Fundamental Limits of Molecular Communication Christopher Rose 1 I. - - PowerPoint PPT Presentation
Fundamental Limits of Molecular Communication Christopher Rose 1 I. Saira Mian 2 1 School of Engineering, Brown University 2 University College London CTW16 Nafplio, Greece May18, 2016 1 Wireless With Molecules Preamble A Simple Statement
Christopher Rose1
1School of Engineering, Brown University 2 University College London
CTW’16 Nafplio, Greece May18, 2016
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Wireless With Molecules Preamble
A Simple Statement of Fact
School of Engineering@Brown University CTW 2016
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Wireless With Molecules Preamble
A Simple Statement of Fact
School of Engineering@Brown University CTW 2016
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Wireless With Molecules Preamble
A Simple Statement of Fact
School of Engineering@Brown University CTW 2016
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Wireless With Molecules Preamble
A Simple Statement of Fact
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Wireless With Molecules Preamble
Followed That Hammer Into Outer Space
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Wireless With Molecules Preamble
“Inscribed Matter” Led To Inner Space
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Wireless With Molecules Preamble
“Inscribed Matter” Led To Inner Space
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Wireless With Molecules Preamble
What Is A ...
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Wireless With Molecules Preamble
What Is A ...
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Wireless With Molecules Preamble
A REALLY Simple Signaling Molecule (Token) Naked (and clothed) Ca++
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Wireless With Molecules Preamble
A Simple Signaling Molecule (Token) Quorum sensing signal
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Wireless With Molecules Preamble
A More Complex Signaling Molecule (Token) Nerve Growth Factor (protein)
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Wireless With Molecules Preamble
What Is A ...
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Wireless With Molecules Preamble
What Is A ...
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Wireless With Molecules Preamble
Receptor Specificity Cartoon Ligand (token) docks with receptor (protein)
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Wireless With Molecules Preamble
A More Detailed Receptor Specificity Cartoon Ligands (tokens) dock with receptor (protein)
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Wireless With Molecules Preamble
What Are Some ...
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Wireless With Molecules Preamble
What Are Some ...
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Wireless With Molecules Preamble
Reception and Transduction Cartoon Ligand → Receptor → Gene Tickling
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Wireless With Molecules Preamble
Identical Tokens: bacteria
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Wireless With Molecules Preamble
Identical Tokens: neurons ACh release → postsynaptic uptake
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Wireless With Molecules Preamble
Tokens with Payloads: transcription Nuclear DNA → mRNA → Ribosome → Protein
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Wireless With Molecules Preamble
Active Transport Bacterial Microtubules
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Wireless With Molecules Preview
Setup + Punchline Preview
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Wireless With Molecules Preview
Setup + Punchline Preview
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Wireless With Molecules Preview
Setup + Punchline Preview
A game of release (time t) and catch (time s = t + d)
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Wireless With Molecules Preview
Setup + Punchline Preview
A game of release (time t) and catch (time s = t + d) Multiple identical molecules: t → s → s
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Wireless With Molecules Preview
Setup + Punchline Preview
A game of release (time t) and catch (time s = t + d) Multiple identical molecules: t → s → s Molecules with embedded payloads (similar math)
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Wireless With Molecules Preview
Setup + Punchline Preview
A game of release (time t) and catch (time s = t + d) Multiple identical molecules: t → s → s Molecules with embedded payloads (similar math)
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Wireless With Molecules Preview
Diffusion Cartoon
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Wireless With Molecules Preview
Diffusion Cartoon
t = t1
