Information Theory for Mobile Ad-Hoc Networks (ITMANET): The FLoWS Project

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

3. Metrics and Upper Bounds • Objective: • Develop a framework for new fundamental performance metrics (in conjunction with 3) • Develop meaningful upper boundsbased 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 Metric design Define relevant metrics that reconcile capacity with network-centric views of throughput and delay 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 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 dest1 source 1 relay dest2 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. Achievements Overview – early Zheng: error exponents UEP New bounding techniques Effros, Koetter: source coding region for “line networks” Koetter: likelihood forwarding Code construction Network information theory Moulin: covert channel by timing information Goldsmith: Interference channel with cognitive user, “asymmetric” cooperation Koetter, Effros, Medard: Equivalence classes of networks, including multipoint channels Metrics Goldsmith, Medard, Katabi:analog network coding Medard, Koetter: network coding capacity based on conflict graphs Networking and optimization Combinatorial Tools

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

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

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

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