimizing Per-packet Delay in Time-division Duplex Systems (Lucani, Medard, Stojanovic 09) –Node can transmit and receive, but not at the same time –Not necessarily half time for transmitter and half for receiver –How much should we talk before stopping to listen? –Scheme can be modelled as a Markov chain: States: reported degrees of freedom required to decode Transition time or energy depends on starting state –We determined moment generating function of completion time and energy

10. New bounding techniques Achievements Overview – early Koetter: likelihood forwarding Medard, Koetter: network coding capacity based on conflict graphs Moulin: covert channel by timing information Koetter, Effros, Medard: Equivalence classes of networks, including multipoint channels Goldsmith: Interference channel with cognitive user, “asymmetric” cooperation Code construction Network information theory Networking and optimization Combinatorial Tools Zheng: error exponents UEP Metrics Goldsmith, Medard, Katabi: analog network coding Effros, Koetter: source coding region for “line networks”

11. New bounding techniques Achievements Overview – recent Code construction Network information theory Networking and optimization Combinatorial Tools Ozdaglar, Medard: Rate allocation in multiple access networks Zheng, Medard: unifying MDC and MR, distortion-diversity Ozdaglar, Medard: Network coding for downloading delay Metrics Ozdaglar, Medard: Cross-layer optimization under different metrics Goldsmith: generalized source-channel coding Effros: effect of side information on network capacity Effros: source coding continuity Coleman: Broadcast timing channel capacity Effros: linear network coding

12. New bounding techniques Achievements Overview- latest Code construction Network information theory Networking and optimization Combinatorial Tools Metrics Medard: coded time-division duplex for delay or energy minimization Goldsmith: multiple sender interference channel Moulin: converse for Gelfand-Pinsker MAC Effros: networks with side information Effros: effect of feedback in networks Shah: multicast capacity of large wireless networks Koetter, Medard: joint coding and scheduling in wireless networks Zheng: unequal error protection converse Moulin: mobility for interference mitigation Effros: game-theoretic approaches to network coding

13. Thrust Synergies: A Taxonomy Thrust 1 Upper Bounds Thrust 2 Layerless Dynamic Networks Thrust 3 Application Metrics and Network Performance Moulin: interference-mitigating mobility Medard: time-division duplex channel energy or delay minimization Zheng: unequal-error protection coding Koetter, Medard: joint scheduling and coding using conflict graphs Effros: networks with side information Goldsmith: multiple source interference channel Effros: game-theoretic approaches to network coding

14. Thrust Alignment with Phase 2 Goals Evolve results in all thrust areas to examine more complex models, robustness/security, more challenging dynamics, and larger networks: –Scaling laws for large networks with multicast –Networks with unequal error protection –Large networks with side information Demonstrate synergies between thrust areas: compare and tighten upper bounds and achievability results for specific models and metrics; apply generalized theory of distortion and utility based on performance regions developed in Thrusts 1-2: –New approach to optimize coding and scheduling – thrust 1-3 –New game-theoretic approach to network coding – thrusts 1-3 –New approaches to unequal error protection – thrusts 1-2 –Interference mitigating mobility – thrusts 1-2-3 –Interference forwarding – thrusts 1-2 Demonstrate that key synergies between information theory, network theory, and optimization/control lead to at least an order of magnitude performance gain for key metrics: –Use of coding-based TDD systems has order of magnitude throughput versus uncoded –Unbounded gain in network capacity with feedback