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

1. Information Theory for Mobile Ad-Hoc Networks (ITMANET): The FLoWS Project Thrust 1

2. ACHIEVEMENT DESCRIPTION STATUS QUO END-OF-PHASE GOAL COMMUNITY CHALLENGE NEW INSIGHTS Unequal Error Protection: Application and Performance Limits S. Borade, B. Nakiboglu, L. Zheng • “bits” as the universal measure of information and interface to physical layer: a homogenous view. • High priority control messages are sent over separated channels. • No performance limits on UEP • Perfect reliability assumed on network controls • Complete UEP tradeoff with geometric approach • Data driven network controls, Layering and QoS as interface • MAIN RESULT: • Optimizing the overall resource, the reliability of control signals has a threshold effect; • Communicating at capacity, not even a single bit can be protected with positive exponent; • Message-wise prioritization yields better tradeoffs than bit-pipe partitioning. • HOW IT WORKS: • Protecting special message is much easier than special bit; • With feedbacks, a two-phase scheme can be used, where critical message is used to initiate retransmissions; New interface to the physical layer leads to more flexible higher layer functionalities, and system level optimizations; the new interface also needs to be backward compatible to bit based networks • Joint coding allows flexible resource allocation; • Priority of critical data in the form/costs of better error protections; • Global optimization of resource allocation among heterogeneous data; Better tradeoff in UEP has significant effects on overall system performance Embedding control messages/significant data with UEP

3. [UPPER BOUNDS] The conventional approach used for deriving (weak) converses, based on Fano’s inequality, is insufficient. There remains a gap between inner (achievable) and outer rate regions. • The approach could potentially be extended to the broadcast channel and possibly to complex networks • First item planned.Extend approach to degraded broadcast channel. • Second item planned. Extend approach to more complexnetworks. STATUS QUO IMPACT • For MACs, the strong converse with maximum-error criterion seems to be more tractable than average-error criterion • Some creativity is needed to guess a suitable reference distribution over output space Extend this technique to more general networks NEXT-PHASE GOALS NEW INSIGHTS Towards Strong Converses for MANETs: Moulin • MAIN ACHIEVEMENT: • Derived capacity region for multiple-access Gelfand-Pinsker channel. The GP channel models transmission in the presence of known interference • HOW IT WORKS: • A set of typical channel outputs is defined. • 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. • The approach is based on elementary statistics of the difference between empirical mutual informations (aka “self-informations” of codewords, or “information densities”) • ASSUMPTIONS AND LIMITATIONS: • Memoryless channel, but this is not a fundamental limitation of the approach • This has been verified for a few problems (Verdu’s information spectrum, and Moulin’s fingerprinting problem) New tools are needed to derive tighter outer bounds on capacity regions

4. Information Theory for Mobile Ad-Hoc Networks (ITMANET): The FLoWS Project Thrust 2

5. ACHIEVEMENT DESCRIPTION Finite-State Channel Yi-1 STATUS QUO Xi p(yi,si|xi,si-1) Yi Tx IMPACT Rx D Si Si-1 NEXT-PHASE GOALS NEW INSIGHTS Indecomposable Finite-State Channels With Feedback Ron Dabora and Andrea Goldsmith Understand how to combine code synchronization into the design of communication networks with Markov dynamics Identify classes of inhomogeneous indecomposable FSCs for which feedback achieves the maximum over all initial states • MAIN ACHIEVEMENT: • We identified classes of practical channels that can be modeled as indecomposable FSCs. We showed that their capacity with feedback is equal to the maximum over all channel states. • HOW IT WORKS: • We identified classes of practical channels that can be modeled as indecomposable FSCs. We showed that their capacity with feedback is equal to the maximum over all channel states. • ASSUMPTIONS AND LIMITATIONS: • The previous state contains all the past information. The current output and state depends on both the current input and previous state. • Many practical communication channels are represented as inhomogeneous indecomposable FSCs • When feedback is present, the capacity of indecomposable channels does not achieve the maximum over all states. Introduce the notion of “weakly indecomposable” FSCs, i.e., FSC that are indecomposable only without feedback Capacity of indecomposable FSCs with feedback can be found without searching over all channels states Coding schemes that incorporate Tx-Rx synchronization into the code can achieve the maximum over all states for certain indecomposable channels • Extension to multiuser channels with feedback • Translation of the results obtained for the discrete channel to Gaussian channels with ISI and feedback Most communication channels are subject to correlated time variations

