Transcript Information Theory for Mobile Ad-Hoc Networks (ITMANET): The FLoWS Project Thrust 1

Information Theory for Mobile Ad-Hoc Networks (ITMANET):
The FLoWS Project
Thrust 1
ACHIEVEMENT DESCRIPTION
• “bits” as the universal
measure of information and
interface to physical layer:
a homogenous view.
• High priority control
messages are sent over
separated channels.
• No performance limits on
UEP
MAIN RESULT:
• Optimizing the overall resource, the reliability of
control signals has a threshold effect;
• Communicating at capacity, not even a single bit
can be protected with positive exponent;
• Message-wise prioritization yields better tradeoffs
than bit-pipe partitioning.
HOW IT WORKS:
END-OF-PHASE GOAL
STATUS QUO
Unequal Error Protection: Application and Performance
Limits
S. Borade, B. Nakiboglu, L. Zheng
• Complete UEP
tradeoff with
geometric approach
• Data driven
network controls,
Layering and QoS
as interface
NEW INSIGHTS
• Protecting special message is much easier than
special bit;
• Joint coding allows
flexible resource allocation;
• Priority of critical data in
the form/costs of better
error protections;
• Global optimization of
resource allocation among
heterogeneous data;
• With feedbacks, a two-phase scheme can be
used, where critical message is used to initiate
retransmissions;
Better tradeoff in UEP
has significant effects
on overall system
performance
COMMUNITY CHALLENGE
• Perfect reliability
assumed on network
controls
New interface to the
physical layer leads to
more flexible higher
layer functionalities,
and system level
optimizations; the new
interface also needs to
be backward
compatible to bit based
networks
Embedding control messages/significant data with UEP
Towards Strong Converses for MANETs: Moulin
[UPPER BOUNDS]
There remains a gap between inner
(achievable) and outer rate regions.
MAIN ACHIEVEMENT:
Derived capacity region for multiple-access
Gelfand-Pinsker channel. The GP channel models
transmission in the presence of known interference
The approach could potentially
be extended to the broadcast
channel and possibly to
complex networks
IMPACT
STATUS QUO
The conventional approach used for
deriving (weak) converses, based on
Fano’s inequality, is insufficient.
•First item planned. Extend
approach to degraded broadcast
channel.
•Second item planned. Extend
approach to more complex
networks.
NEW INSIGHTS
• This has been verified for a few
problems (Verdu’s information
spectrum, and Moulin’s fingerprinting
problem)
•For MACs, the strong converse
with maximum-error criterion
seems to be more tractable than
average-error criterion
•Some creativity is needed to
guess a suitable reference
distribution over output space
• A set of typical channel outputs is defined.
• A sphere packing analysis is conducted to bound
the number of codewords that can be packed
based on the requirement that the error probability
is small for exponentially many codewords.
• The approach is based on elementary statistics of
the
difference
between
empirical
mutual
informations (aka “self-informations” of codewords,
or “information densities”)
ASSUMPTIONS AND LIMITATIONS:
• Memoryless channel, but this is not a fundamental
limitation of the approach
NEXT-PHASE GOALS
HOW IT WORKS:
Extend this technique to more
general networks
New tools are needed to derive tighter outer bounds on capacity regions
Information Theory for Mobile Ad-Hoc Networks (ITMANET):
The FLoWS Project
Thrust 2
Indecomposable Finite-State Channels With Feedback
Ron Dabora and Andrea Goldsmith
•Many practical communication
channels are represented as
inhomogeneous indecomposable
FSCs
•When feedback is present, the
capacity of indecomposable
channels does not achieve the
maximum over all states.
Finite-State Channel
Yi-1
Tx
Xi
p(yi,si|xi,si-1)
Si-1
D
Yi
Si
Rx
IMPACT
STATUS QUO
ACHIEVEMENT DESCRIPTION
MAIN ACHIEVEMENT:
We identified classes of practical channels that
can be modeled as indecomposable FSCs. We
showed that their capacity with feedback is equal
to the maximum over all channel states.
