Network Coding and Reliable
Communications Group
(Network) Coding in
Uncertain Networks
Daniel E. Lucani
Network Coding and Reliable
Communications Group
Sources of Uncertainty
user rate
changes with time,
user, other users
Rate uncertainty
packets
are Channel
lost
cannot
Delay react
quickly
Interference
collisions
Network Coding and Reliable
Communications Group
Motivations for Research
Which
transmissions
have greatest
impact?
Rate uncertainty
Channel
How to
perform
efficient
rateless
transmission?
HowCapacity
much to
talk
before
improvement
stopping
to
through
listen?
simple,
distributed
algorithms?
Interference
Delay
Uncoded rate
without
additional
cost?
Network Coding and Reliable
Communications Group
Network Coding
• A new means of conveying information
– Throughput gains, robustness against failures and erasures
– Routing/traditional network: data can only be forwarded or replicated
– Network coding: data is an algebraic entity
• In wireless networks
– Broadcast advantage
– Packet erasures (losses)
Routing
Network Coding
A
A
B
A
B
B
A+B
A+B
Network Coding and Reliable
Communications Group
Network Coding
• In wireless networks
– Broadcast advantage
– Packet erasures (losses)
p1+ p2 + p3
p2
p3
p1
p1
p1+ p2 + p3
p3
p2
p3
p1
p2
p1+ p2 + p3
Network Coding and Reliable
Communications Group
On Coding for Delay
How much to
talk before
stopping to
listen?
Rate uncertainty
Channel
Joint work with:
Muriel Médard
Milica Stojanovic
David Karger
Interference
Delay
Network Coding and Reliable
Communications Group
Application: dissemination of information
• Time-Division Duplexing or ‘Half-Duplex’ channels
– How much should we talk before stopping to listen?
• Large latency channels
– Satellite and deep space communications
• Very long distances (~10,000 km and up)
– Underwater acoustic communications
• Low propagation speed (~1500 m/s)
• Long distances (~km)
• Previous work for link/broadcast scenarios
– ARQ schemes
– FEC schemes: block-based (no feedback) or rateless
– Hybrid schemes
Network Coding and Reliable
Communications Group
Cases
Link
Tx
Rx
•Mean completion time: close to full duplex (gold standard)
•Mean completion energy: close to optimal
Tx with M packets
Rx N
1-to-all Broadcast
Rx 2
Rx 1
•Mean completion time: can be better than scheduling schemes
with full duplex capabilities
•Optimization: Hard, but have good heuristics
Network Coding and Reliable
Communications Group
Cases
all-to-all Broadcast
Node 1
M1 packets
Node N
MN packets
Node 3
M3 packets
Node 2
M2 packets
•Mean completion time: can be better than scheduling schemes
with full duplex capabilities
•Optimization: hard, but have algorithm+heuristics
Network Coding and Reliable
Communications Group
Description of Scheme: Link
• Goal: reliable transmission of a block of data packets
Tx
Rx
Erasure Channel
Generates N Mi
random linear coded packets
Header
h bits
M data
packets
..
.
ACK i
Coded Data
C1 … CM
Received k coded packets,
only M-i independent
g bits
linear combinations
n bits
ACK degrees of freedom
required to decode (dofs req’d):
Not particular data packet
..
.