6. ACHIEVEMENT DESCRIPTION STATUS QUO IMPACT NEXT-PHASE GOALS NEW INSIGHTS Mutual information and estimation in channelsof exponential family type: Coleman and Raginsky New results on broadcast and secrecy capacity without relying on explicit degradation assumptions. New results on mutual information and estimation beyond the AWGN channel and squared error criterion. • MAIN ACHIEVEMENT: • Analysis of dependence of mutual information on channel quality reduces to an estimation-theoretic problem with distortion function r(x,y) • HOW IT WORKS: • Structure of E-type channels leads to a dual estimation-theoretic characterization of mutual information as the minimum rate needed to describe the channel output with a given constraint on E[r(X,Y)] • We can leverage this duality to prove monotonicity of I(X;Y) w.r.t. b under an additional (reasonable) assumption on the behavior of posterior estimators • ASSUMPTIONS AND LIMITATIONS: • For a general E-type channel, can prove montonicity of mutual info only in high-SNR (high-b) regime How does channel quality impact performance? • Need to explicitly assume channel family is ordered by degradation • Need to check appropriate conditions on case-by-case basis • Many channels have this exponential family structure. Can connect information theory to estimation theory and statistics. • Exploit maximum entropy character of exponential families • Instead of degradation, exploit the b-monotonicity of information gain Explore connections between information theory and statistics of E-type channels to obtain new performance results in the network setting. New insights into information/estimation lead to robust design principles for MANETs.

7. ACHIEVEMENT DESCRIPTION STATUS QUO IMPACT NEW INSIGHTS NEXT-PHASE GOALS Dynamics and Control Principles for Feedback Encoder DesignsColeman • Provides explict capacity-achieving recursvie encoders for degraded broadcast channels • Can be extended to many networks with tight converses MAIN RESULT: 101 StochasticControl and Lyapunov theory combined with converse theorems provide a canonical methodology to design low-complexity iterative encoders with feedback in MANETs that achieve capacity The use of feedback is of the utmost importance in designing scalable, robust, reliable communication schemes Design principles for provably good iterative feedback encoders (essentially) limited to Gaussian scenarios 111 • Converse to coding theorems with feedback directly guides us how encoders should operate • State of the system is posterior distribution on message given • Feedback encoder should be interpreted as a controller, trying to drive state to certainty. • Formulate a stochastic control problem and find optimal policy 101 • HOW IT WORKS: • Converse theorems specify a stochastic control problem. An optimal policy implies the existence of a Lyapunov function • The KL divergence acts as a Lyapunov function on the state of the system • This directly implies achievabililty of all rates in capacity region with this explicit iterative encoding scheme 111 • Use Stochastic Control methodology for a principled, canonical approach to address:: • noisy feedback (POMDP) • Unknown channel (Q-learning) • Delayed feedback Xn Y1 …. Yn • ASSUMPTIONS AND LIMITATIONS: • Noiseless feedback • Memoryless Channels A Canonical Controls Methodology to Design Iterative Feedback Coding Systems in MANETs

8. ACHIEVEMENT DESCRIPTION STATUS QUO IMPACT NEXT-PHASE GOALS NEW INSIGHTS Optimal ARQ Protocol For Multihop MIMO Relay NetworksYao Xie, Deniz Gunduz, Andrea Goldsmith Found optimal ARQ protocol in multihop MIMO relay networks. Characterized DMDT surfaces provide insights for practical optimal ARQ protocols design. • MAIN RESULTS • 3D DMDT Surfaces for Various ARQ protocols ((4,1,3) system) • ASSUMPTIONS AND LIMITATIONS: • Long-term/short-term static channel • Total number of ARQ rounds is L • Decode-and-forward relaying strategy • Channel state information at Rx, Rayleigh Fading • Special cases: closed form DMDT; general case: DMDT • solved using convex optimization diversity What is the rate-reliability-delay tradeoff in multihop MIMO relay network? Fractional variable L = 1 rate Block variable • There are • Diversity-multiplexing tradeoff (DMT) analysis for relay channel • •Diversity-multiplexing-delay tradeoff (DMDT) for point-to-point MIMO with ARQ Block Variable ARQ Fractional Variable ARQ L = 10 (2,2,2) system Long-term • We characterize the diversity-multiplexing-delay tradeoff (DMDT) surface for various ARQ protocols • •Theorem: the fractional variable ARQ protocol achieves optimal DMDT • “Relay should talk ASAP” ARQ 1 ARQ 2 diversity How it works: ARQ protocols in ARQ MIMO relay networks H2 H1 Short-term Optimal Operational Point rate • Optimal ARQ protocol for general relay network • Effects of power control • Joint source-channel coding in MIMO relay network ARQ provides one more dimension of tradeoff in MIMO relay networks.