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Wireless With Molecules Preview
Diffusion Cartoon
t = t1
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Wireless With Molecules Preview
Diffusion Cartoon
t = t1
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Wireless With Molecules Preview
Diffusion Cartoon
t = t1
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Wireless With Molecules Preview
Diffusion Cartoon
t = t1
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Wireless With Molecules Preview
Diffusion Cartoon
t = t1
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Wireless With Molecules Preview
Diffusion Cartoon
t = t1
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Wireless With Molecules Preview
Diffusion Cartoon
t = t1
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Wireless With Molecules Preview
Diffusion Cartoon
t = t1
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Wireless With Molecules Preview
Diffusion Cartoon
t = t1
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Wireless With Molecules Preview
Diffusion Cartoon
t = t1
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Wireless With Molecules Preview
Diffusion Cartoon
t = t1 s = t1 + d
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Wireless With Molecules Preview
Transport (passive) Receptor Kinetics (ignore)
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Wireless With Molecules Preview
Transport (passive) Receptor Kinetics (ignore)
(T ,B )
k k j j
(S ,B )
~
capture
emission
Coding → Emission → Transport → Capture → Decoding
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Wireless With Molecules Preview
Could Even Add Some Drift
(T ,B )
k k j j
(S ,B )
~
capture
emission Coding → Emission → Transport → Capture → Decoding
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Wireless With Molecules Timing Channel Detail Review
Mathematical Abstraction For Identical Tokens
S M
1
S
1
D
1
T
M
T
M
D
S
+ +
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Wireless With Molecules Timing Channel Detail Review
Mathematical Abstraction For Identical Tokens
S M
1
S
1
D
1
T
M
T
M
D
S
+ +
S = T + D
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Wireless With Molecules Timing Channel Detail Review
Mathematical Abstraction For Identical Tokens
S M
1
S
1
D
1
T
M
T
M
D
S
+ +
S = T + D
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Wireless With Molecules Timing Channel Detail Review
Mathematical Abstraction For Identical Tokens
S M
1
S
1
D
1
T
M
T
M
D
S
+ +
S = T + D
First passage time: E[D] = 1/µ
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Wireless With Molecules Timing Channel Detail Review
Token Timing Departures
S5 T5 T4 S4 T3 S3 T2 S2 S 2 S 3 S 4 S 5 T1 S1 S 1 t
Arrivals
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Wireless With Molecules Timing Channel Detail Review
Mutual Information: I(S; T)
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Wireless With Molecules Timing Channel Detail Review
Mutual Information: I(S; T)
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Wireless With Molecules Timing Channel Detail Review
Mutual Information: I(S; T)
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Wireless With Molecules Timing Channel Detail Review
Mutual Information: I(S; T)
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Wireless With Molecules Timing Channel Detail Review
Mutual Information: I(S; T)
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Wireless With Molecules Timing Channel Detail Review
Hypersymmetries Departures
S5 T5 T4 S4 T3 S3 T2 S2 S 2 S 3 S 4 S 5 T1 S1 S 1 t
Arrivals
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Wireless With Molecules Timing Channel Detail Review
Hypersymmetries Departures
S 2 S 3 S 4 S 5 S 1 S1 T1 T2 S2 S4 T4 T5 S5 T3 S3 t
Arrivals
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Wireless With Molecules Timing Channel Detail Review
Hypersymmetry Buys You
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Wireless With Molecules Timing Channel Detail Review
Hypersymmetry Buys You
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Wireless With Molecules Timing Channel Detail Review
Hypersymmetry Buys You
{ S, Ω} ↔ S
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Wireless With Molecules Timing Channel Detail Review
Hypersymmetry Buys You
{ S, Ω} ↔ S
⇓
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Wireless With Molecules Timing Channel Detail Review
Hypersymmetry Buys You
{ S, Ω} ↔ S
⇓
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Wireless With Molecules Timing Channel Detail Review
Channel Use Formalities
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Wireless With Molecules Timing Channel Detail Review
Channel Use Formalities
2 1 k
γ( Μ,ε )
Guard Interval: γ(M, ǫ) Overflow Probability: ǫ
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Wireless With Molecules Timing Channel Detail Review