Capacity of indecomposable
FSCs with feedback can be
found without searching over all
channels states
Coding schemes that incorporate
Tx-Rx synchronization into the
code can achieve the maximum
over all states for certain
indecomposable channels
Identify classes of
inhomogeneous
indecomposable FSCs for
which feedback achieves the
maximum over all initial
states
HOW IT WORKS:
We identified classes of practical channels that
can be modeled as indecomposable FSCs. We
showed that their capacity with feedback is equal
to the maximum over all channel states.
ASSUMPTIONS AND LIMITATIONS:
• The previous state contains all the past
information. The current output and state
depends on both the current input and previous
state.
NEXT-PHASE GOALS
NEW INSIGHTS
Introduce the notion of “weakly
indecomposable” FSCs, i.e.,
FSC that are indecomposable
only without feedback
Understand how to combine
code synchronization into the
design of communication
networks with Markov
dynamics
•Extension to multiuser channels
with feedback
•Translation of the results
obtained for the discrete channel
to Gaussian channels with ISI and
feedback
Most communication channels are subject to correlated time variations
Mutual information and estimation in channels
of exponential family type: Coleman and Raginsky
MAIN ACHIEVEMENT:
Analysis of dependence of mutual information on
channel quality reduces to an estimation-theoretic
problem with distortion function r(x,y)
How does channel quality
impact performance?
• Need to explicitly assume channel
family is ordered by degradation
IMPACT
STATUS QUO
ACHIEVEMENT DESCRIPTION
• Need to check appropriate
conditions on case-by-case basis
New results on mutual
information and estimation
beyond the AWGN channel and
squared error criterion.
Many channels have this
exponential family structure.
Can connect information theory to
estimation theory and statistics.
• Exploit maximum entropy
character of exponential families
• Instead of degradation, exploit the
b-monotonicity of information gain
NEXT-PHASE GOALS
NEW INSIGHTS
HOW IT WORKS:
Structure of E-type channels leads to a dual
estimation-theoretic characterization of mutual
information as the minimum rate needed to
describe the channel output with a given
constraint on E[r(X,Y)]
We can leverage this duality to prove
monotonicity of I(X;Y) w.r.t. b under an additional
(reasonable) assumption on the behavior of
posterior estimators
ASSUMPTIONS AND LIMITATIONS:
• For a general E-type channel, can prove
montonicity of mutual info only in high-SNR (highb) regime
New results on broadcast and
secrecy capacity without
relying on explicit degradation
assumptions.
Explore connections
between information theory
and statistics of E-type
channels to obtain new
performance results in the
network setting.
New insights into information/estimation lead to robust design principles for MANETs.
Dynamics and Control Principles for Feedback Encoder Designs
Coleman
ACHIEVEMENT DESCRIPTION
The use of feedback is of the utmost
importance in designing scalable, robust,
reliable communication schemes
Stochastic Control and Lyapunov theory
combined with converse theorems provide a
canonical methodology to design low-complexity
iterative encoders with feedback in MANETs that
achieve capacity
Design principles for provably good
iterative feedback encoders (essentially)
limited to Gaussian scenarios
101
IMPACT
STATUS QUO
MAIN RESULT:
111
• Provides explict capacityachieving recursvie encoders for
degraded broadcast channels
• Can be extended to many
networks with tight converses
HOW IT WORKS:
•Converse to coding theorems with
feedback directly guides us how
encoders should operate
•StateXn of the system is posterior
distribution on message given
Y1 …. Yn
•Feedback encoder should be
interpreted as a controller, trying
to drive state to certainty.
•Formulate a stochastic control
problem and find optimal policy
•Converse theorems specify a stochastic control problem.
