Information-theoretic problems in molecular and nanoscale communication
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Information-theoretic problems in molecular and nanoscale communicationAndrew 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?
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.Bacteria transmit rudimentary chemical messages to theirneighbors to estimate the local population of their species.
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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.Bacteria transmit rudimentary chemical messages to theirneighbors to estimate the local population of their species.
This communication is poorly understood from an information-theoretic perspective.
- Biological literature tends to explain, not exploit- However, genetic components of quorum sensing can be engineered
[Weiss et al. 2003]- Recognized as an important emerging technology
[Hiyama et al. 2005], [Eckford 2007]
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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
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
Communications model
Tx Rx
1, 2, 3, ..., |M|M:
m
Tx
m
Noise
m'
m = m'?
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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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Communication Model
Communications model
Tx Rx
1, 2, 3, ..., |M|M:
m
Tx
m
Noise
m'
m = m'?
Medium
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Propagation Medium
Tx
Rx
d0
Two-dimensional Brownian motion
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Propagation Medium
Tx
Rx
d0
Two-dimensional Brownian motion
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Propagation Medium
Tx
Rx
d0
Two-dimensional Brownian motion
Uncertainty in propagation is the main source of noise!
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Approaches
Two approaches:
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Approaches
Two approaches:
• Discrete time, ISI allowed
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Approaches
Two approaches:
• Discrete time, ISI allowed• Delay Selector Channel
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Approaches
Two approaches:
• Discrete time, ISI allowed• Delay Selector Channel
• Continuous time, ISI not allowed
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Approaches
Two approaches:
• Discrete time, ISI allowed• Delay Selector Channel
• Continuous time, ISI not allowed• Additive Inverse Gaussian Channel
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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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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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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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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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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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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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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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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
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.
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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
Bounds on capacity subject to input constraint E[X] ≤ m:
[Srinivas, Adve, Eckford, sub. to Trans. IT; arXiv]
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What is the potential?
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What is the potential?
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What is the potential?
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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
Contact
Email: [email protected]: http://www.andreweckford.com/Twitter: @andreweckford