Symbol Level Network Coding

1. Symbol Level Network Coding By Sachin Katti, Dina Katabi, Hari Balakrishnan, Muriel Medard Sigcomm 2008

2. Mesh Networks Borrowed the Internet Contract Conflicts with wireless mesh characteristics Current contract builds reliability on a link by link basis Spatial diversity more naturally provides reliability across multiple links

3. Wireless Naturally Provides Reliability Across Links 99% (10-3 BER) 0% R1 R2 D S 0% 99% (10-3 BER) Even 1 bit in 1000 incorrect  Packet loss of 99%

4. Wireless Naturally Provides Reliability Across Links 99% (10-3 BER) Loss 0% R1 R2 D S Loss 0% 99% (10-3 BER) Current contract  Link by link reliability  50 transmissions

5. Wireless Naturally Provides Reliability Across Links 99% (10-3 BER) 0% R1 R2 D S 0% 99% (10-3 BER) Spatial diversity: Even if no correct packets, every bit is likely received correctly at some node Current contract  50 tx  Low throughput Exploit wireless characteristics 3 tx  High throughput Exploit wireless characteristics 3 transmissions

6. Useful with High Quality Links? R1 1% 0% Loss Sa Da Pa 0% Pa 2% R2 Loss Pa R3 1% Loss 0% Pb Db Sb 0% R4 3% Pb Loss Pb

7. Useful with High Quality Links? R1 1% 0% Sa Da Pa 0% Pa 2% R2 Pa R3 1% 0% Pb Current contract  Inhibits concurrency Exploit wireless characteristics  Enables high concurrency Db Sb 0% R4 3% Pb Pb

8. Current Contract • Limits throughput, inhibits concurrency New Contract Exploiting Wireless Characteristics • High throughput, high concurrency

9. MIXIT • New contract between layers to harness wireless characteristics • Novel symbol-level network code that scalably routes correct symbols • High concurrency MAC

10. How does a Router Identify Correct Symbols? • PHY already estimates a confidence for every decoded symbol [JB07] • PHY + LL delivers high confidence symbols to network layer PHY Confidence Packet

11. What Should Each Router Forward? R1 R2 D S P1 P2 P1 P2 P1 P2

12. What Should Each Router Forward? R1 R2 D S P1 P1 P2 P2 P1 P2 P1 P1 P2 P2 • But overlap in correctly received symbols • Potential solutions • Forward everything Inefficient • Coordinate Unscalable

13. MIXIT Prevents Duplicates using Symbol Level Network Coding R1 R2 D S P1 P2 P1 P2 P1 P2 Forward random combinations of correct symbols

14. MIXIT Prevents Duplicates using Symbol Level Network Coding D R2 R1 … … … … … … Routers create random combinations of correct symbols

15. MIXIT Prevents Duplicates using Symbol Level Network Coding D … R2 R1 … Solve 2 equations Randomness prevents duplicates without co-ordination Destination decodes by solving linear equations

16. MIXIT Prevents Duplicates using Symbol Level Network Coding D R2 R1 … … … … … … Routers create random combinations of correct symbols

17. MIXIT Prevents Duplicates using Symbol Level Network Coding D … R2 R1 … Solve 2 equations • Symbol Level Network Coding • No duplicates  Efficient • No coordination  Scalable Destination decodes by solving linear equations

18. Destination needs to know which combinations it received (if both symbols were correct) (if only s1 was correct) (if only s2 was correct) Nothing (if neither symbol was correct)

19. Destination needs to know which combinations it received Use run length encoding Coded Packet Original Packets

20. Destination needs to know which combinations it received Use run length encoding Coded Packet Original Packets

21. Destination needs to know which combinations it received Use run length encoding Coded Packet Original Packets

22. Destination needs to know which combinations it received Use run length encoding Coded Packet Original Packets

23. Destination needs to know which combinations it received Use run length encoding Run length encoding efficiently expresses combinations

24. Routers May Forward Erroneous Bits Despite High Confidence MIXIT has E2E error correction capability Decode ECC ECC Symbol-Level Network Coding Data Data Source Destination MIXIT’s Error Correcting Code (ECC) Routers are oblivious to ECC Optimal error correction capability Rateless

25. High Concurrency MAC w& x  NO! w& u YES! u w x • Each node maintains a map of conflicting transmissions • Map is based on empirical measurements and built in distributed, online manner

26. Evaluation • Implementation on GNURadio SDR and USRP • Zigbee (IEEE 802.15.4) link layer • 25 node indoor testbed, random flows • Compared to: • Shortest path routing based on ETX • MORE: Packet-level opportunistic routing

27. Throughput Comparison CDF 2.1x MIXIT 3x MORE Shortest Path Throughput (Kbps) Throughput increase: 3x over SPR, 2x over MORE

28. Where do the gains come from? CDF MIXIT MORE Shortest Path Throughput (Kbps) Take concurrency away from MIXIT

29. Where do the gains come from? CDF MIXIT without concurrency 1.5x MORE Shortest Path Throughput (Kbps) Without concurrency, 1.5x gain over MORE Take concurrency away from MIXIT

30. Where do the gains come from? MIXIT CDF MIXIT without concurrency MORE Shortest Path Gains come from both moving to the symbol level and high concurrency Throughput (Kbps)

31. Where do the gains come from?Higher Concurrency? CDF 1.4x Throughput (Kbps) MORE, enhanced with higher concurrency is only 1.4x better

32. Where do the gains come from? CDF 1.5x 2.1x Higher concurrency MAC fully exploits symbol-level diversity Throughput (Kbps)

33. Conclusion • MIXIT • New contract harnesses wireless characteristics • Symbol-level network coding to scalably route correct symbols • High concurrency • Implementation and evaluation demonstrating • 3-4x over shortest path,2-3xgains over MORE