An optimal policy implies the existence of a Lyapunov
function
•The KL divergence acts as a Lyapunov function on the
state of the system
•This directly implies achievabililty of all rates in capacity
region with this explicit iterative encoding scheme
ASSUMPTIONS AND LIMITATIONS:
•Noiseless feedback
•Memoryless Channels
NEXT-PHASE GOALS
NEW INSIGHTS
101
111
Use Stochastic Control
methodology for a principled,
canonical approach to address::
• noisy feedback (POMDP)
•Unknown channel (Q-learning)
• Delayed feedback
A Canonical Controls Methodology to Design Iterative Feedback Coding Systems in MANETs
Optimal ARQ Protocol For Multihop MIMO Relay Networks
Yao Xie, Deniz Gunduz, Andrea Goldsmith
MAIN RESULTS
diversity
3D DMDT Surfaces for Various ARQ protocols ((4,1,3) system)
What is the rate-reliabilitydelay tradeoff in multihop
MIMO relay network?
Fractional Variable ARQ
Block Variable ARQ
DMDT of (4,1,3) multi-hop relay channel
2.5
d(r)
2
3
1.5
1
2.5
2.5
0.5
2
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
d(r,L)
x
1.5
L=1
1.5
DMDT of (4,1,3) multi-hop relay channel, L = 10
3
1
1
Fractional Variable ARQ
Block Variable ARQ
2.5
0.5
0.5
•Diversity-multiplexing tradeoff
(DMT) analysis for relay channel
•Diversity-multiplexing-delay tradeoff
(DMDT) for point-to-point MIMO with
ARQ
2
0
0
4
1
2
2
1
6
3
5
10
L
Block Variable ARQ
r
2
1.5
4
1
6
3
8
4
8
4
d(r)
2
0
0
5
0.5
IMPACT
3
2
There are
Fractional variable
DMDT of (4,1,3) multi-hop relay channel, L = 2
3
DMDT of (4,1,3) multi-hop relay channel, Block Variable ARQ
d(r,L)
STATUS QUO
ACHIEVEMENT DESCRIPTION
rate
Block variable
10
L
r
0
Fractional Variable ARQ
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
x
Found optimal ARQ protocol in
multihop MIMO relay networks.
L = 10
(2,2,2) system
DMT of (2,2,2) multi-hop relay channel, long-term static, L = 4
4
Fractional Variable ARQ
Fixed ARQ, L1 = L2 = L/2
3.5
Long-term
Fixed ARQ, optimal L1 L2
Block Variable ARQ
d22(r)
3
d(r)
2.5
2
1.5
1
Characterized DMDT surfaces
provide insights for practical
optimal ARQ protocols design.
0.5
DMT of (2,2,2) multi-hop relay channel, L = 4
1
2
3
4
r
8
5
6
7
8
Short-Term Static Channel
Long-Term Static Channel
Short-term
7
H1
6
ARQ 2
H2
d(r)
ARQ 1
How it works: ARQ protocols
4
3
2
in ARQ MIMO relay networks
NEW INSIGHTS
5
• We characterize the diversitymultiplexing-delay tradeoff
(DMDT) surface for various ARQ
protocols
1
0
0
1
2
3
4
5
6
7
8
r
ASSUMPTIONS AND LIMITATIONS:
• Long-term/short-term static channel
• Total number of ARQ rounds is L
•Theorem: the fractional variable
ARQ protocol achieves optimal
DMDT
• Decode-and-forward relaying strategy
“Relay should talk ASAP”
solved using convex optimization
• Channel state information at Rx, Rayleigh Fading
• Special cases: closed form DMDT; general case: DMDT
diversity
NEXT-PHASE GOALS
0
9 0
Optimal
Operational
Point
rate
• Optimal ARQ protocol for general
relay network
• Effects of power control
• Joint source-channel coding in
MIMO relay network
ARQ provides one more dimension of tradeoff in MIMO relay networks.
Exact capacity regions
are hard to obtain even
with three nodes.
MAIN RESULT:
Random codes are
capacity achieving for
many models.
Decode-and-forward
relaying used in most
practical systems.