9. FLOWS & NEQUIT ACHIEVEMENT STATUS QUO END-OF-PHASE GOAL COMMUNITY CHALLENGE NEW INSIGHTS The Multi-Way Relay ChannelDeniz Gündüz, Aylin Yener, Andrea Goldsmith and Vincent Poor Exact capacity regions are hard to obtain even with three nodes. Random codes are capacity achieving for many models. Decode-and-forward relaying used in most practical systems. • Consider inter and/or intra cluster reception • Combine structured and random codes • Characterize non-symmetric achievable rate points MAIN RESULT: MODEL: Clusters of users: Each user in a cluster wants messages of all other users in the same cluster. Communication is enabled by the relay. ASSUMPTIONS AND LIMITATIONS: No signal received from other users Symmetric capacity for a symmetric system is analyzed * Achievable symmetric rate is characterized and compared to the upper bound Joint source-channel coding techniques to achieve higher rates Structured codes might provide higher rates than random coding in some networks • Can we scale structured codes to multiple users? • Design of practical codes based on joint source-channel coding techniques Compress-and-forward relaying achieves symmetric rates within a constant gap of capacity. This gap decays with increasing number of users.

10. Random Linear Network Coding for Time Division Duplexing (TDD) Lucani, Médard, Stojanovic ACHIEVEMENT DESCRIPTION Cluster Network STATUS QUO IMPACT NEW INSIGHTS NEXT-PHASE GOALS • Novel network coding strategy for TDD • Use of feedback (ACK) improves delay/energy/ throughput performance, especially for high latency- high errors scenarios • Random linear coding allows extension to networks MAIN RESULTS: Novel network coding scheme for TDD channels 1. Delay and Energy Analysis for Link and Broadcast cases 2. Exists optimal transmission time in terms of minimizing block delay, with close-to-optimal energy performance. 3. Outperforms Selective Repeat schemes in high latency- high error scenarios. Similar performance otherwise. 4. Delay/throughput is close to full duplex network coding, requiring much less energy • Network coding has studied throughput or delay performance considering minimal feedback • TDD has used ARQ/FEC schemes 1. Use feedback to improve delay performance: ACK states required number of coded packets to decode data 2. Transmit coded packets for some time, stop to wait for ACK HOW IT WORKS: 1. Transmission time computed to minimize delay in data block transmissions, using ACK and channel conditions 2. Stop transmission to wait for ACK from receiver (s). ACK used to update transmission time • Extend broadcast: effect of clusters of cooperative nodes • Sensitivity analysis • Extend to general network scenario 3. Transmission time depends on ACK and channel conditions: Exists optimal choice ASSUMPTIONS AND LIMITATIONS: Random linear coding, prior knowledge/estimate of propagation delay and errors Feedback, coding and optimal choice of transmission time minimizes delay, while keeping throughput performance similar or better than typical TDD ARQ schemes

11. ACHIEVEMENT DESCRIPTION STATUS QUO IMPACT NEXT-PHASE GOALS NEW INSIGHTS Layered Source-Channel Schemes: A Distortion-Diversity Perspective: Medard, Zheng • Three-layer schemedominates previous double-layer schemes • Distortion-diversity tradeoff provides useful comparison in different operating regions • MAIN ACHIEVEMENT: • A three-layer source-channel scheme, which includes previous multi-resolution-based and multi-description-based schemes as special cases • HOW IT WORKS: • Multi-description source code with a common refinement component • Superposition coding with successive interference cancellation • Joint source-channel decoding exploits source code correlation • ASSUMPTIONS AND LIMITATIONS: • Quasi-static block-fading channel • Receivers have perfect channel state information, but the transmitter only has statistical knowledge of the channel • Conventional source-channel scheme achieves a single level of reconstruction • Diversity is usually achieved in the channel coding component • Diversity can be achieved through source coding techniques, like multiple description codes • We characterize source-channel schemes with distortion-diversity tradeoff • Extend multi-description-based source-channel scheme while preserving the interface between source and channel coding • More general channel model Distortion-diversity tradeoff better characterizes layered source-channel schemes

12. The Capacity Region of the Cognitive Z-interference Channel with a Noiseless Non-cognitive LinkNan Liu, Ivana Marić, Andrea Goldsmith and Shlomo Shamai ACHIEVEMENT DESCRIPTION Capacity of networks with cognitive users are unknown. Consequently, optimal ways how to operate such networks are not understood, nor it is clear how cognitive nodes should exploit the obtained information. IT channel models suitable for networks with cognitive users still need to be proposed. Capacity of Z-interference channel is still unknown. Z-interference channel • MAIN ACHIEVEMENT: • 1) The capacity region of the discrete cognitive Z- interference channel with a noiseless non-cognitive link2) An inner and outer bound for the cognitive Z-interference channel • 3) Solution to the generalized Gel’fand- Pinsker (GP) problem in which a transmitter-receiver pair communicates in the presence of interference non causally known to the encoder. Our solution determines the optimum structure of interference. • HOW IT WORKS: • Non-cognitive encoder uses superposition coding to enable partial decoding of interference. The cognitive encoder precodes against the rest of interference using GP encoding. • ASSUMPTIONS AND LIMITATIONS: • The considered channel model: 1) Optimal scheme for some channels 2) Superposition coding and Gel’fand-Pinsker coding may be required in order to minimize interference, in some channels. This is in contrast to the Gaussian channel. 3) For the GP problem, the optimal interference has a superposition structure STATUS QUO IMPACT W1 W1 dest1 source 1 W2 W2 dest2 source 2 • Evaluate a numerical example • Apply proposed encoding scheme to larger networks and to different cognitive node models NEXT-PHASE GOALS In some scenarios, interference can be minimized by exploiting the structure of interference and cognition at the nodes. Cognition should be used by the encoder to precode against part of the interference caused to its receiver. W1, W2 W1 dest1 cognitive encoder NEW INSIGHTS W2 W2 non-cognitive encoder dest2 Encoding scheme was proposed that exploits cognition and is optimal in certain scenarios