Channel Use Formalities
2 1 k
γ( Μ,ε )
Guard Interval: γ(M, ǫ) Overflow Probability: ǫ
Power Constraint (tokens cost energy):
ǫ→0 lim M→∞
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Wireless With Molecules Timing Channel Detail Review
Limiting Details
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Wireless With Molecules Timing Channel Detail Review
Limiting Details
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Wireless With Molecules Timing Channel Detail Review
Limiting Details
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Wireless With Molecules Timing Channel Detail Review
Limiting Details
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Wireless With Molecules Timing Channel Detail Review
Limiting Details
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Wireless With Molecules Timing Channel Detail Review
Omitting the Details (or summary :) )
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Wireless With Molecules Timing Channel Detail Review
Omitting the Details (or summary :) )
Set: ρ ≡
M τ(M)
Define: χ ≡ µ (first passage rate) ρ (token launch rate) Require: E[D] < ∞ Cm(M) = max
hypersymm fT()
S; T)/M
M→∞ Cm(M)
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Wireless With Molecules Timing Channel Detail Review
My Past Personal Struggles
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Wireless With Molecules Timing Channel Detail Review
My Past Personal Struggles
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Wireless With Molecules Timing Channel Detail Review
My Past Personal Struggles
fT() h(S) + H(Ω|
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Wireless With Molecules Timing Channel Detail Review
My Past Personal Struggles
fT() h(S) + H(Ω|
fT() h(S) + H(Ω|
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Wireless With Molecules Timing + Payload
Timing + Payload
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Wireless With Molecules Timing + Payload
Timing + Payload Identical tokens → timing info only
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Wireless With Molecules Timing + Payload
Timing + Payload Identical tokens → timing info only Payloads → chop message into M B-bit pieces
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Wireless With Molecules Timing + Payload
Timing + Payload Identical tokens → timing info only Payloads → chop message into M B-bit pieces
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Wireless With Molecules Timing + Payload
Timing + Payload Identical tokens → timing info only Payloads → chop message into M B-bit pieces
(for re-sequencing)
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Wireless With Molecules Timing + Payload
Energy
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Wireless With Molecules Timing + Payload
Energy
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Wireless With Molecules Timing + Payload
Energy
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Wireless With Molecules Timing + Payload
Energy
substrate: c1 joules per token payload bit B: B∆c1 joules per token
K∆c1 joules per token, so
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Wireless With Molecules Timing + Payload
Energy
substrate: c1 joules per token payload bit B: B∆c1 joules per token
K∆c1 joules per token, so H(Ω| S, T) ≤ MK ≤ log M!
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Wireless With Molecules Timing + Payload
And Now ...
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Wireless With Molecules Timing + Payload
And Now ...
using exponential first passage
(the timing channel’s “Gaussian”)
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Wireless With Molecules Bounds
Timing-Only Bits/Joule
Theorem 1.
χ
∞
S, T)/M: average per-token order-uncertainty
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Wireless With Molecules Bounds
Payload-Only Bits/Joule Theorem 2. CP = B c1 + ∆c1
MH(Ω|
S, t)
CP ≥ B c1 + ∆c1 B + e− 1
χ
∞
1 χ k (kχ − 1)log k! k!
S, T)/M: average per-token order-uncertainty
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Wireless With Molecules Bounds
Payload + Timing Bits/Joule Lower Bound Theorem 4. RP +T ≈ log
e
c1 + ∆c1 B + e− 1
χ
∞
1 χ k (kχ − 1)log k! k!
S, T)/M: average per-token order-uncertainty
where RP +T ≤ CP +T.
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Wireless With Molecules Bounds
Info per Unit Energy
χ ↔ passage rate per launch rate c0 = 1, c1 = 0, ∆c1 = 1
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Wireless With Molecules Bounds
Info per Passage per Unit Energy
1 χ ↔ launch rate per passage rate
c0 = 1, c1 = 0, ∆c1 = 1
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Wireless With Molecules Play Time
And Now ....
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Wireless With Molecules Play Time
And Now ....