Degrees of freedom
needed by Rx:
Degrees of freedom
needed to decode:
M
i
M
i
Note: Choice of Ni, i determines performance of scheme
[ITA’09, Infocom’09, ICC’09]
Network Coding and Reliable
Communications Group
Description of Scheme: Link
• Scheme can be modeled as a Markov chain
– States: degrees of freedom (dof) required to decode
– Transition time ( T ( i )) depends on starting state
• We determined moment generating functioni of
completion time [ITA’09]
M T ,n ( s) 
e
n 1
sT ( n )
1  Pnn e
sT ( n )

Pni MT ,i (s)
MT ,0 (s)  1
i 0
• Optimizing N i , i to minimize completion time:
– No closed-form expressions
– Ni are integer-valued: hard
– Exploit recursion, performed off-line
Network Coding and Reliable
Communications Group
Minimizing Completion Time or Energy
Full Duplex Network Coding:
TDD constraint
• Ni, i chosen to minimize
Tx
Rx
– Mean completion time [ITA’09 Infocom’09]
– Mean completion energy [ICC’09]
Channel
ACK ACK
Mean
Time (s)
MeanCompletion
Completion Energy
0.8
3
2.5
0.6
2
Time
Energy
TDD Opt. Energy
1.5
0.4
1
Pe = 0.8
0.2
0.5
0 -4
10
3
)
TDD Opt. Time
Full Duplex
TDD Opt. Energy
TDD Opt. Time
Full Duplex
1.15dB
Pe = 0.8
-3
10
-2
-2
-1
-1
10
10
Probability
Erasure Probability
Packet Erasure
Packet
0
0
10
e.g: M = 10, round trip time = 250 ms, Rate = 1.5 Mbps
1.1dB
Network Coding and Reliable
Communications Group
Effect of Field Size [GLOBECOM’09]
Tx
Rx 1
Channel / Network
(Packet Losses)
Inputs random linear
network coded packets
(M original packets)
–We are interested in
j coded
packets
arrive
n ind. linear
combinations
needed
P  n ' n , j  =  j (n,n')
–Modeled as a Markov chain
q-M
q-M+1
M-1
M
1 – q-M
q-1
…
1
1
1 – q-2
0
with transition
probability matrix

1 – q-1
Shown that each receiver requires in average less than M + 2
coded packets to decode regardless of field size (q)
Network Coding and Reliable
Communications Group
Systematic coding: a free lunch?
• Can we use smaller field size
(simpler operations) and still
perform close to large field
size?
0.6
Systematic + RLNC with XOR
RLNC with XOR
0.55
Completion Time (s)
RLNC Large Field Size (220)
– Ans. Yes + reduction in
decoding complexity
0.5
• Systematic network coding:
0.45
– First M transmissions are
the original packets
– All other transmissions:
random linear combinations
0.4
0.35
• Decoding complexity down
from O(M3) to O(Pe3M3)
0.3
10
-3
-2
-1
10
10
Packet Erasure Probability (Pe)
10
0
– Pe = 0.1 → 1000 times less
operations in average
Network Coding and Reliable
Communications Group
Inter-Layer Coding for Multicast
Rate uncertainty
Channel
Joint work with:
Muriel Médard
MinJi Kim
Fang Zhao
Shirley Shi
Interference
Delay
Capacity
improvement
through
simple,
distributed
algorithms?
Network Coding and Reliable
Communications Group
Layered Multicast with Network Coding
• Directed acyclic graph, unit capacity links
r1
s
Base
Layer
Multicast
Network
X1
r2
X1
X1 , X 2 , X 3
• n-layer multicast:
Refinement
layers
r3
X1, X2 , X3
– If n = 2, multicast all layers to all but one receiver: achieves mincut with linear codes [Koetter et al ‘03]
– Otherwise: min-cut not achievable with linear codes in general
• Previous work, e.g. [Wu et. al, ‘08], [Sundaram et. al ‘05]
– “Intra-layer” coding and no “inter-layer” coding
– Centralized, LP
Network Coding and Reliable
Communications Group
Pushback Algorithm [Infocom’10]
• Distributed, random linear network coding
• Message passing: two stages
• Guarantees decodability of base layer
q(v)
c(m
1)
100
v
95
% of Happy Nodes
q(v) )
c(m
2
c(mq(u)
4)
c(m3)
90
u
85
pt2pt
Steiner
Layered
PB min-req
PB min-cut
80
75
70
3
4
5
6
7
No. of Receivers (|R|)
8
9
Network Coding and Reliable
Communications Group
Conclusions
• Sources of uncertainty are not restricted to channel
limitations/constraints, but also include network topologies
and interactions between network nodes
• On Coding for Delay:
– Tailoring feedback and coding can reduce mean delay for successful
in-order transmission of packets
– Coding is designed to minimize delay
– Have looked at queueing analysis
– Currently using these intuitions to improve satellite networks
• Inter-layer coding multicast:
– Simple, distributed algorithm to determine liner network codes
– Benefits in coding (when done appropriately)
– Extension: use a modified version to determine uncoded rate that
can be guaranteed to users
Network Coding and Reliable
Communications Group
Extra Slides
Network Coding and Reliable
Communications Group
Effect of field size [GLOBECOM’09]
1.6
0.8
• Computation: Smaller
field size, simpler
operations
• How much do we loose
in performance?