13. Information Theory for Mobile Ad-Hoc Networks (ITMANET): The FLoWS Project Thrusts 1&2

14. Relaying for Multiple Communicating PairsIvana Marić, Ron Dabora and Andrea Goldsmith ACHIEVEMENT DESCRIPTION Several relaying strategies for forwarding information to a single receiver exist Capacity of networks are still unknown; one of the key obstacles: how to handle and exploit interference? How to relay for multiple sources?Traditional approach: routing 1) Interference forwarding can increase rates • MAIN ACHIEVEMENT: • 1) Achievable rate region for the interference channel with a relay channel • 2) Strong interference conditions under which forwarding messages and interference achieves capacity • 3) A new sum-rate outer bound to the performance • HOW IT WORKS: • The relay forwards an unwanted message, thus increasing the interference at the receiver. This allows the receiver to decode and cancel the interference. • For the outer bound: a genie enables receiver to decode both messages • ASSUMPTIONS AND LIMITATIONS: • The considered channel model: the interference channel with a relay • Simple encoding schemes investigated STATUS QUO IMPACT 2) A tighter outer bound In networks with multiple sources, relays can help beyond forwardinguseful information, by increasing interference at the receivers. This allows receivers to decode the interference and cancel it prior to decoding their desired messages NEXT-PHASE GOALS dest1 source 1 • Consider interference forwarding in combination with other encoding strategies • Apply interference forwarding and the outer bound to larger networks relay NEW INSIGHTS dest2 source 2 A relaying strategy for networks with multiple sources that can improve rates and achieve capacity in certain scenarios proposed. A tighter sum-rate bound on the performance developed.

15. ACHIEVEMENT DESCRIPTION IMPACT STATUS QUO NEXT-PHASE GOALS NEW INSIGHTS Cooperation and cognition in MIMO cognitive networksYing Chang and Andrea Goldsmith • We derive the optimal achievable rate for MISO secondary users under coexistence constraints • We propose practical strategies for cognition and cooperation in MIMO systems • We find the relation between secondary user’s achievable rate and primary user’s power allocation scheme • MAIN ACHIEVEMENT: • HOW IT WORKS: • Secondary user has non causal knowledge of primary users’ transmission and performs cognition together with cooperation to compensate the interference to primary receiver. • We study the cases with MISO and MIMO secondary transmission system and multiple primary receivers. • ASSUMPTIONS AND LIMITATIONS: • Primary users’ transmission rate is unchanged Single-primary-user cognitive network Multi-primary-user cognitive networks System model We consider a MIMO cognitive network as shown below. The cognitive transmitter determines its codeword as a function of the messages mp and mc . In this case, the primary transmitter broadcasts to several primary receivers. To maintain the capacity region of primary users, the cognitive user cooperate with each primary receiver. Power allocation scheme is developed for MISO and MIMO cognitive user. When the capacity region of the primary broadcast channel is achieved, the transmission rate for the cognitive user is as follows: Interestingly, we find out the relation between the primary users’ sum rate and cognitive user’s transmission rate is not monotonic. • In literature, achievable rates of single-antenna secondary user is well studied • How to do cooperation and cognition with multiple antennas and multiple primary users is our main focus MISO , single primary user MIMO Single primary user MISO multiple primary users • Decompose the MIMO channel into orthogonal components and leverage secondary user’s beneficial and deteriorative impact to the primary user. • Introduce cooperation to broadcast system How to utilize new degrees of freedom brought by MIMO technique? To not impact the transmission rate of primary (licensed) user, the cognitive user performs cooperation to compensate the interference it causes to the primary user. Encoding rule for the cognitive user: The cognitive encoder acts in two stages. For every message pair (mp, mc), the cognitive encoder first generates a codeword for the primary message mp. In the second stage, the cognitive encoder generates a codeword for mc using Costa pre-coding. The two codewords are superimposed to form the cognitive codeword. • Study multiple primary receivers with multiple antennas • Information theoretical bounds on MIMO cognitive networks In MIMO networks, we are more flexible to deal with interference • MIMO cognitive user • In this case, we have a MIMO cognitive transmission pair. We propose two sub-optimal transmission strategies for the cognitive user: • Direct Channel SVD (D-SVD) • The precoding matrix is obtained from the SVD of the cognitive user’s channel • Projected Channel SVD (P-SVD) • The cognitive user’s channel is projected onto the null space of the channel between the cognitive transmitter and primary receiver. Than SVD is performed on the projection. • Under different power constraint, the performances of the two strategies are compared with the MIMO channel capacity. MISO cognitive user In this case, we have a MISO cognitive transmission pair. We propose an optimal transmission strategy for the cognitive user which projects its beamformingvector onto orthogonal and aligned channel components. The relation between the primary user’s rate and cognitive user’s rate is as follows:

