Optimal Grouping and Matching for Network Coded Cooperative Communications

1. Optimal Grouping and Matching for Network Coded Cooperative Communications Yi Shi Intelligent Automation Inc. with Sushant Sharma (Brookhaven National Laboratory), Thomas Hou, Scott Midkiff (Virginia Tech), SastryKompella (Naval Research Laboratory)

2. Synopsis • Focus: Network-Coded Cooperative Communications (NC-CC) with multiple relay nodes • Session/relay grouping and matching • NP-hard • An efficient heuristic solution • Results • High gains in data rate • Near-optimality of proposed heuristic solution

3. CC: A Review • A traditional wireless link Sender Receiver • Cooperative Communications (CC): Exploit antennas on neighbors to create diversity Amplify-and-Forward or Decode-and-Forward Relay Node 2ndtime slot 1sttime slot 1sttime slot Sender Receiver

4. CC for Multiple Sessions time slots s1 d1 3 5 4 1 2 6 1 1 2 Relay 2n time-slots Too much waste NC can improve efficiency 4 3 6 3 s2 d2 5 5 s3 d3

5. Single Relay NC-CC d1 s1 1 time slots 1 4 1 4 2 3 Relay NC can reduce time-slots from 2n to n+1 What about multiple relays? 2 4 s2 d2 4 3 s3 d3

6. Multi Relay NC-CC d1 s1 Simultaneous transmissions from multiple relay nodes s2 d2

7. Mutual Information Comparison Single-relay case is a special case of multi-relay NC-CC Single-Relay NC-CC Multi-Relay NC-CC

8. Overview • Background • Types of NC-CC • Single relay NC-CC • Multi relay NC-CC • Grouping and matching problem • G2M algorithm • Initialization phase • Main Program • Results

9. Grouping and Matching Problem Objective:Maximize the weighted sum of data rates of all sessions. Problem:How to break session and relays into groups and match them up optimally?

10. NP-Hardness: Sketch of Proof • Related Work: Grouping and Relay node Selection (GRS) problem [Sharma et al. INFOCOM 2011] • Restricts the size of each relay group to one • Shown to be NP-hard • Our problem • General form of GRS with unrestricted size of relay groups • Also NP-hard

11. Overview • Background • Types of NC-CC • Single relay NC-CC • Multi relay NC-CC • Grouping and matching problem • G2M algorithm • Initialization phase • Main Program • Results

12. G2M Algorithm: Basic Idea • Start with matching each session with a group of relay nodes • Try to merge some pairs of session groups to improve objective. • Repeat Step 2 until objective stops improving.

13. Overview • Background • Types of NC-CC • Single relay NC-CC • Multi relay NC-CC • Grouping and matching problem • G2M algorithm • Initialization phase • Main Program • Results

14. G2M Algorithm: Initialization Phase • For each session (s, d): Initially assign all relays to its group • Iteration: • Check each relay (r) from the minimum SNRsr to the maximum SNRsr • If removing r increases objective, then r is removed • If any relay is removed during an iteration, then repeat Step 2 in the next iteration • Check if rate is greater than direct transmission • If not, then use direct transmission Find a relay group for each session (NP-hard).

15. Overview • Background • Types of NC-CC • Single relay NC-CC • Multi relay NC-CC • Grouping and matching problem • G2M algorithm • Initialization phase • Main Program • Results

16. G2M Algorithm: Main Program (Merging Session Groups) Runs in iterations • Start with a list of matchings obtained during initialization • Consider merger of every pair of current session groups • Intelligently merge the corresponding relay groups • If merger of session groups is favorable to objective • Then store the merged group (and relay group) in a temp-list • Otherwise, store each group separately with zero gain in the temp-list if not already there • We now have a temp-list with beneficial matchings and some matchings with zero gain

17. G2M Algorithm: Operate on Temp-list • If all the matchings in the temp-list have zero gain, then we stop • Otherwise, build an empty new-list and then check each matching in the temp-list in decreasing order of gains • If none of the sessions in current matching appears in new-list, then add this matching in the new-list • Otherwise, recover the matching for non-appearing sessions and add it back in the temp-list • We now have a new-list with every session appearing exactly once in some group • Repeat the iteration with this new-list

18. G2M Algorithm: Merging Relay Groups • When we merge two session groups, we need to merge their relay groups • Start with a group that includes relay nodes from both relay groups • Consider each relay that is not in both groups • Remove the considered relay from the relay group • If the sum rate of the merged sessions decrease, then add the relay back to the group

19. Overview • Background • Types of NC-CC • Single relay NC-CC • Multi relay NC-CC • Grouping and matching problem • G2M algorithm • Initialization phase • Main Program • Results

20. Simulation Settings • Preceived = Ptransmitted* ChannelGain • Channel path loss index: 4 • SNR = Preceived/σ2 • σ2: White Gaussian noise with variance 10-10 W • Ptransmitted = 1 W • 100 randomly generated networks • Area of 1200m x 1200m • 7 sessions, 16 relay nodes

21. G2M vs. Direct Transmission Equal weight for all sessions Average Ratio: 2.53 Ratio of Objectives Network Instance

22. G2M vs. Direct Transmission Random session weights Average Ratio: 2.67 Ratio of Objectives Network Instance

23. Near Optimality of G2M • Formulated the problem as an optimization problem • An integer linear program • Solved optimization problem using CPLEX • Exponential time to obtain optimal solution • Compared the objective from G2M with optimal objective

24. Near Optimality of G2M Equal weight for all sessions Ratio of Objectives Average Ratio: 0.98 Network Instance

25. Near Optimality of G2M Random session weights Ratio of Objectives Average Ratio: 0.97 Network Instance

26. Conclusion • Considered multi-relay NC-CC in a network setting • Identified a session/relay grouping and matching problem • NP-hard • Designed an efficient heuristic algorithm: G2M • Validated the performance of G2M • Near-optimal

27. Thank You