Models and Capacities of Molecular Communication

1. Andrew W. Eckford Department of Computer Science and Engineering, York University Joint work with: N. Farsad and L. Cui, York University K. V. Srinivas, S. Kadloor, and R. S. Adve, University of Toronto S. Hiyama and Y. Moritani, NTT DoCoMo Models and Capacitiesof Molecular Communication

2. How do tiny devices communicate?

3. How do tiny devices communicate?

4. How do tiny devices communicate?

5. How do tiny devices communicate?

6. How do tiny devices communicate? Most information theorists are concerned with communication that is, in some way, electromagnetic: - Wireless communication using free-space EM waves - Wireline communication using voltages/currents - Optical communication using photons

7. How do tiny devices communicate? Most information theorists are concerned with communication that is, in some way, electromagnetic: - Wireless communication using free-space EM waves - Wireline communication using voltages/currents - Optical communication using photons Are these appropriate strategies for nanoscale devices?

8. How do tiny devices communicate? There exist “nanoscale devices” in nature.

9. How do tiny devices communicate? There exist “nanoscale devices” in nature. Image source: National Institutes of Health

10. How do tiny devices communicate? Bacteria (and other cells) communicate by exchanging chemical “messages” over a fluid medium. - Example: Quorum sensing.

11. How do tiny devices communicate? Bacteria (and other cells) communicate by exchanging chemical “messages” over a fluid medium. - Example: Quorum sensing. Poorly understood from an information-theoretic perspective.

12. Communication Model Communications model

13. Communication Model Communications model m Tx Tx Rx Medium m m' 1, 2, 3, ..., |M| m = m'? M:

14. Communication Model Communications model Noise m Tx Tx Rx Medium m m' 1, 2, 3, ..., |M| m = m'? M:

15. Say it with Molecules Transmit: 1 0 1 1 0 1 0 0 1 0

16. Say it with Molecules Quantity: Sending 0 Release no molecules Cell 1 Cell 2

17. Say it with Molecules Quantity: Sending 1 Release lots of molecules Cell 1 Cell 2

18. Say it with Molecules Quantity: Receiving Measure number arriving Cell 1 Cell 2

19. Say it with Molecules Identity: Sending 0 Release type A Cell 1 Cell 2

20. Say it with Molecules Identity: Sending 1 Release type B Cell 1 Cell 2

21. Say it with Molecules Identity: Receiving Measure identity of arrivals Cell 1 Cell 2

22. Say it with Molecules Timing: Sending 0 Release a molecule now Cell 1 Cell 2

23. Say it with Molecules Timing: Sending 1 WAIT … Cell 1 Cell 2

24. Say it with Molecules Timing: Sending 1 Release at time T>0 Cell 1 Cell 2

25. Say it with Molecules Timing: Receiving Measure arrival time Cell 1 Cell 2

26. Ideal System Model “All models are wrong, but some are useful” -- George Box

27. Ideal System Model Communications model Noise m Tx Tx Rx m m' 1, 2, 3, ..., |M| m = m'? M:

28. Ideal System Model What is the best you can do?

29. Ideal System Model What is the best you can do?

30. Ideal System Model What is the best you can do?

31. Ideal System Model In an ideal system:

32. Ideal System Model In an ideal system: 1) Transmitter and receiver are perfectly synchronized.

33. Ideal System Model In an ideal system: 1) Transmitter and receiver are perfectly synchronized. Transmitter perfectly controls the release times and physical state of transmitted particles.

34. Ideal System Model In an ideal system: 1) Transmitter and receiver are perfectly synchronized. 2) Transmitter perfectly controls the release times and physical state of transmitted particles. 3) Receiver perfectly measures the arrival time and physical state of any particle that crosses the boundary.

35. Ideal System Model In an ideal system: 1) Transmitter and receiver are perfectly synchronized. 2) Transmitter perfectly controls the release times and physical state of transmitted particles. 3) Receiver perfectly measures the arrival time and physical state of any particle that crosses the boundary. 4) Receiver immediately absorbs (i.e., removes from the system) any particle that crosses the boundary.

36. Ideal System Model In an ideal system: 1) Transmitter and receiver are perfectly synchronized. 2) Transmitter perfectly controls the release times and physical state of transmitted particles. 3) Receiver perfectly measures the arrival time and physical state of any particle that crosses the boundary. 4) Receiver immediately absorbs (i.e., removes from the system) any particle that crosses the boundary. Everything is perfect

37. Ideal System Model Two-dimensional Brownian motion Tx Rx 0 d

38. Ideal System Model Two-dimensional Brownian motion Tx Rx 0 d

39. Ideal System Model Two-dimensional Brownian motion Tx Rx 0 d Uncertainty in propagation is the main source of noise!

40. Ideal System Model Theorem. I(X;Y) is higher under the ideal system model than under any system model that abandons any of these assumptions.

41. Ideal System Model Theorem. I(X;Y) is higher under the ideal system model than under any system model that abandons any of these assumptions. Proof. 1, 2, 3: Obvious property of degraded channels. 4: ... a property of Brownian motion.

42. Ideal System Model One-dimensional Brownian motion Tx Rx 0 d

43. Ideal System Model One-dimensional Brownian motion Tx Rx 0 d

44. Ideal System Model One-dimensional Brownian motion Tx Rx 0 d

45. Ideal System Model One-dimensional Brownian motion Tx Rx 0 d

46. Ideal System Model One-dimensional Brownian motion Tx Rx 0 d First hitting time is the only property of Brownian motion that we use.

47. Ideal System Model What is the best you can do?

48. Ideal System Model What is the best you can do?

49. Approaches • Two approaches: • Continuous time, single molecules • Additive Inverse Gaussian Channel • Discrete time, multiple molecules • Delay Selector Channel

50. Additive Inverse Gaussian Channel