Rethinking Information Theory for Mobile Ad-Hoc Networks By J. Andrews, S. Shakkottai, R. Heath, N. Jindal, M. Haenggi,

1. Rethinking Information Theory for Mobile Ad-Hoc NetworksBy J. Andrews, S. Shakkottai, R. Heath, N. Jindal, M. Haenggi, R. Berry, D. Guo, M. Neely, S. Weber, S. Jafar, A. Yener Presented by: Victoria Manfredi May 9, 2010

2. Overview First paper challenge: capacity theory for MANETs overviews 3 problems to address to solve this introduces (?) functional capacity Second paper challenge: capacity theory for communication networks? summarizes networks work that has info theory flavour (up to ~1998) mostly a list of examples

3. Rethinking Information Theory for Mobile Ad-Hoc NetworksBy J. Andrews, S. Shakkottai, R. Heath, N. Jindal, M. Haenggi, R. Berry, D. Guo, M. Neely, S. Weber, S. Jafar, A. Yener

4. Outline Challenge Why is this difficult? 3 roadblocks Importance of constraints Functional capacity The way forward Conclusions Some thoughts

5. Challenge Develop a capacity theory for MANETs what are fundamental performance limits? at what rate can data be transmitted with arbitrarily low bit error (and received within given delay)? Want bounds that are useful in practice in same way Shannon limit useful in practice for links

6. Link capacity for channel subject to Gaussian noise Shannon limit: max rate at which data can be transmitted error-free C = B log2 (1+SNR) Link capacity for channel in MANET which channel? K mobile devices: K(K-1) possible channels Shannon limit: unknown for K>2, even for non-time-varying channels Why is this difficult?

7. Extending Info Theory to Networks Known as multi-terminal or network information theory Difficulty of extensions led to investigating capacity scaling Gupta-Kumar stationary nodes per-session capacity scales as O(1 / vK) as K increases Grossglauser-Tse mobile nodes, 2-phase relaying per-session capacity scales as ?(1) as K increases But still ignores several issues essential to MANETs basic assumptions different network stack (should be) different control overhead

8. 1st Roadblock: Basic Assumptions Different Traditional info theory to compute link capacity consider arbitrarily long blocks of data achieve vanishingly small error probability but: unbounded delay but assumptions still reasonable in practice, achieve acceptable delay and high reliability while also approaching capacity MANETs delays due to not just transmission, propagation, but also queuing, traffic, channel access, multihop routing, retransmissions, mobility consider arbitrarily long blocks of data delay now unacceptable in practice (sec or min, not realtime) cannot average over dynamics

9. Timescales for MANET Algorithms

10. 2nd Roadblock: Network Stack (Should Be) Different Traditional info theory decompose centralized wireless network into links e.g., cellular networks network ? cells cells ? point-to-multipoint and multipoint-to-point channels multiuser channels ? point-to-point links physical layer bit pipe, higher layers provide bits: optimize separately MANETs node interactions change over time/space define layers by timescale of relevant changes Change traditional separation in network stack network layer: nodes communicate if they are within range physical layer: ignore networking concerns

11. 3rd Roadblock: Control Overhead Traditional info theory ignores a lot of control overhead assume connection established, synchronization achieved, packet headers already sent acceptable for links costs either minor, accounted for as lump sum, or non-recurring MANETs cannot ignore control overhead 99% of throughput can be control in military MANETs in dynamic network cost of maintaining routes may be high relaying, cooperative diversity, beamforming, opportunistic scheduling, backpressure routing require substantial real-time overhead When does incurring control overhead increase capacity?

12. Outline Challenge Why is this difficult? 3 roadblocks Importance of constraints Functional capacity The way forward Conclusions Some thoughts

13. Importance of Constraints Functional capacity: capacity with constraints what can potentially be achieved with “great engineering” and “tenable assumptions” Constraints peak and average power, amount of channel state feedback, delay (Unknown) Shannon limit likely very optimistic

14. Pitfalls of Ignoring Constraints Inteference cancellation simultaneous radio transmission and reception in same frequency possible for some classes of multiuser channels problem power of received signals may be much larger in MANETs: interference cancellation not practical Mobility and infinite delay suppose given infinite time, all nodes eventually meet use Grossglasuer-Tse 2-phase forwarding problem capacity may be large, but so is delay Shannon framework needs further constraints to be as robust for MANETs as for links

15. The Way Forward Goal: non-equilibrium information theory Outage capacity non-equilibrium theory for fading channel assume separation of timescales average out some randomness (additive noise) but not other (fading) Lessons From Physics model communication system as thermodynamic system wireless networks constrained by laws of physics e.g., found can’t beat Gupta-Kumar scaling law statistical physics methodologies used to compute capacity of multi-user and MIMO systems. non-equilibrium statistical mechanics theories for dynamic interacting many-particle systems vehicular systems