16. ACHIEVEMENT DESCRIPTION STATUS QUO IMPACT NEXT-PHASE GOALS NEW INSIGHTS On Networks with Side InformationA. Cohen, S. Avestimehr and M. Effros • Tight results for several families of networks with side information. • A wider range of scenarios where cut-set analysis applies. • An interesting and fruitful connection to successive refinement of information. X ENC • MAIN ACHIEVEMENT: • New inner and outer bounds were derived for networks with side information. • The bounds are tight • for several network • topologies. • HOW IT WORKS: • Converse results for the canonical problem are generalized to multi-node networks. • The achievable schemes are used at the terminals (sources and sinks), together with network coding. • Successive refinement of both the source and side information descriptions is used when there are multiple sinks. • ASSUMPTIONS & LIMITATIONS: • One source node; one helper. • Bounds are not tight in general. X DEC Y ENC To large extent, our knowledge of networks with side information is limited to the model above. However, we are interested in more complex networks: • • Canonical source coding problems can be used to derive bounds for more complex networks. • Network coding can play a key role even in non-multicast problems. Extend this methodology to various source coding problems. • Derive new bounds and find network topologies for which they are tight. • Different demand models(e.g. distortion) Strategies intended for small problems, joint with network codes, can solve complex networks

17. ACHIEVEMENT DESCRIPTION STATUS QUO IMPACT NEXT-PHASE GOALS NEW INSIGHTS Feedback and Network CodingEffros and Bakshi Increase in capacity is potentially unbounded. Power consumption by remote sources can be decreased by employing feedback from the central receivers. • MAIN ACHIEVEMENT: • In several examples networks, the capacity with feedback is strictly bigger than that without feedback • - Butterfly network • - Source coding with coded side information • - Multiterminal source coding • HOW IT WORKS: • Receiver sends back everything it knows to the transmitter nodes. • e.g. • - Encoder 2 knows X after the feedback. • - Sum rate required is only H(X) • ASSUMPTIONS AND LIMITATIONS: • Feedback links are assumed to have infinite capacity • Sources nodes are assumed to have sufficient processing power In today’s networks, bulk of transmission from sources to sinks • Remote sources have often lesser power available than sinks • Feedback is studied mostly in the context of channel knowledge, not source knowledge Feedback increases the capacity region. By knowing what the receiver already knows from other sources, source nodes can avoid unnecessary transmission. Cost of feedback?. • Feedback links may not always be “free” Feedback increases the capacity of networks

18. Multicast Capacity Region of a Large Wireless NetworkUrs Niesen Piyush Gupta Devavrat Shah ACHIEVEMENT STATUS QUO IMPACT NEXT-PHASE GOALS NEW INSIGHTS • Optimal two-layer network co-operative scheme for any traffic demand built on multi-hop and hierarchical scheme • Geometry of capacity region: it is nice and round • MAIN ACHIEVEMENT: • Characterization of dim. multicast region • Easily computable in terms of 2n `weighted cuts’ • Under Gaussian fading channel model • HOW IT WORKS: • Achievability • Realize `tree’ network using co-operative relay built on multi-hop and hierarchical (virtual MAC and BC) depending upon channel characteristics • Use this as multicast `tree’ • Converse • Establish tightness of 2n cuts, each of them corresponds to a `node’ of tree • ASSUMPTIONS AND LIMITATIONS: • Random node placement • Very little known about multicast capacity region of wireless network of n nodes • It is dimensional • Lack of fundamental understanding of co-operative relay schemes • Equivalence relation • Wireless network = “tree-structure” • This decides optimal structure for network-wide co-operation • Multicast capacity scaling • Arbitrary node placement Complete characterization of multicast capacity region: separation of NET and PHY layer