END-OF-PHASE GOAL
FLOWS & NEQUIT ACHIEVEMENT
• Consider inter and/or
intra cluster reception
• Combine structured
and random codes
• Characterize nonsymmetric achievable
rate points
MODEL:
Joint source-channel
coding techniques to
achieve higher rates
Clusters of users: Each user in a cluster
wants messages of all other users in the
same cluster.
Communication is enabled by the relay.
ASSUMPTIONS AND LIMITATIONS:
No signal received from other users
Structured codes might
provide higher rates
than random coding in
some networks
Symmetric capacity for a symmetric system
is analyzed
* Achievable symmetric rate is characterized
and compared to the upper bound
COMMUNITY CHALLENGE
STATUS QUO
NEW INSIGHTS
The Multi-Way Relay Channel
Deniz Gündüz, Aylin Yener, Andrea Goldsmith and Vincent Poor
- Can we scale
structured codes to
multiple users?
- Design of practical
codes based on joint
source-channel coding
techniques
Compress-and-forward relaying achieves symmetric rates within a constant gap of
capacity. This gap decays with increasing number of users.
Random Linear Network Coding for Time Division
Duplexing (TDD)
Lucani, Médard, Stojanovic
•TDD has used ARQ/FEC schemes
1. Use feedback to improve
delay performance: ACK states
required number of coded
packets to decode data
2. Transmit coded packets for
some time, stop to wait for
ACK
Transmit Time
Wait Time ACK Transmit Time
3. Transmission time
depends on ACK and channel
conditions: Exists optimal
choice
1. Delay and Energy Analysis for Link and
Broadcast cases
IMPACT
Network
MAIN RESULTS: Novel network coding
scheme for TDD channels
2. Exists optimal transmission time in terms of
minimizing block delay, with close-to-optimal
energy performance.
3. Outperforms Selective Repeat schemes in high
latency- high error 4 x 10
scenarios.
3.5
R = 10 Mbps
Similar performance
3
otherwise.
5
4. Delay/throughput
is close to
full duplex
network coding,
requiring
much less energy
R = 1 Mbps
2
1.5
•Novel network coding
strategy for TDD
•Use of feedback (ACK)
improves delay/energy/
throughput performance,
especially for high latencyhigh errors scenarios
•Random linear coding allows
extension to networks
2.5
 (bps)
•Network coding has studied
throughput or delay performance
considering minimal feedback
GBN Window = 10
SR Window = 10
Network Coding TDD Optimal M = 10
1
0.5
R = 0.1 Mbps
HOW IT WORKS:
0 -5
10
-4
10
-3
-2
10
10
Packet Erasure Probability
-1
10
1. Transmission time computed to minimize delay in
data block transmissions, using ACK and channel
conditions
2. Stop transmission to wait for ACK from receiver (s).
ACK used to update transmission time
ASSUMPTIONS AND LIMITATIONS:
Random linear coding, prior knowledge/estimate of
propagation delay and errors
0
10
NEXT-PHASE GOALS
NEW INSIGHTS
STATUS QUO
ACHIEVEMENT DESCRIPTION
Cluster
•Extend broadcast: effect of
clusters of cooperative nodes
•Sensitivity analysis
•Extend to general network
scenario
Feedback, coding and optimal choice of transmission time minimizes delay, while
keeping throughput performance similar or better than typical TDD ARQ schemes
Layered Source-Channel Schemes: A Distortion-Diversity
Perspective: Medard, Zheng
ACHIEVEMENT DESCRIPTION
Laptop 1
Three-layer
Laptop 2
PDA 2
HOW IT WORKS:
ib1
...010111100...
...101011011...
