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Models and Capacitiesof Molecular Communication
Andrew W. EckfordDepartment 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 TorontoS. Hiyama and Y. Moritani, NTT DoCoMo
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How do tiny devices communicate?
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How do tiny devices communicate?
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How do tiny devices communicate?
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How do tiny devices communicate?
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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
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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?
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How do tiny devices communicate?
There exist “nanoscale devices” in nature.
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How do tiny devices communicate?
There exist “nanoscale devices” in nature.
Image source: National Institutes of Health
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How do tiny devices communicate?
Bacteria (and other cells) communicate by exchanging chemical “messages” over a fluid medium.
- Example: Quorum sensing.
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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.
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Communication Model
Communications model
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Communication Model
Communications model
Tx Rx
1, 2, 3, ..., |M|M:
m
Tx
m
m'
m = m'?
Medium
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Communication Model
Communications model
Tx Rx
1, 2, 3, ..., |M|M:
m
Tx
m
Noise
m'
m = m'?
Medium
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Say it with Molecules
Transmit: 1 0 1 1 0 1 0 0 1 0
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Say it with Molecules
Cell 1 Cell 2
Quantity: Sending 0
Release no molecules
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Say it with Molecules
Cell 1 Cell 2
Quantity: Sending 1
Release lots of molecules
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Say it with Molecules
Cell 1 Cell 2
Quantity: Receiving
Measure number arriving
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Say it with Molecules
Cell 1 Cell 2
Identity: Sending 0
Release type A
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Say it with Molecules
Cell 1 Cell 2
Identity: Sending 1
Release type B
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Say it with Molecules
Cell 1 Cell 2
Identity: Receiving
Measure identity of arrivals
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Say it with Molecules
Cell 1 Cell 2
Timing: Sending 0
Release a molecule now
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Say it with Molecules
Cell 1 Cell 2
Timing: Sending 1
WAIT …
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Say it with Molecules
Cell 1 Cell 2
Timing: Sending 1
Release at time T>0
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Say it with Molecules
Cell 1 Cell 2
Timing: Receiving
Measure arrival time
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Ideal System Model
“All models are wrong,but some are useful”
-- George Box
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Ideal System Model
Communications model
Tx Rx
1, 2, 3, ..., |M|M:
m
Tx
m
Noise
m'
m = m'?
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Ideal System Model
What is the best you can do?
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Ideal System Model
What is the best you can do?
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Ideal System Model
What is the best you can do?
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Ideal System Model
In an ideal system:
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Ideal System Model
In an ideal system:
1) Transmitter and receiver are perfectly synchronized.
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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.
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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.
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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.
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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.
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Ideal System Model
Tx
Rx
d0
Two-dimensional Brownian motion
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Ideal System Model
Tx
Rx
d0
Two-dimensional Brownian motion
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Ideal System Model
Tx
Rx
d0
Two-dimensional Brownian motion
Uncertainty in propagation is the main source of noise!
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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.
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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.
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Ideal System Model
Tx
Rx
d0
One-dimensional Brownian motion
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Ideal System Model
Tx
Rx
d0
One-dimensional Brownian motion
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Ideal System Model
Tx
Rx
d0
One-dimensional Brownian motion
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Ideal System Model
One-dimensional Brownian motion
Tx
Rx
d0
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Ideal System Model
One-dimensional Brownian motion
Tx
Rx
d0
First hitting time is the only property ofBrownian motion that we use.
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Ideal System Model
What is the best you can do?
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Ideal System Model
What is the best you can do?
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Approaches
Two approaches:
• Continuous time, single molecules• Additive Inverse Gaussian Channel
• Discrete time, multiple molecules• Delay Selector Channel
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Additive Inverse Gaussian Channel
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Additive Inverse Gaussian Channel
Tx
Rx
d0
Two-dimensional Brownian motion
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Additive Inverse Gaussian Channel
Tx
Rx
d0
Two-dimensional Brownian motion
Release: t
Arrive: t + n
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Additive Inverse Gaussian Channel
Tx
Rx
d0
Two-dimensional Brownian motion
First passage time is additive noise!
Release: t
Arrive: t + n
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Additive Inverse Gaussian Channel
Brownian motion with drift velocity v:
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Additive Inverse Gaussian Channel
Brownian motion with drift velocity v:
First passage time given by inverse Gaussian (IG) distribution.
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Additive Inverse Gaussian Channel
Brownian motion with drift velocity v:
First passage time given by inverse Gaussian (IG) distribution.
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Additive Inverse Gaussian Channel
Brownian motion with drift velocity v:
First passage time given by inverse Gaussian (IG) distribution.
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Additive Inverse Gaussian Channel
Brownian motion with drift velocity v:
First passage time given by inverse Gaussian (IG) distribution.
IG(λ,μ)
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Additive Inverse Gaussian Channel
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Additive Inverse Gaussian Channel
Let h(λ,μ) = differential entropy of IG.
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Additive Inverse Gaussian Channel
Let h(λ,μ) = differential entropy of IG.