19. Information Theory for Mobile Ad-Hoc Networks (ITMANET): The FLoWS Project Thrust 3

20. ACHIEVEMENT DESCRIPTION STATUS QUO END-OF-PHASE GOAL COMMUNITY CHALLENGE NEW INSIGHTS Relaxation Techniques for Net Opt W. Chen & S. Meyn • Implementation – Consensus algorithms & Information distribution • Adaptation – Reinforcement learning techniques • Integration with Network Coding projects: Code around network hot-spots What is the state of the art and what are its limitations? Notes from Austin: MW routing inflexible, and does not easily incorporate multi-access capacity region in wireless. Workload relaxation techniques: Tremendous value for policy synthesis based on dynamic hot-spots in the network Can these techniques be extended to wireless models? MAIN RESULT: Numerical findings: With many flows, the rate region appears smooth even in a static interference model Impact: Network cut is no longer a useful concept Infinite complexity leads to simple solution: Dynamics of 720 queues Half space relaxation provides: • KEY NEW INSIGHTS: • Extend to wireless? YES Geometric picture is very different. Interpretation: The number of resources is infinite • Structure of optimal solution to relaxation is very simple, even for very complex networks • New application of relaxation: Q-learning and TD-learning for routing and power control • Lower bound on performance and • Tools for policy synthesis HOW IT WORKS: Step 1: Estimate capacity region near estimated allocation rate vector Step 2: Construct ellipsoidal, and half-space relaxations Step 3: Optimal policy for relaxation, and interpret for original network • Un-consummated union challenge: Integrate coding and resource allocation • Generally, solutions to complex decision problems should offer insight Algorithms for dynamic routing: Visualization and Optimization

21. ACHIEVEMENT DESCRIPTION STATUS QUO IMPACT NEXT-PHASE GOALS NEW INSIGHTS Stochastic resource allocationBoyd and Akuiyibo • MAIN RESULT: • Explicit optimal control laws for resource allocation in a system with quadratic cost, linear dynamics, and random linear constraints. • ASSUMPTIONS AND LIMITATIONS: • Assumes that the first and second moments of the resources are known • Utility is quadratic; dynamics must be linear Stochastic allocation of competing network resources i.e., bandwidth, power, flow rates, etc. Simple control laws (linear coefficients can be computed ahead of time). Current resource allocation research focus on iterative methods. These automatically adapt to changing data assuming they are held constant. Target value, x =6 averaging input algorithm greedy algorithm trajectory optimal trajectory • Formulate as stochastic control problem • Resource limits are random • Allocate resources based on availability and system state Utility maximizing estimation techniques • Decentralized solutions Optimal dynamic resource allocation with heterogeneous flows

22. A Distributed Newton Method for Network Optimization Jadbabaie and Ozdaglar ACHIEVEMENT DESCRIPTION STATUS QUO IMPACT NEXT-PHASE GOALS NEW INSIGHTS Significant performance improvements with the distributed Newton method compared to standard subgradient methods. • MAIN ACHIEVEMENT: • We developed a Newton method that solves network optimization problems in a distributed manner. • We provide convergence and rate of convergence guarantees for the proposed method. • Simulation experiments on a series of randomly generated graphs suggest superiority of the distributed Newton method over dual subgradient methods. • HOW IT WORKS: • Constrained Newton method • Dual Newton step found by solving a discrete Poisson equation involving the graph Laplacian. • Using a consensus-based local averaging scheme, this can be done using only local information. • ASSUMPTIONS AND LIMITATIONS: • Solves minimum cost network flow problems • Extension to network utility maximization All existing distributed optimization methods rely on dual decomposition and subgradient (first order) algorithms • These algorithms easy to distribute • However, they can be quite slow to converge limiting their use in rapidly changing dynamic wireless networks. • Second order methods for distributed network optimization • Suggests an extensive research agenda for the investigation of these methods in decentralized environments Combine Newton (second order) methods with consensus policies to distribute the computations associated with the dual Newton step Distributed Second Order Methods with Convergence Guarantees

23. FLOWS ACHIEVEMENT STATUS QUO IMPACT $ $ $ NEXT-PHASE GOALS NEW INSIGHTS Distributed Scheduling and Equilibrium Dynamics in Wireless Networks with Correlated Fading Channels (Candogan, Menache, Ozdaglar, Parrilo) • Game-theoretic scheduling models allow the flexibility to incorporate different user objectives and arrive at an efficient operating point in a distributed manner. • Correlated channel states are more realistic than existing models as they incorporate joint fading effects. • Robust system design in the presence of non-cooperative users utilizing the desirable properties of potential games. Achievements • Game-theoretic analysis of a distributed approach to scheduling that adapts to dynamically varying channel conditions. • Simple convergent distributed dynamics and equilibrium characterization. • Efficiency loss analysis suggests that finer state quantization can improve equilibrium performance. How it works: • Design incentives for the mobiles to project the game onto an (exact) potential game with desirable properties (such as convergence of simple dynamics)‏ • Improved bounds on equilibrium performance can be obtained as a function of a technology related system parameter. Assumptions and limitations: • Full correlation across individual channel state processes. • Fixed number of users and an uplink scenario. Equilibrium Combine tools from optimization and game theory • Potential games allow establishing existence and uniqueness of equilibrium, and convergence of simple distributed algorithms. Example: Collision Channel with two users. The resulting game is an ordinal potential game with two equilibria (TX, I) & (I, TX)‏ • Partial channel state correlation • Projection of general games to ordinal potential games • Convergence of dynamics with asynchronous updates • Multi-hop network topologies Local components (buildings)‏ A potential game approach for distributed scheduling in wireless networks