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Wireless With Molecules Play Time
Play Time Setup
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Wireless With Molecules Play Time
Play Time Setup
R source sink
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Wireless With Molecules Play Time
Play Time Setup
R source sink
“Binary Protein” Token Construction 4BATP = 3.2B × 10−19J
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Wireless With Molecules Play Time
Play Time Setup
R source sink
“Binary Protein” Token Construction 4BATP = 3.2B × 10−19J Diffusion Coefficient, D in air: ≈ 10−5m2/s Mean First Passage Time, E[D] ≈ R2
2D
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Wireless With Molecules Play Time
Play Time Setup
R source sink
“Binary Protein” Token Construction 4BATP = 3.2B × 10−19J Diffusion Coefficient, D in air: ≈ 10−5m2/s Mean First Passage Time, E[D] ≈ R2
2D
Across a table (1m): E[D] ≈ 14hrs (need fan )
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Wireless With Molecules Play Time
Play Time Setup
R source sink
“Binary Protein” Token Construction 4BATP = 3.2B × 10−19J Diffusion Coefficient, D in air: ≈ 10−5m2/s Mean First Passage Time, E[D] ≈ R2
2D
Across a table (1m): E[D] ≈ 14hrs (need fan ) Across a 0.1mm gap: E[D] = 0.5ms
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Wireless With Molecules Play Time
Play Time Numbers
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Wireless With Molecules Play Time
Play Time Numbers
1 χ = ρ µ = 1 (w/ identical tokens)
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Wireless With Molecules Play Time
Play Time Numbers
1 χ = ρ µ = 1 (w/ identical tokens) Across a table: ≈ 2 bits/day (≈ 7 × 10−24 W) Across a 0.1mm gap: ≈ 10kb/s (≈ 3.2 fW)
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Wireless With Molecules Play Time
Play Time Numbers
1 χ = ρ µ = 1 (w/ identical tokens) Across a table: ≈ 2 bits/day (≈ 7 × 10−24 W) Across a 0.1mm gap: ≈ 10kb/s (≈ 3.2 fW) 1 χ = ρ µ = 1000 (w/ B = 1000-bit tokens)
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Wireless With Molecules Play Time
Play Time Numbers
1 χ = ρ µ = 1 (w/ identical tokens) Across a table: ≈ 2 bits/day (≈ 7 × 10−24 W) Across a 0.1mm gap: ≈ 10kb/s (≈ 3.2 fW) 1 χ = ρ µ = 1000 (w/ B = 1000-bit tokens) Across a table: ≈ 2Kb/day (≈ 7 × 10−21 W) Across a 0.1mm gap: ≈ 10Mb/s (≈ 3.2 pW)
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Wireless With Molecules Play Time
Play Time Numbers
1 χ = ρ µ = 1 (w/ identical tokens) Across a table: ≈ 2 bits/day (≈ 7 × 10−24 W) Across a 0.1mm gap: ≈ 10kb/s (≈ 3.2 fW) 1 χ = ρ µ = 1000 (w/ B = 1000-bit tokens) Across a table: ≈ 2Kb/day (≈ 7 × 10−21 W) Across a 0.1mm gap: ≈ 10Mb/s (≈ 3.2 pW)
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Wireless With Molecules Play Time
Appropriately Awed Response
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Wireless With Molecules Dreamin’
Netflix/SensorNet Distribution Fantasy
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Wireless With Molecules Dreamin’
Disk Farm Fantasy
Suppose token construction energy cost ≪ fan energy cost
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Wireless With Molecules Dreamin’
Disk Farm Fantasy
Suppose token construction energy cost ≪ fan energy cost
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Wireless With Molecules Summary
Molecular Communication Summary
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Wireless With Molecules Summary
Molecular Communication Summary
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Wireless With Molecules Summary
Molecular Communication Summary
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Wireless With Molecules Summary
Molecular Communication Summary
Slow release with timing &/or small payload
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Wireless With Molecules Summary
Molecular Communication Summary
Slow release with timing &/or small payload
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Wireless With Molecules Summary
Molecular Communication Summary
Slow release with timing &/or small payload
Fast release with payload + timing or large payload
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Wireless With Molecules Summary
Molecular Communication Summary
Slow release with timing &/or small payload
Fast release with payload + timing or large payload
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Wireless With Molecules Summary
Molecular Communication Summary
Slow release with timing &/or small payload
Fast release with payload + timing or large payload
(beware transport latency)
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Wireless With Molecules Summary
If You Only Remember One Slide A truck filled with storage media, driven across town, is a very reliable high bit rate channel.
–Comm. Theory Collective Subconscious
BUT ...
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Wireless With Molecules Summary
If You Only Remember One Slide A truck filled with storage media, driven across town, is a very reliable high bit rate channel.
–Comm. Theory Collective Subconscious
BUT ...
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Wireless With Molecules Summary
If You Only Remember One Slide A truck filled with storage media, driven across town, is a very reliable high bit rate channel.
–Comm. Theory Collective Subconscious
BUT ...
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Wireless With Molecules Summary
If You Only Remember One Slide A truck filled with storage media, driven across town, is a very reliable high bit rate channel.
–Comm. Theory Collective Subconscious
BUT ...
School of Engineering@Brown University CTW 2016
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Wireless With Molecules Summary
If You Only Remember One Slide A truck filled with storage media, driven across town, is a very reliable high bit rate channel.
–Comm. Theory Collective Subconscious
BUT ...
School of Engineering@Brown University CTW 2016