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Additive Inverse Gaussian Channel
Let h(λ,μ) = differential entropy of IG.
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Additive Inverse Gaussian Channel
Additivity property:
Let a ~ IG(λa,μa) and b ~ IG(λb,μb) be IG random variables.
If λa/μa2 = λb/μb
2 = K, then
a + b ~ IG(K(μa + μb)2, μa + μb).
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Additive Inverse Gaussian Channel
Let h(λ,μ) = differential entropy of IG, E[X] ≤ m.
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Additive Inverse Gaussian Channel
Let h(λ,μ) = differential entropy of IG, E[X] ≤ m.
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Additive Inverse Gaussian Channel
Let h(λ,μ) = differential entropy of IG, E[X] ≤ m.
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Additive Inverse Gaussian Channel
Let h(λ,μ) = differential entropy of IG, E[X] ≤ m.
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Additive Inverse Gaussian Channel
Bounds on capacity subject to input constraint E[X] ≤ m:
[Srinivas, Adve, Eckford, sub. to Trans. IT; arXiv]
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Delay Selector Channel
Transmit: 1 0 1 1 0 1 0 0 1 0
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Delay Selector Channel
Transmit: 1 0 1 1 0 1 0 0 1 0
Delay: 1
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Transmit: 1 0 1 1 0 1 0 0 1 0
Delay: 1
Receive: 0 1 0 0 0 0 0 0 0 0
Delay Selector Channel
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Transmit: 1 0 1 1 0 1 0 0 1 0
Delay: 1
Receive: 0 1 0 0 1 0 0 0 0 0
Delay Selector Channel
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Transmit: 1 0 1 1 0 1 0 0 1 0
Delay: 1
Receive: 0 1 0 0 2 0 0 0 0 0
Delay Selector Channel
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Transmit: 1 0 1 1 0 1 0 0 1 0
Delay: 1
Receive: 0 1 0 0 2 0 0 1 0 0
Delay Selector Channel
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Transmit: 1 0 1 1 0 1 0 0 1 0
Delay: 1
Receive: 0 1 0 0 2 0 0 1 1 0
Delay Selector Channel
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Transmit: 1 0 1 1 0 1 0 0 1 0
Delay:
Receive: 0 1 0 0 2 0 0 1 1 0
Delay Selector Channel
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I
Receive: 0 1 0 0 2 0 0 1 1 0
Delay Selector Channel
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I
Receive: 0 1 0 0 2 0 0 1 1 0
… Transmit = ?
Delay Selector Channel
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Input-output relationship
For n particles,
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Input-output relationship
For n particles,
First hitting time distribution
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Input-output relationship
For n particles,
Sum over all possible arrival permutations
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Input-output relationship
For n particles,
Sum over all possible arrival permutations
Intractable for any practical number of particles.(Bapat-Beg theorem)
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The Delay Selector Channel
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The Delay Selector Channel
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Delay Selector Channel
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Delay Selector Channel
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Delay Selector Channel
[Cui, Eckford, CWIT 2011]
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Delay Selector Channel
The DSC admits zero-error codes.
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Delay Selector Channel
The DSC admits zero-error codes.
E.g., m=1: 1: [1, 0] 0: [0, 0]
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90
Delay Selector Channel
The DSC admits zero-error codes.
E.g., m=1: 1: [1, 0] 0: [0, 0]
Receive:0 0 1 0 0 1 1 0 0 0 0 1
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91
Delay Selector Channel
The DSC admits zero-error codes.
E.g., m=1: 1: [1, 0] 0: [0, 0]
Receive:0 0 1 0 0 1 1 0 0 0 0 1
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92
Delay Selector Channel
The DSC admits zero-error codes.
E.g., m=1: 1: [1, 0] 0: [0, 0]
Receive:0 0 1 0 0 1 1 0 0 0 0 1
0 0 1 0 1 0 1 0 0 0 1 0
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93
Delay Selector Channel
The DSC admits zero-error codes.
E.g., m=1: 1: [1, 0] 0: [0, 0]
Receive:0 0 1 0 0 1 1 0 0 0 0 1
0 0 1 0 1 0 1 0 0 0 1 0
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94
Delay Selector Channel
The DSC admits zero-error codes.
E.g., m=1: 1: [1, 0] 0: [0, 0]
Receive:0 0 1 0 0 1 1 0 0 0 0 1
0 0 1 0 1 0 1 0 0 0 1 0
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Ideal System Model
What is the best you can do?
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Ideal System Model
What is the best you can do?
About 1 bit/s
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What is the vision?
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What is the vision?
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99
What is the vision?
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For more information
http://molecularcommunication.ca
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For more information
Acknowledgments
Satoshi Hiyama, Yuki Moritani NTT DoCoMo, Japan
Ravi Adve, Sachin Kadloor, Univ. of Toronto, CanadaK. V. Srinivas
Nariman Farsad, Lu Cui York University, Canada
Research funding from NSERC
Contact
Email: [email protected]: http://www.andreweckford.com/Twitter: @andreweckford