16. The Way Forward Don’t just characterize throughput/capacity also characterize delay, reliability leverage work from wireline networks need to model transient Random graphs, stochastic geometry, percolation theory nodes randomly located in ad-hoc network if i.i.d., model with Poisson point process interference distributions and outage probabilities can be derived use to quantify connectivity and spatial throughput

17. The Way Forward Capacity Approximation Techniques degrees of freedom approach, deterministic channel models approximations focus on interference rather than noise interference alignment possible to use half of channel resources with no interference structured (rather than random) codes likely necessary since code for one user designs interference to another user Robust control theory “robust control refers to the control of unknown plants with unknown dynamics subject to unknown disturbances” [15] work in info theory channel capacity when channel distributions are uncertain

18. Conclusions To achieve capacity theory for MANETs need non-equilibrium information theory that characterizes effects of dynamics First steps look at capacity with constraints (functional capacity) leverage work in other areas (physics, robust control …)

19. Some Thoughts Non-equilibrium information theory during different time periods (with own equilibria?), same network can be fundamentally different need to know distribution of time network spends in these different states to say something about network as a whole? Seems like 2 problems need to determine bandwidth available as network changes and noise properties of those channels need to determine how best to use that bandwidth (coding, etc) Impact of predictable vs unpredictable network changes? What is wrong with modeling network as a channel?

21. Outline Challenge Case studies protocol overhead timing channels multiaccess communication traffic modeling Some thoughts

22. Challenge Information theory has not had same impact on communication networks as on communication theory Why has it not had same impact? ignores burstiness of source traffic since for link, can ignore idle periods ignores delay Paper overviews work in networks using ideas similar to those in info theory ? we’ll look at: subset of work that seems most interesting

23. Gallager [22] (we’ll discuss paper next time) how much protocol info per pkt needed to reconstruct at dest? Found entropy rate of sources ? mean rate of data bits extra capacity needed to transmit msg start and end info ? call this protocol information price paid to multiplex bursty sources can dominate total transmitted info In real systems protocols so inefficient, overhead due to burstiness relatively small Protocol Overhead

24. Timing Channels Gallager [22] again “to an information theorist, a protocol is a source code for representing control information” What if can delay pkts? won’t recover inter-msg delay exactly, but will save control info Rate-distortion problem how much protocol info per pkt should be transmitted (rate) to reconstruct pkt seq at dest within specified mean delay (distortion)? Alternatively, timing can convey info suppose source uses all symbols {0,1,i} when coding can send info at rate log23 rather than log22 bits per channel use C = max p(x) I(X;Y) max p(0,1,i) = 1/3, 1/3, 1/3 H(x) = - 1/3 log 1/3 - 1/3 log 1/3 - 1/3 log 1/3 = log 3 C = max p(x) I(X;Y) max p(0,1,i) = 1/3, 1/3, 1/3 H(x) = - 1/3 log 1/3 - 1/3 log 1/3 - 1/3 log 1/3 = log 3

25. Multi-Access Communication Simplest system Multiuser information theory at what rates can sources emit bits to ensure received error-free? Slepian-Wolf data compression for correlated sources Multiuser detection theory Like multiuser info theory but focuses on finite (not asymptotic) performance criteria Multiaccess network model Detection theory: goal is to distinguish between signal and noise?Detection theory: goal is to distinguish between signal and noise?

26. Multi-Access Communication Multiaccess network model time-slotted channel if more than one user transmits in slot, collision simplest feedback: slot idle, successful transmission, collision transmission strategies should achieve high throughput small access delay Early work: ALOHA sources attempt transmissions randomly and independently has info theory flavour simple model that captures essence of (contention) process

27. Traffic Modeling and Bursty Sources Effective bandwidth (data rate) of a datastream actual rate at which data can be transmitted info theory: effective information rate of data source entropy or rate-distortion function of data source “effective-bandwidth versus distortion” function? Unlike info theory, values of bits don’t matter Effective bandwidth and thermodynamics Hui, Karasan [51]

28. Outline Challenge Case studies protocol overhead timing channels multiaccess communication traffic modeling Some thoughts

29. Some Thoughts Rate-distortion theory rate at which to send info to ensure that received signal is within specified distortion of transmitted signal seems like natural way to capture overhead both Gallager paper and Wang and Abouzeid paper use this approach other applications? What are simple models, like ALOHA or channel models that capture essence of problem of capacity theory for networks? Should capacity theory for networks be extension of that for links? seems like capacity theory for networks should be able to say more should capture something about the system as a whole as well (like neurons + brain)