• Diversity can be achieved through
source coding techniques, like
multiple description codes
• We characterize source-channel
schemes with distortion-diversity
tradeoff
s
Multiple
Description
with
Common
Refinement
ir
ib 2
1-D Channel
Encoder
(SNR)
1-D Channel
Encoder
(SNR)
xb1
2-D Channel
Encoder
(SNR1-b )
+
x1
Channel 1
xr1
xr 2
iˆb1 or iˆb 2
y1
Joint SourceChannel
Decoder
+
xb 2 x2
iˆb1 , iˆb 2
Channel 2
y2
iˆb1 , iˆb 2 , and iˆr
5/6
7/9
1/ 3
 partial
1
• Multi-description source code with a common
refinement component
• Superposition coding with successive
interference cancellation
• Joint source-channel decoding exploits source
code correlation
•Diversity is usually achieved in the
channel coding component
Multi-description
Multi-resolution
IMPACT
PDA 1
A three-layer source-channel scheme, which
includes previous multi-resolution-based and
multi-description-based schemes as special
cases
•Conventional source-channel
scheme achieves a single level of
reconstruction
NEW INSIGHTS
 refine ,  full
MAIN ACHIEVEMENT:
4/3
• Three-layer scheme dominates
previous double-layer schemes
• Distortion-diversity tradeoff
provides useful comparison in
different operating regions
sˆpartial
sˆfull
sˆrefine
ASSUMPTIONS AND LIMITATIONS:
• Quasi-static block-fading channel
• Receivers have perfect channel state information,
but the transmitter only has statistical knowledge
of the channel
NEXT-PHASE GOALS
STATUS QUO
Source (Image)
...010011100...
PDA 1
Laptop 1
PDA 2
Laptop 2
•Extend multi-description-based
source-channel scheme while
preserving the interface between
source and channel coding
•More general channel model
Distortion-diversity tradeoff better characterizes layered source-channel schemes
The Capacity Region of the Cognitive Z-interference Channel
with a Noiseless Non-cognitive Link
Nan Liu, Ivana Marić, Andrea Goldsmith and Shlomo Shamai
IT channel models suitable for
networks with cognitive users still
need to be proposed.
Capacity of Z-interference channel
is still unknown.
W1
W1
source 1
dest1
W2
source 2
W2
dest2
Z-interference channel
In some scenarios, interference
can be minimized by exploiting
the structure of interference and
cognition at the nodes. Cognition
should be used by the encoder
to precode against part of the
interference caused to its
receiver.
MAIN ACHIEVEMENT:
1) The capacity region of the discrete
cognitive Z- interference channel with a
noiseless non-cognitive link
2) An inner and outer bound for the
cognitive Z-interference channel
3) Solution to the generalized Gel’fandPinsker (GP) problem in which a transmitterreceiver pair communicates in the presence
of interference non causally known to the
encoder. Our solution determines the
optimum structure of interference.
HOW IT WORKS:
Non-cognitive encoder uses superposition
coding to enable partial decoding of
interference. The cognitive encoder precodes
against the rest of interference using GP
encoding.
ASSUMPTIONS AND LIMITATIONS:
• The considered channel model:
W1, W 2
cognitive
encoder
W2
non-cognitive
encoder
W1
dest1
W2
dest2
IMPACT
Capacity of networks with
cognitive users are unknown.
Consequently, optimal ways how
to operate such networks are not
understood, nor it is clear how
cognitive nodes should exploit the
obtained information.
1) Optimal scheme for some
channels
2) Superposition coding and
Gel’fand-Pinsker coding
may be required in order to
minimize interference, in
some channels. This is in
contrast to the Gaussian
channel.
3) For the GP problem, the
optimal interference has a
superposition structure
NEXT-PHASE GOALS
NEW INSIGHTS
STATUS QUO
ACHIEVEMENT DESCRIPTION
• Evaluate a numerical example
• Apply proposed encoding
scheme to larger networks and
to different cognitive node
models
Encoding scheme was proposed that exploits cognition and is optimal in certain scenarios
Information Theory for Mobile Ad-Hoc Networks (ITMANET):
The FLoWS Project
Thrusts 1&2
Capacity of networks are still
unknown; one of the key
obstacles: how to handle and
exploit interference?
