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And now for something c ompletely different. case-14Oct2011. Andrew W. Eckford Department of Computer Science and Engineering, York University Joint work with: L . Cui, York University P . Thomas and R. Snyder, Case Western Reserve University. - PowerPoint PPT Presentation
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case-14Oct2011And now for somethingcompletely different.
Models and Capacitiesof Molecular Communication
Andrew W. EckfordDepartment of Computer Science and Engineering, York University
Joint work with: L. Cui, York University P. Thomas and R. Snyder, Case Western Reserve University
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How do these things talk?
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Why do this? … Engineering
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Why do this? … Medicine/Biology
Model and calculate capacity of a molecular communication channel
Show that information theory can predict biological parameters
Show that information theory plays an important role in physiology/medicine
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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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Communication Model
Fundamental assumptions
1. Molecules propagate via Brownian motion
2. Molecules don’t interact with each other (no reaction, motions are independent)
3. Molecules don’t disappear or change identity
Say it with Molecules
Cell 1 Cell 2
Identity: Sending 0
Release type A
Say it with Molecules
Cell 1 Cell 2
Identity: Sending 1
Release type B
Say it with Molecules
Cell 1 Cell 2
Identity: Receiving
Measure identity of arrivals
Say it with Molecules
Cell 1 Cell 2
Quantity: Sending 0
Release no molecules
Say it with Molecules
Cell 1 Cell 2
Quantity: Sending 1
Release lots of molecules
Say it with Molecules
Cell 1 Cell 2
Quantity: Receiving
Measure number arriving
Say it with Molecules
Cell 1 Cell 2
Timing: Sending 0
Release a molecule now
Say it with Molecules
Cell 1 Cell 2
Timing: Sending 1
WAIT …
Say it with Molecules
Cell 1 Cell 2
Timing: Sending 1
Release at time T>0
Say it with Molecules
Cell 1 Cell 2
Timing: Receiving
Measure arrival time
Ideal System Model
“All models are wrong,but some are useful”
-- George Box
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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.
Everyt
hing i
s perf
ect
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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
Two-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
Two-dimensional Brownian motion
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Ideal System Model
Two-dimensional Brownian motion
Tx
Rx
d0
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Ideal System Model
Two-dimensional Brownian motion
Tx
Rx
d0
First hitting time is the only property ofBrownian motion that we use.
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Input-output relationship
Additive Noise: y = x + n
n = First arrival time
fN(n) = First arrival time PDF
fN(y-x) = Arrival at time y given release at time x
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Input-output relationship
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Input-output relationship
Bapat-Beg theorem
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Delay Selector Channel
Transmit: 1 0 1 1 0 1 00 1 0
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Delay Selector Channel
Transmit: 1 0 1 1 0 1 00 1 0
Delay: 1
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Transmit: 1 0 1 1 0 1 00 1 0
Delay: 1
Receive: 0 1 0 0 0 0 00 0 0
Delay Selector Channel
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Transmit: 1 0 1 1 0 1 00 1 0
Delay: 1
Receive: 0 1 0 0 1 0 00 0 0
Delay Selector Channel
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Transmit: 1 0 1 1 0 1 00 1 0
Delay: 1
Receive: 0 1 0 0 2 0 00 0 0
Delay Selector Channel
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Transmit: 1 0 1 1 0 1 00 1 0
Delay:1
Receive: 0 1 0 0 2 0 01 0 0
Delay Selector Channel
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Transmit: 1 0 1 1 0 1 00 1 0
Delay:1
Receive: 0 1 0 0 2 0 01 1 0
Delay Selector Channel
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Transmit: 1 0 1 1 0 1 00 1 0
Delay:
Receive: 0 1 0 0 2 0 01 1 0
Delay Selector Channel
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I
Receive: 0 1 0 0 2 0 01 1 0
Delay Selector Channel
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I
Receive: 0 1 0 0 2 0 01 1 0
… Transmit = ?
Delay Selector Channel
Delay Selector Channel
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]
Delay Selector Channel
Delay Selector Channel
Max over px
Delay Selector Channel
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Delay Selector Channel
Let m = 1, q1 = 0.5:
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Delay Selector Channel
Let m = 1, q1 = 0.5:
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Delay Selector Channel
Let m = 1, q1 = 0.5:
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Ligand-receptor channels
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Ligand-receptor channels
X = concentration (H/L)
Y = binding state (B/U)
Cell
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Ligand-receptor channels
Cell
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Ligand-receptor channels
Cell
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Ligand-receptor channels
Cell
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Ligand-receptor channels
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Ligand-receptor channels
Theorem:
If αL = 0, αH = 1, β = 1, capacity is log2 ϕ = 0.6942.
Proof sketch:
“BB” subsequences are forbidden at the receiver.
Furthermore, the transmitter always knows the binding state.
[Thomas, Snyder, Eckford, ISIT 2012, in prep]
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Ligand-receptor channels
Conjecture:
In general, feedback-capacity-achieving input distribution is iid.
[Thomas, Snyder, Eckford, ISIT 2012, in prep]
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For more information
http://molecularcommunication.ca
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For more information
Acknowledgments
Lu Cui York Univ., Canada
Peter Thomas, Robin Snyder Case Western Reserve Univ., USA
Research funding from NSERC
Contact
Email: [email protected]: http://www.andreweckford.com/Twitter: @andreweckford