XOR (q=2)
20
1.4
0.75
Mean Completion Time (s)
Mean Completion Time (s)
0.7
1.2
0.65
qXOR
= 2 (q=2)
q = 22
q = 23
q = 230
– Shown that each
receiver requires in
average less than M + 2
coded packets to
decode regardless of
field size (q)
0.61
0.55
0.8
0.5
0.6
0.45
M = 30, Difference<0.28dB
0.4
0.4
0.35
0.2 -4
10
• If q large, roughly M
M = 20, Difference<0.4dB
M = 5, Difference<0.6dB
-3
10
-2
-1
10
10
Packet
Packet Erasure
Erasure Probability
0
10
– If M is large, not much
performance
degradation
Network Coding and Reliable
Communications Group
Motivations for Research
Which
transmissions
have greatest
impact?
Rate uncertainty
Channel
How to
perform
efficient
rateless
transmission?
HowCapacity
much to
talk
before
improvement
stopping
to
through
listen?
simple,
distributed
algorithms?
Interference
Delay
Network Coding and Reliable
Communications Group
Future work: Midterm goals
• Simple distributed MAC layer data dissemination
protocol
• Online network coding in large latency half-duplex
channels
• Improvement of pushback algorithm: can we send
uncoded packets while maintaining rate?
• Scaling laws for underwater networks  scale
frequency
Network Coding and Reliable
Communications Group
Future work: Long term goals
• General wireless networks that are challenged by
high packet losses and large latency
– Special interest in underwater and satellite
• Trade-off between cost and rate of sending uncoded
packets in network coding
• Data dissemination in wireless networks
– Theoretical bounds for half-duplex systems
– MAC level schemes for fast and efficient dissemination
• Voice and video transmission in networks and how to
best incorporate network coding and feedback in the
network
Network Coding and Reliable
Communications Group
Other Research Topics
1. Queuing analysis for large latency halfduplex scheme [ISIT’09]
2. Underwater acoustic networks
Channel models
[Oceans’08, JSAC’08]
Fundamental limits [JSAC’08, Asilomar’08,
Submitted to IT Trans.]
Joint work with:
Muriel Médard
Milica Stojanovic
Network Coding and Reliable
Communications Group
Results
• Proposed first simple tractable model relating
transmission power, band, capacity [Oceans’08, JSAC’08]
• Proposed approximate channel models for transmission
power [Oceans’08, JSAC’08]
– Convex for practical purposes [ISITA’08, JSAC’08]
• Lower bound to transmission power for multicast
[ISITA’08, JSAC’08]
– Based on network coding subgraph selection problem
– Use (approximate) channel models as cost function
• Capacity scaling [Asilomar’08, Submitted to IT Trans.]
– Proposed upper bounds for transport capacity for the
underwater networks for different setups

1
nk

 
exp W0 O n 1/ k
 , with n    exp  W O  n    1
1/ k
0
Network Coding and Reliable
Communications Group
Underwater Acoustic Channel
• Path loss:
A(l, f )  (l lref ) a( f )
k
1 k  2
l
• Noise N ( f ) :
Parameters ( w, s )
Spherical geometry k = 2
A(l,f)N(f)
l
Cylindrical geometry k = 1
l
f
Network Coding and Reliable
Communications Group
• Power:
Underwater Acoustic Channel
P(l , C ) 

S (l , C, f )df
B ( l ,C )
where S (l , C, f )  K (l , C )  A(l , f ) N ( f ) , f  B(l , C )
• Capacity (water filling principle):
K (l , C )
C
log 2
df
B ( l ,C )
A(l , f ) N ( f )

where B(l , C ) optimum band, K (l , C ) constant
fc(l)
100 km
B(l , C )
A(l,f)N(f)
A(l,f)N(f)
K(l,C)
50 km
A(l,f)N(f)
P
B(l,C’)
K(l,C’)
f
10 km
fc(l)
f
l<<1 km
5 km
fc(l)
l
f
Network Coding and Reliable
Communications Group
Random Linear Network Coding
• Generating a random linear network coded packet (CP)
CPj 
C P
i i
i
• Operations over finite field of size q = 2g.