NEW INSIGHTS
How to relay for multiple sources?
Traditional approach: routing
ACHIEVEMENT DESCRIPTION
MAIN ACHIEVEMENT:
1) Achievable rate region for the interference
channel with a relay channel
2) Strong interference conditions under which
forwarding messages and interference
achieves capacity
3) A new sum-rate outer bound to the
performance
HOW IT WORKS:
The relay forwards an unwanted message,
thus increasing the interference at the
receiver. This allows the receiver to decode
and cancel the interference.
For the outer bound: a genie enables receiver
to decode both messages
ASSUMPTIONS AND LIMITATIONS:
• The considered channel model: the interference
channel with a relay
In networks with multiple
sources, relays can help beyond
forwarding useful information, by
increasing interference at the
receivers. This allows receivers
to decode the interference and
cancel it prior to decoding their
desired messages
source 1
source 2
dest1
relay
dest2
• Simple encoding schemes investigated
1) Interference forwarding can
increase rates
IMPACT
Several relaying strategies for
forwarding information to a single
receiver exist
2) A tighter outer bound
NEXT-PHASE GOALS
STATUS QUO
Relaying for Multiple Communicating Pairs
Ivana Marić, Ron Dabora and Andrea Goldsmith
•Consider interference
forwarding in combination with
other encoding strategies
• Apply interference forwarding
and the outer bound to larger
networks
A relaying strategy for networks with multiple sources that can improve rates and achieve capacity
in certain scenarios proposed. A tighter sum-rate bound on the performance developed.
Cooperation and cognition in MIMO cognitive networks
Ying Chang and Andrea Goldsmith
ACHIEVEMENT DESCRIPTION
MAIN ACHIEVEMENT:
Single-primary-user
cognitive network
Pp=5
7
3.4
IMPACT
SVD
P-SVD
D-SVD
6
3.6
5
3.2
Rs
3
3
2.8
2.6
2
2.4
1
• In literature, achievable rates of
single-antenna secondary user is
well studied
• How to do cooperation and
cognition with multiple antennas and
multiple primary users is our main
focus
2.2
2
0.4
0
0
0.6
0.8
1
1.2
Rp
1.4
1.6
1.8
2
4
6
8
10
Ps
2
12
14
16
18
20
• We propose practical
strategies for cognition and
cooperation in MIMO systems
1.3
1.2
MISO , single primary user
1
SVD
P-SVD
D-SVD
0.8
5
0.7
4
0.6
0.5
3
0
0
2
4
6
16
18
20
HOW IT WORKS:
Secondary user has non causal knowledge of primary
users’ transmission and performs cognition together with
cooperation to compensate the interference to primary
receiver.
We study the cases with MISO and MIMO secondary
transmission system and multiple primary receivers.
ASSUMPTIONS AND LIMITATIONS:
•
Primary users’ transmission rate is unchanged
0.8
Rp1
1
1.2
1.4
• Study multiple primary receivers
with multiple antennas
• Information theoretical bounds on
MIMO cognitive networks
7
SVD
P-SVD
D-SVD
SVD
P-SVD
D-SVD
6
Interestingly, we find out the
relation between the primary
users’ sum rate and cognitive
user’s transmission rate is not
monotonic.
Pp=15
Pp=5
6
5
5
4
4
3
3
2
• Direct Channel SVD (D-SVD)
0.14
2
1
0.13
1
0
0
The precoding matrix is obtained from the SVD of the cognitive
user’s channel
1.6
When the capacity region of
the primary broadcast channel
is achieved, the transmission
rate for the cognitive user is
as follows:
7
In this case, we have a MIMO cognitive transmission pair. We
propose two sub-optimal transmission strategies for the
cognitive user:
• Projected Channel SVD (P-SVD)
3.8
0.6
In MIMO networks, we are more flexible to deal with interference
2
4
6
8
10
Ps
12
14
16
18
20
0.12
0
0
2
4
6
8
10
Ps
12
14
16
18
20
0.11
0.1
Pp=15
Pp=5
7
7
SVD
P-SVD
D-SVD
SVD
P-SVD
D-SVD
0.09
6
6
4
0.4
To maintain the capacity
region of primary users, the
cognitive user cooperate with
each primary receiver. Power
allocation scheme is
developed for MISO and
MIMO cognitive user.
