1. Local Phy + Global Routing: A Fundamental Layering Principle for Wireless Networks Pramod Viswanath, University of Illinois July, 2011

2. Wireless Network Architectures Wireless Networks Cellular Heterogeneous Ad hoc Multiple Layers Cross layer design engineering principles We seek for fundamental layering principles lens of information theory

3. Information Theory of Wireless Networks Long standing open question even for wireline networks approximate capacity results scaling law results Engineering implication unclear even for known solutions -- complicated (nonlayered) strategies Goals: approximate capacity of wireless networks engineering guidelines

4. Wireline Networks Wireline network composed of independent noisy channels Layered Design: separate PHY and Network layers [Koetter, Effros, Medard 2010] Layering is capacity optimal in wireline networks

5. Layering in Wireline Networks Layered Design: separate PHY and Network layers [Koetter, Effros, Medard 2010] Layering is capacity optimal Capacity is still unknown Network layer potentially uses network coding

6. Bit pipe Wireline Networks Routing conceptually simple different traffic flows never mix practical -- efficient algorithms Routing is optimal for unicast traffic [Ford Fulkerson, 1956] max flow = min cut Network coding required in general optimal for multicast Focus of this talk: Multiple unicast traffic

7. Multiple Unicast in Wireline Networks Directed graphs network coding arbitrarily better than routing min cut far from any efficient algorithm [Chuzhoy Khanna, 2006] Undirected graphs no example of network coding being better than routing routing close to min cut [Leighton Rao, 1988]

8. Engineering Implication for Wireline Networks Separate Phy and Network layers Routing in network layer

9. Features of Wireless Channel Broadcast: one to many Superposition: many to one In general both features Partial Frequency reuse networks No edge involved in both broadcast and superposition

10. Partial Frequency Reuse Networks Cellular Networks Neighboring cells use different frequencies Uplink-Downlink design + routing Enterprise Wi-Fi networks

11. Wireless Frequency Reuse Networks No edge involved in both broadcast and superposition frequency planning packet erasure networks

12. Packet Erasure Networks Communication link is an erasure channel Broadcast constraint only Broadcast erasure channel degraded time sharing optimal [Dana Hassibi 2005] very far from min cut

13. A Non-layered Scheme Layering very suboptimal even for unicast Do not layer! [Gowaikar et. al. 2003] global network coding for unicast traffic wireless network coding = min cut need to use broadcast feature of medium

14. Abstraction by Wireline Networks create detailed bit pipes multiple multicast traffic allow general network coding [Koetter, Effros, Medard, 2010] Approximate optimality degree two broadcast and superposition

15. Reprise Layering in wireline networks is successful separation of Phy, MAC, network layers routing in network layer -- undirected Reciprocity in wireless channels Use reciprocity to simultaneously show separation of Phy and network layers routing in network layer This talk: approximate optimality of separation + routing multiple unicast traffic

16. Reciprocity Wired infrastructure is bidirected Wireless point-to-point channel is reciprocal even when scatterers are present Maxwell equations are reciprocal:

17. Point to Point Channel is Reciprocal Reverse source and destination traffic flow reversed power capability reversed Capacity is unchanged Also true with MIMO total power across antennas preserved capacity only depends on singular values [Telatar, 2001]

18. Uplink Downlink Reciprocity Broadcast channel -- broadcast Multiple access channel -- superposition Channels reciprocal Communication rates also reciprocal reciprocal linear strategies reciprocity of SIC and DPC Can create a bidirected network

19. Polymatroidal Networks Constraints on in/out rates submodular rate region is a polymatroid exact for superposition approximate for broadcast Bidirected network Symmetric inflow and outflow constraints

20. Unicast in Polymatroidal Networks Directed polymatroidal network Various application areas operations research Unicast: Max flow = Min cut [Lawler Martel, 1982] and [Edmonds Giles,1975] Cut subset of edges, removal disconnect source and sink grouping of edges which share a vertex value of cut is sum of submodular function on each partition

21. Main Technical Result Multiple unicast traffic Bidirected polymatroidal network, general demands Max flow Min cut approximation result generalizes [Leighton Rao, 1988] Min cut is a fundamental upper bound information theoretic Approximation result also true: directed polymatroidal network, symmetric demands [Klein Plotkin Rao Tardos 1995]

22. Game Plan: Application in Wireless Networks Physical layer strategy use feedback converts medium into bit pipes polymatroidal achievable rate region Cut set bound typically polymatroidal achievable scheme is close enough Wireless Network approximated by polymatroidal network harness max flow min cut approximation result Result: local Phy + global Routing is near optimal

23. Packet Erasure Networks with Feedback Erasure network with broadcast constraints Feedback via natural reciprocal channels Optimal Phy scheme not time sharing a form of hybrid ARQ coding [Georghiades Tassiulas 2010] capacity region now close to min cut (order log d) Min cut region is polymatroidal

24. Layering Principle for Packet Erasure Networks Critical use of feedback both in Phy (local) and in routing (global) Summary: Local Phy with feedback + Global routing with feedback is near optimal

25. Gaussian Partial Reuse Networks Superposition constraint Capacity rate region is polymatroidal Capacity equals min cut region Broadcast constraint Min cut region is polymatroidal Capacity (P) contains min cut (P/d) Thus both in and out flow constraints are submodular symmetric (due to reciprocity)

26. Gaussian Partial Reuse Networks Local Phy superposition coding for broadcast SIC for multiple access feedback used for channel state information Global routing feedback useful for bidirectional structure Summary: Local Phy + Global routing nearly achieves min cut

27. Full Reuse Networks Every node uses same frequency interference is a central feature Begin with specific channel models fading channels (slow/fast fading) Geographic Networks scaling laws; heirarchical MIMO + routing [Niesen, Gupta, Shah 2010]

28. PHY Layering Where to draw the line? Phy ends and routing begins Treat each hop as separate Phy layer Phy is over the X channel multihop routing

29. X Channel Every source has independent message for every destination more general than interference channel Capacity region unknown Look for new Phy schemes

30. Phy Scheme for X Channel Approach: consider interference channels subset of source and destinations Phy scheme for interference channels ergodic/real interference alignment reliable communication at half direct link capacity Time sharing across all interference channels

31. Min Cuts in X Channel Specific cuts lead to polymatroidal constraints cuts separate one node from rest General cuts do not fit our framework Turns out: cuts of interest are essentially minimal [Niesen 2010]

32. Feedback Feedback used in Phy scheme to convey channel state information Treating each hop as Phy layer leads to a directed network Need bidirected network feedback used for efficient global routing

33. Layering Principle Local Phy X channel Global routing Main result

34. Summary Layering of wireless networks common engineering practice Our contribution Fundamental view of layering Feedback critically useful in both Phy and Routing A framework to use good Phy schemes in a network context No natural place for network coding Credit: Sreeram Kannan, Adnan Raja, Chandra Chekuri