P1
C1
+
D
x
A T
x
x
n bits
C1 C1
+
+
A T
x
x
C1
+
A
x
1
x
g bits
C1
+
2
x
C2
C2
C2
C2
C2
D
x
P2
Header
h bits
A
x
e.g. g = 8 bits, q = 256
Coded Data
n bits
C1 C2
g bits
Network Coding and Reliable
Communications Group
Throughput
• Ni, i chosen to minimize mean completion time for channel
conditions
T = 0.025 s
• e.g: M = 10, Rate = 10 Mbps 10
rt
6
Throughput Metric
• Increasing latency, favors
network coding TDD scheme
 (bps)
 = #bits / E[Time]
10
10
Trt = 0.25 s
5
Trt = 2.5 s
4
• Better performance than
Go-back-N (GBN) and Selective
Repeat (SR) for TDD
GBN TDD Window = 10
SR TDD Window = 10
Network Coding TDD Optimal M = 10
3
10 -3
10
-2
-1
10
10
Packet Erasure Probability
10
0
Network Coding and Reliable
Communications Group
Energy Per Bit
n = # of data bits per packet
Fixed bit error probability: n  , packet erasure prob. 
Fixed transmission power
Energy per Bit
10-5
10-6
Full Duplex
TDD-T
TDD-E
Packet Erasure Probability
<1.4dB
4000
1
10000
20000 30000
Bits per coded packet (n)
100000
10000
20000 30000
Bits per coded packet (n)
100000
0.5
0
4000
Optimizing for time or energy: similar performance in energy
Network Coding and Reliable
Communications Group
Sensitivity
0.65
Errors in estimate of
probability of erasure
Underestimate of Pe :
Better performance
at high Pe
0.6
Mean Completion Time (s)
Over /Underestimate
of Pe : similar results
at low Pe
Perfect
-1dB
ErrorEstimate
in Estimate
2dB
Estimate
Perfect
-3dBError
Error
Estimate
Estimate
-2dB
Error
Estimate
1dB
3dB
Error
Error
Estimate
Estimate
0.55
±1dB
±2dB
±3dB
0.5
0.45
0.4
<2dB
<0.2dB
<0.84dB
<0.67dB
0.35
-4
10
-3
10
-2
10
Packet Erasure Probability
-1
10
Network Coding and Reliable
Communications Group
Variance of Completion Time
0
10
0.03
Variance (s 2)
0.02
-2
10
Mean Completion Time (s)
Variance (s 2)
40
Upper Bound on Variance (s 2)
Lower Bound on Variance (s 2)
Change inChange
NM Change
in NMin NM
As packet erasure prob.
increases, number of coded 0.01
-3
10
packets sent Ni increases
20
-4
10 0 -4
-4
1010
M
-1
N
Variance is not continuous
w.r.t packet erasure prob. 10
Why?
60
-3
-3
10
10
-2 -2
-1
-1
1010
10 10
Packet
Erasure
Probability
(Pe)
Packet
Erasure
Probability
0
0
10
Network Coding and Reliable
Communications Group
Broadcast: viable scheme
M=3
• Number of variables:
Reduce to M variables
Ni , where i  max(i1 , i2 ,..., iN )
max dof = 3
•Optimization:
•# of operations depends on
# of states, i.e. ~(M+1)N
3,3
3,2
3,1
3,0
2,3
2,2
2,1
2,0
•Develop heuristics to
reduce computation
•Worst Link
•Combined Erasures
1,3
1,2
1,1
1,0
0,3
0,2
0,1
0,0
Network Coding and Reliable
Communications Group
Description of scheme: two nodes
Node 1
Node 2
ACK M2
ACK
i1
Erasure
Channel
Generates N(Mi11,Mi22, 0 )
random linear coded packets
Header
h bits
..
