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

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

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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!

Approaches

Two approaches:

Approaches

Two approaches:

• Discrete time, ISI allowed

Approaches

Two approaches:

• Discrete time, ISI allowed• Delay Selector Channel

Approaches

Two approaches:

• Discrete time, ISI allowed• Delay Selector Channel

• Continuous time, ISI not allowed

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

The Delay Selector Channel

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: aeckford@yorku.caWeb: http://www.andreweckford.com/Twitter: @andreweckford