Analog Network Coding

1. Analog Network Coding Sachin Katti Shyamnath Gollakota and Dina Katabi

2. Current Wireless C Router

3. Current Wireless C Router Traditional Routing requires 4time slots

4. Current Wireless C Router Traditional Routing requires 4time slots

5. Last Year  Network Coding  COPE C Router = XOR Traditional Routing requires 4 time slots

6. Last Year  Network Coding  COPE C Router Traditional Routing requires 4 time slots

7. Last Year  Network Coding  COPE C Router = XOR = XOR Traditional Routing requires 4 time slots COPE requires 3 time slots  Higher throughput Can we do it in 2 time slots?

8. Analog Network Coding (ANC) Instead of router mixing packets… Exploit that the wireless channelnaturally mixes signals

9. Analog Network Coding C Router

10. Analog Network Coding C Router Interference Dina and Jon transmit simultaneously

11. Analog Network Coding C Router Dina and Jon transmit simultaneously Router amplifies and broadcasts interfered signal

12. Analog Network Coding C Router Dina and Jon transmit simultaneously Router amplifies and broadcasts interfered signal Dina subtracts known signal from interfered signal

13. Analog Network Coding C Router Dina and Robert transmit simultaneously Router amplifies and broadcasts interfered signal Dina subtracts known signal from interfered signal • Analog Network Coding requires 2 time slots • Higher throughput

14. It Is More Than Going From 3 To 2! • Philosophical shift in dealing with interference • Strategically exploit interference instead of avoiding it • Promises new ways of dealing with hidden terminals

15. Hidden Terminal Scenario C C C C Src R2 R1 Dst

16. Hidden Terminal Scenario C C C C Src R2 R1 Dst P1

17. Hidden Terminal Scenario C C C C Src R2 R1 Dst P1 P2 Src and R2 transmit simultaneously

18. Hidden Terminal Scenario C C C C Src R2 R1 Dst P1 P2 Src and R2 transmit simultaneously R1 subtracts P1, which he relayed earlier to recover P2 that he wants

19. Hidden Terminal Scenario C C C C Src R2 R1 Dst P1 P2 • R2 and Src are hidden terminals • Today : Simultaneous transmission  Collision • ANC : Simultaneous transmission  Success!

20. Hidden Terminal Scenario C C C C Src R2 R1 Dst • Other Benefits of ANC: • First step toward addressing hidden terminals • ANC extends network coding to new scenarios

21. How do we make it work?

22. Practical Challenges C • Interfered signal is not exactly the sum • Channel distorts signals • Two signals are never synchronized • It is not sD(t) + sJ(t)but f1(sD(t)) + f2(sJ(t-T)) • Prior work assumes full synchronization and ignores channel distortion Not Practical!

23. Key Idea: Exploit Asynchrony!

24. Signal No Interference No Interference Time Key Idea: Exploit Asynchrony! • Dina uses interference-free parts toestimate channel and timing • Dina compensates for her interfering signal • Jon runs the same algorithm backwards! Exploit asynchrony to make it practical

25. Cross layer realization of our idea

26. Protocol • Router senses idle medium and broadcasts a trigger to Dina and Jon • Dina and Jon jitter their start times randomly and transmit • Router amplifies and forwards interfered signal • Dina and Jon receive and decode How do they decode?

27. Primer on Modulation • Nodes transmit vectors on channel • Focus on MSK (Minimum Shift Keying) modulation D2 leads D1 by 90 degrees  Bit “1” D2 lags D1 by 90 degrees  Bit “0” D2 D1 D2 D1

28. Attenuation Primer on Channel Effects D2 D2 Channel D1 D1 D2 and D1 are attenuated by the same amount

29. Attenuation • Rotation Primer on Channel Effects D2 D2 Channel D1 D1

30. Attenuation • Rotation Primer on Channel Effects D2 D1 Channel D2 D1 To decode, receiver computes angle between received vectors Angle (D2,D1)= 90 degrees Bit “1” was transmitted Angle between vectors is preserved

31. Signal Time So, How Does Dina Decode? No Interference No Interference Dina’s Signal Jon’s Signal

32. Signal Time So, How Does Dina Decode? No Interference No Interference Interference • Small uninterfered part at the start • Decodes uninterfered part via standard MSK demodulation • Once interference starts, Dina changes decoding algorithm

33. What did Dina send? D2 D1

34. What did Dina send? • What did Jon send? J1 D1 D2 J2

35. What is Interference  Vector addition X1 D1 J1 D2 J2 X2

36. What does Dina know? D2 X1 D1 J1 D2 D1 J2 X2

37. What does Dina know? D2 X1 β α D1 X2 No Interference Amplitude of Jon’s Vectors  β Amplitude of her Vectors  α

38. What does Dina know? D2 X1 D1 D1’ J1’ J1 D1 X2 • Dina finds solutions for X1 and X2

39. What does Dina know? D2 X1 D1 D1’ J1’ J1 J2’ D2 D1 J2 X2 D2’ • Dina finds solutions for X1 and X2 Two solutions for each interfered vector!

40. What does Dina know? D2 X1 D1 D1’ J1’ J1 J2’ D2 D1 J2 X2 D2’ • Dina finds solutions for X1 and X2 Four possible angles!

41. What does Dina know? D2 X1 D1 D1’ J1’ J1 J2’ D2 D1 J2 X2 D2’ • Dina finds solutions for X1 and X2 Four possible angles!

42. What does Dina know? D2 D1 X1 D1’ J1’ J1 J2’ D2 D1 J2 X2 D2’ • Dina finds solutions for X1 and X2 Four possible angles!

43. What does Dina know? D2 X1 D1 D1’ J1’ J1 J2’ D2 D1 J2 X2 D2’ • Dina finds solutions for X1 and X2 Four possible angles!

44. What does Dina know? D2 X1 D1 D1’ J1’ J1 J2’ D2 D1 J2 X2 D2’ • Dina finds solutions for X1 and X2 Four possible angles!

45. What does Dina know? D2 X1 D1 D1’ J1’ J1 J2’ D2 D1 J2 X2 D2’ • Dina finds solutions for X1 and X2 Pick the correct angle  90 degrees

46. What does Dina know? D2 X1 D1 D1’ J1’ J1 J2’ D2 D1 J2 X2 D2’ • Dina finds solutions for X1 and X2 Pick the correct angle  +90 degrees

47. What does Dina know? D2 X1 D1 D1’ J1’ J1 J2’ D2 D1 J2 X2 D2’ • Dina finds solutions for X1 and X2 Dictates solution for Jon’s vectors!

48. What does Dina know? D2 X1 D1 J1 D2 D1 J2 X2 • Dina finds angle between J1 and J2 and decodes

49. Signal Time Decoding Algorithm – Decoding interference Interference • Decode rest of the interfered part using this algorithm • Decode final uninterfered part from Jon via standard MSK demodulation

50. Performance