.
M1 data
packets
..
.
ACK i1
Generates
)
Coded
Data N( i1C,M1 2,1…
CM
random linear coded packets
g bits
n bits
Degrees of freedom
needed by Node 2:
Degrees of freedom
needed to decode:
M
i11
M
i22
..
.
..
.
M2 data
packets
Degrees of freedom Degrees of freedom
needed by Node 1: needed to decode:
M2
M
i11
Note: Choice of N(i,j,t), I,j,t determines performance of scheme
Network Coding and Reliable
Communications Group
Description of the scheme
• Modeled as Markov chain
– # states N (M1+1)N−1(M2 + 1)N−1...(MN + 1)N−1
– N absorbing states
• # of variables: large, even for two nodes
• Structure:
2,2,1
2,2,0
2,1,1
2,1,0
1,2,1
1,2,0
2,0,0
1,1,1
1,0,1
1,0,0
1,1,0
0,2,1
0,2,0
2,0,1
0,1,1
0,1,0
0,0,1
0,0,0
– Round robin assignment of Tx:
Periodicity
– Node “sees” the system as a
broadcast problem [Netcod’09]
with round trip time variable,
Absorbing
depends on initial state
States
Network Coding and Reliable
Communications Group
Algorithm
• Step1: Initialize N(i,j,0) = i, N(i,j,1) = j
• Step 2: j’ , fix j’ compute N(i,j’,0) i
Node 1
N(i,j’,0)
Trt + E[ N(i’,j’,1)
P(i,j’,0) -> (i’,j’,1) ] Tp
Node 2
Dofs needed i’
Fixed value
• Step 3: i’ , fix i’ compute N(i’,j,1) j
Node 1
Dofs needed j’
N(i’,j,1)
Trt + E[ N(i’,j’,0)
P(i’,j,1) -> (i’,j’,0) ] Tp
Node 2
Fixed, computed in step 2
• Step 4: Converges, then STOP
Network Coding and Reliable
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Number of Iterations of Algorithm
• M1 = M2 = M
• Small number of
iterations needed
before converging
to a solution
• For Pe < 10-3:
algorithm
converges to
initialization values
5
M=5
M = 10
M = 15
Number of Iterations (n)
4
3
2
1
0
-4
10
10
-3
-2
10
Packet Erasure Probability
10
-1
Network Coding and Reliable
Communications Group
Comparison Schemes: Two node case
TDD using Round Robin:
Node 1 1 2 3 …M1
1
Node 2
3
M1
Channel
M2 2
M2… 2 1
Full Duplex using Round Robin:
Node 1
1 2 3 …M1 1 2 3
Channel
1 M2 2
1
3
M1
Node 2
2 1 M2… 2 1
Full Duplex using Network Coding:
Node 1
Node 2
Channel
Network Coding and Reliable
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Greedy algorithm
coding horizon for device i
coding horizon for device 1
100%
75%
50%
backward healing
25%
device i forward dissemination
device j
Network Coding and Reliable
Communications Group
Breaking ties
Break tie: node with the most knowledge
Tc(1)
 K 1
M

 N 
M Data Packets, K nodes, transmit to N nodes downstream
Break tie: schedule that benefits nodes with less data
 K 1
Tc(2)  3( M  1)  

 N 
M Data Packets, K nodes, transmit to N nodes downstream
Network Coding and Reliable
Communications Group
• Objective: minimize dissemination time, arbitrary
wireless networks
• Assumptions:
2
– Slotted time
l1{2}as hypergraph
– Network modeled
l
• Optimal scheme
1{2,3,4}
l1{2,3}
4
1
– Involves choosing the sequence of transmissions
– Hard problem
3
• Proposed a greedy algorithm
– Chooses hyperarcs that maximize impact at each slot
• Impact: Avg. # of nodes that benefit from transmission
– Breaks ties in favor of transmissions that disseminate
information to nodes with small # degrees of freedom
Network Coding and Reliable
Communications Group
Dissemination time gains: losses
Pe2
1
M
3
2
Pe1
0
3
Pe1
0
4
0
Pe1 = 0.2, Pe2 = 0.6 (Simulation)
2.8
…
…
K
0
Initial
Number
of
packets
Pe1 = 0.5, Pe2 = 0.6 (Simulation)
2.6
Gain
Pe1
Pe2
Pe1 = 0.2, Pe2 = 0.4 (Simulation)
2.4
Pe1 = 0, Pe2 = 1
2.2
Pe1 = 0, Pe2 = 0
•Fixed number of nodes
•Overhearing reduces gain,
but reduces completion time