24. ACHIEVEMENT DESCRIPTION STATUS QUO IMPACT NEXT-PHASE GOALS NEW INSIGHTS A Game Theoretic Approach to Network CodingMarden and Effros Approach provides guarantees independent of network structure. Guarantees existence of an equilibrium that achieves a system cost of at most 50% higher than the optimal. This offers an improvement over opportunistic coding. • MAIN ACHIEVEMENT: • Introduced game theory as a distributed tractable mechanism to obtain good network performance • HOW IT WORKS: • Model interactions as a non-cooperative game • - players (unicast flows) • - actions (available paths) • Assign each player a “cost” function • Analyze efficiency of equilibrium behavior • ASSUMPTIONS AND LIMITATIONS: • Limited form of network coding (reverse carpool) • Players have knowledge of available paths • Players equilibrate faster than network changes Global Objective: Efficiently use network using network coding Approach: Centralized solutions. (e.g., opportunistic coding) Fix paths, use coding opportunities if available Understand the potential of game theory in network coding problems Establish desirable distributed learning algorithms with good convergence rates Extend game theoretic approach to more general network coding problems What about distributed solutions? What if flows were allowed to select path in response to local “cost”? Goal: Let users create coding opportunities to improve efficiency Game theory is an applicable tool for distributed optimization in network coding

25. ACHIEVEMENT DESCRIPTION STATUS QUO IMPACT State of device i State of other devices Action of device i NEXT-PHASE GOALS NEW INSIGHTS Oblivious equilibrium for stochastic games with concave utilityS. Adlakha, R. Johari, G. Weintraub, A. Goldsmith MAIN RESULT: Consider stochastic games per-period utility and state dynamics that are increasing, concave, submodular. Then in a large system, each node can find approximately optimal policies by treating the state of other nodes as constant. HOW IT WORKS: Under our assumptions, no single node is overly influential )we can replace other nodes’ states by their mean.So the optimal policies decouple between nodes. ASSUMPTIONS AND LIMITATIONS: This result holds under much more general technical assumptions than our early results on the problem. A key modeling limitation, however, is that the limit requires all nodes to interact with each other.Thus the results apply only to densenetworks. • Our results provide a general framework to study the interaction of multiple devices. • Further, our results: • unify existing models for which such limits were known • and provide simple exogeneous conditions that can be checked to ensure the main result holds Next state Utility Current state orcurrent action Current state orcurrent action Many cognitive radio models do notaccount for reaction of other devicesto a single device’s action. In prior work, we developed a generalstochastic game model to tractably capture interactions of many devices. # of other devices withgiven state In principle, tracking state of other devices is complex. We approximate state of other devices via a mean field limit. State We will apply our results to a modelof interfering transmissions among energy-constrained devices. Our main goal is to develop arelated model that applies when a single node interacts with a small number of other nodes each period. Real environments are reactive and non-stationary;this requires new game-theoretic models of interaction

26. ACHIEVEMENT DESCRIPTION … … … STATUS QUO … … IMPACT “Micro” “Macro” N(t) N(t) Time t Time t NEXT-PHASE GOALS NEW INSIGHTS Fluid limits for gossip processesV. Manshadi and R. Johari MAIN RESULT: We consider a random graph model where each nodehas d neighbors, and we consider a limit where thenumber of nodes Napproaches infinity. We prove that the (random) sample path of themicro model converges to the (deterministic) pathof the corresponding macro model. HOW IT WORKS: We approximately characterize howinformation flows in the micro model between the sets of informed and uninformed nodes. This approximation is exact as N! infinity. ASSUMPTIONS AND LIMITATIONS: Our results currently only apply under specific topological assumptions. Micro and macro models of gossip processes have been available for several decades. Unifying these will allow us to translate macro-level control insights to micro-level system designs. Gossip is a simple model for communication between nodes:at random times, each node contacts a neighbor and relays its information. Prior work has studied the time until all nodes acquire the information.Two versions of this model: a “micro” model and a “macro” model. Nodes that currently have the info Nodes that currently do not have the info • Several goals: • Extend fluid analysis to include heterogeneous random graphs. • Get finer understanding of behavior when initial number of informed nodes is constant as N ! infinity. • Extend the model to include link failures. The micro model tracks exactly which nodes have the information. The macro model is a mean field limit: what fraction of nodes have learned the information? We connect these two models. The simplicity of macroscopic models for information gossipcan be combined with the accuracy of microscopic stochastic models