2
1.8
•Gain increases in presence
of erasures
1.6
1.4
1.2
1
2
4
6
8
Number of Packets (M)
10
12
Network Coding and Reliable
Communications Group
Broadcast
N( M , M ,..., M )
dofs to decode: iM
N Rx N
M packets
iN
i1
i2
i2 Rx 2
dofs to decode: M
Tx
Rx 1
N(i1 ,i2 ,...,iN )
i1
dofs to decode: M
•Challenges:
•Optimal scheme: (M+1)N-1 variables to optimize
N(i1 ,i2 ,...,iN ) , i1 , i2 ,..., iN
•Viable scheme: Reduce to M variables
Ni , where i  max(i1 , i2 ,..., iN )
•Developed heuristics to determine Ni
[NetCod’09, GLOBECOM’09]
Network Coding and Reliable
Communications Group
Mean Completion Time (s)
(a)
Completion Time: Broadcast
Broadcast TDD Optimal
Broadcast TDD Worst Link Channel
Broadcast TDD Combined Erasure Effect
0.6
0.5
Pe  max Pei
0.4
i
Number of Coded Packets
(b)
0.3
10
2
10
10
Worst Link Heuristic:
•Compute Ni’s for link
-3
10
-2
10
-1
Broadcast TDD Optimal
Broadcast TDD Worst Link Channel
Broadcast TDD Combined Erasure Effect
Pe  1 
1 P 
ei
i
N5
1
N1
0
10 -3
10
Combined Erasure:
•Compute Ni’s for link
-2
-1
10
10
Packet Erasure Probability
Worst Link Heuristic:
Performs close to
optimal
Network Coding and Reliable
Communications Group
Comparison Schemes: Broadcast
Full Duplex Broadcast using Round Robin:
Tx
i-th
1 2 3 …M 1 2 3
Channel
Rxi
1
3
M
3
ACK
TDD Broadcast using Round Robin:
Tx
1 2 3
i-th
Channel
Rxi
9
M
ACK
Network Coding and Reliable
Communications Group
Completion Time: Broadcast
•Outperforms TDD
constrained Round
Robin broadcast scheme
(optimal, no coding)
1
Optimal Broadcast with Network Coding TDD
Broadcast Round-Robin (RR) TDD
Broadcast RR Full Duplex (Upper Bound)
Broadcast RR Full Duplex (Lower Bound)
Mean Completion Time (s)
0.9
0.8
0.7
0.8dB @ Pe = 0.8
•For high erasure
probability:
Outperforms
full duplex
Round Robin broadcast
0.6
0.5
0.4
0.3
10
-3
-2
-1
10
10
Packet Erasure Probability
10
0
Pe > 0.3
better than
RR full duplex
Network Coding and Reliable
Communications Group
Sharing information in TDD:
[Allerton’09]
all-to-all broadcast
Node 1
M1 packets
Node N
MN packets
Node 3
M3 packets
Node 2
M2 packets
•Setup:
•Broadcast assumption
•Round robin assignment of channel
•Completion time: Mi original packets of each node i
are successfully transmitted to all N-1 nodes and
receive ACK
Network Coding and Reliable
Communications Group
Description of the scheme
• # of variables: large
• Structure:
– Round robin assignment of Tx: Periodicity
– Node “sees” the system as a broadcast problem with
round trip time variable, depends on initial state
• Algorithm exploits this structure:
– Computes #of coded packets to transmit for broadcast
(using heuristics) from each node
– Couples the effect of other nodes through the average
round trip time
– Converges in a small number of iterations
Network Coding and Reliable
Communications Group
Mean Completion Time
• M1 = M2 = M
TDD Network Coding
Full Duplex Network Coding
Full Duplex Scheduling (Lower Bound)
• At high Pe:
Full Duplex Scheduling (Upper Bound)
2.4
2.2
Mean Completion Time (s)
2
– better than no
coding with a full
duplex channel
– ~3dB more than
network coding full
duplex
TDD Scheduling (Upper Bound)
TDD Scheduling (Lower Bound)
1.8
1.6
1.4
TDD Scheduling
1.2
1
Full Duplex
Scheduling
0.8
0.6
0.4
10
-3
-2
-1
10
10
Packet Erasure Probability
10
0
• At moderate Pe:
1dB away from full
duplex
Network Coding and Reliable
Communications Group
Underwater Rateless Transmission
How to
perform
efficient
rateless
transmission?
Rate uncertainty
Channel
Joint work with:
Muriel Médard
Milica Stojanovic
Interference
Delay
Network Coding and Reliable
Communications Group
Underwater Rateless Transmission
• Underwater constraints
– Large propagation delay, e.g. 1.5 km  1 s
– High packet losses
– Transmission band
• Very limited, typically from ~0Hz to 100 kHz
• Bandwidth decreases as distance increases
• System design
– MAC model: hard to coordinate or perform power control
• ALOHA
– Use implicit ACK in network coding
• Gain information from state of nodes based on their
own coded packet transmissions
• Reduce power consumption of purely rateless scheme
Network Coding and Reliable
Communications Group
Numerical Results
• Node deployed in a square of 1x1 km2
• Schemes transmit power to reach receiver with some SNR
• Gaussian signaling
90
~11 dB
Transmission Power ( dB re 1  Pa)
R  2 kbps
~3 dB
80
R  1 kbps
R  0.2 kbps
70
[WUWNET’07,
ISITA’08,
JSAC’08]
R = 2 kbps
R = 1 kbps
60
Network Coding with Implicit ACK
Routing link-by-link ACK
R = 0.2 kbps
4
6
8
10
Number of Nodes
12
14
16
Network Coding and Reliable
Communications Group
Coding for Data Dissemination
Which
transmissions
have greatest
impact?
Rate uncertainty
Channel
Joint work with:
Muriel Médard
Milica Stojanovic
Frank H. P. Fitzek
Interference
Delay
Network Coding and Reliable
Communications Group
Sharing information in Half-Duplex
[RAWNET’09]
Channels
•Setup:
•Optimal scheme
•Involves choosing the sequence of transmissions
•Hard problem
•Proposed a greedy algorithm
•Chooses hyperarcs that maximize impact at each slot
•Impact: Avg. # of nodes that benefit from
transmission
•Breaks ties in favor of transmissions that disseminate
information to nodes with small # degrees of
freedom
Network Coding and Reliable
Communications Group
Toy example
Progressive Base Station:
Slots
5M/2
2M
M
0
3M/2
M Data Packets
Greater Impact (Vanilla):
backward healing
forward dissemination
2M
3M/2
M/2
0M
M Data Packets
Network Coding and Reliable
Communications Group
Dissemination time gains: no losses
227
•Overhearing
of N = 2
20
186
•20 packets
nodes
16
5
14
12
4
10
Gain = ( 3(M-1) +  (K - 1)/N  ) / ( M  (K-1)/N  )
Max Gain = (1/3)  (K-1)/N 
83
6
42
2
010
Gain = ( 3(M-1) +  (K - 1)/N  ) / ( M  (K-1)/N  )
Max Gain = M
200 3000 4000
400 5000 6000
600 7000 8000
800 9000 10000
1000
1000 2000
Number
(M)
NumberofofPackets
Nodes (K)