27. Information Theory for Mobile Ad-Hoc Networks (ITMANET): The FLoWS Project Thrusts 1,2,&3

28. ACHIEVEMENT DESCRIPTION STATUS QUO IMPACT NEXT-PHASE GOALS NEW INSIGHTS Queuing analysis for coded networks with feedbackJ. Sundararajan, D. Shah, M. Médard, M. Mitzenmacher, J. Barros • Consequences. • Queue size now grows linearly with 1/(1- ρ) • Reduces the amount of storage needed at intermediate nodes for performing re-encoding • Analysis also applies when only some nodes do re-encoding • ACK of degrees of freedom allows traditional queuing results to be applied easily in scenarios with network coding Packets can be dropped from queue only upon confirmation of decoding • This means the queue sizes will be unnecessarily long • In particular, as load factor ρ approaches capacity, queue grows quadratically as a function of 1/(1- ρ) Unseen • MAIN ACHIEVEMENT: • Propose novel ACK mechanism that allows nodes to manage queue occupancy effectively • Characterize expected queue size at each node Seen λx (Time for receiver’s ACK to propagate from source to node k) Decoded 2 1 k N p1 p2 p3 p4 p5 p6 p7 p8 Coefficient vectors of received linear combinations, after Gaussian elimination HOW IT WORKS: Acknowledge “seen” packets 1 0 0 0 1 0 0 0 1 - - - - - - - 1 - - - - - - - 1 - - - - - - - λx (Time between node (i-1) seeing pkt and node iseeing pkt) • Key insight. • With drop-when-decoded, the busy period of the virtual queue contributes to the physical queue size calculation • Responding to ACK of the degrees of freedom ensures only queuing delay of virtual queues contributes to physical queue size Rx Tx Number of seen packets = Rank of matrix Rx Almost as if there is link-by-link feedback… Extend queue management protocol to more general (wireless) scenarios • Multipath routing with coding • Multicast traffic pattern • ASSUMPTIONS AND LIMITATIONS: • Perfect and delay-free feedback used in analysis, though not critical for the approach • Field size assumed to be very large The proposed approach to queue management will play a key role in interfacing TCP with network coding, especially when intermediate nodes re-encode

29. ACHIEVEMENT DESCRIPTION STATUS QUO IMPACT NEXT-PHASE GOALS NEW INSIGHTS Scheduling for Network Coded MulticastMedard, Traskov, Heindlmaier, Koetter No systematic approach to multi-access for network coding. • Shows that the performance of well-known scheduling techniques is very poor. • Suggests a largely improved bandwidth efficiency. • New notion of scheduling conflicts, when network coding is used. • MAIN ACHIEVEMENT: • Hyperarc scheduling outperforms well-known scheduling techniques. • HOW IT WORKS: • Valid network configurations can be identified as stable sets in the conflict graph. • Jointly solve subgraph selection and scheduling problem. • Distributed algorithm. • ASSUMPTIONS AND LIMITATIONS: • Convergence speed of algorithm. • Scaling with the size of the network. Current scheduling techniques use the bandwidth very inefficiently. • Graphical model for conflicts between hyperarcs. • Do not try to minimize the number of collisions per se. • Extension to INTER-session network coding. • Investigations on performance/complexity trade-offs. Scheduling matched to the network coding subgraph largely improves performance.

30. ACHIEVEMENT DESCRIPTION STATUS QUO IMPACT NEXT-PHASE GOALS NEW INSIGHTS Interference-Mitigating Mobility Strategies in MANETs: Naini and Moulin • Identifying the two-fold role of relays as: • being part of the source- receiver link • conveying information about interferer’s signal • Optimal mobility patterns could be used to gain insight into • Optimal relay placement • Positioning of nodes in coexistent interfering networks. • MAIN RESULT: • Derived optimal interference-mitigating strategies for receiver node in a network with fixed relays • Cut-set bound on capacity used as the cost-function. • Saddle point strategies are feasible for the receiver and interferer. • ASSUMPTIONS AND LIMITATIONS: • Greedy mobility strategy is assumed • Nodes know neighboring nodes location and transmission power • Surrogate capacity cost function is used MANETs : Focus has been mainly on mutual interlinking and cooperation of nodes with randomized mobility in the backdrop. Lack of results on interference-mitigating mobility strategies. • Mobility should be seen as a resource to actively avoid interference from other nodes. • Optimal mobility strategies can be established for nodes in noncooperative scenarios Allow for relay mobility Include multi-hop relaying Extension to non-greedy and multi-objective cost function. Exploit mobility to dynamically enlarge capacity regions