Rs
In this case, we have a MISO cognitive
transmission pair. We propose an optimal
transmission strategy for the cognitive user
which projects its beamforming vector onto
orthogonal and aligned channel components.
The relation between the primary user’s rate
and cognitive user’s rate is as follows:
14
0.2
Single primary user
MIMO cognitive user
MISO cognitive user
12
NEXT-PHASE GOALS
NEW INSIGHTS
Encoding rule for the cognitive
user: The cognitive encoder acts in
two stages. For every message pair
(mp, mc), the cognitive encoder first
generates a codeword for the
primary message mp. In the second
stage, the cognitive encoder
generates a codeword for mc using
Costa pre-coding. The two
codewords are superimposed to
form the cognitive codeword.
• Decompose the MIMO
channel into orthogonal
components and leverage
secondary user’s
beneficial and
deteriorative impact to the
primary user.
• Introduce cooperation to
broadcast system
10
Ps
MIMO
MISO
multiple primary users
8
0
• We find the relation between
secondary user’s achievable
rate and primary user’s power
allocation scheme
1
To not impact the transmission rate
of primary (licensed) user, the
cognitive user performs cooperation
to compensate the interference it
causes to the primary user.
0.9
6
2
How to utilize new
degrees of freedom
brought by MIMO
technique?
In this case, the primary
transmitter broadcasts to
several primary receivers.
1.1
Pp=5
7
Rs
We consider a MIMO cognitive
network as shown below. The
cognitive transmitter determines its
codeword as a function of the
messages mp and mc .
STATUS QUO
4
System model
Multi-primary-user
cognitive networks
• We derive the optimal
achievable rate for MISO
secondary users under
coexistence constraints
4
3.8
0.08
5
5
4
4
3
3
2
2
1
1
0.07
3.6
The cognitive user’s channel is projected onto the null space of
the channel between the cognitive transmitter and primary
receiver. Than SVD is performed on the projection.
3.4
Rs
3.2
3
2.8
2.6
2.4
2.2
2
0.4
0.6
0.8
1
1.2
Rp
1.4
1.6
1.8
2
Under different power constraint, the performances of the two
strategies are compared with the MIMO channel capacity.
0
0
2
4
6
8
10
Ps
12
14
16
18
20
0
0
0.06
0.05
0.04
2
4
6
8
10
Ps
12
14
16
18
20
1.3
1.4
1.5
1.6
Rps
1.7
1.8
1.9
2
On Networks with Side Information
A. Cohen, S. Avestimehr and M. Effros
X
ENC
DEC
Y
X
ENC
To large extent, our knowledge of
networks with side information is limited
to the model above. However, we are
interested in more complex networks:
MAIN ACHIEVEMENT:
• New inner and outer bounds were derived for
networks with side information.
• The bounds are tight
for several network
topologies.
IMPACT
STATUS QUO
ACHIEVEMENT DESCRIPTION
• Tight results for several families
of networks with side
information.
• A wider range of scenarios
where cut-set analysis applies.
• An interesting and fruitful
connection to successive
refinement of information.
HOW IT WORKS:
• Canonical source coding problems
can be used to derive bounds for
more complex networks.
• Network coding can play a key
role even in non-multicast
problems.
• The achievable schemes are used at the terminals
(sources and sinks), together with network coding.
• Successive refinement of both the source and side
information descriptions is used when there are
multiple sinks.
ASSUMPTIONS & LIMITATIONS:
• One source node; one helper.
• Bounds are not tight in general.
NEXT-PHASE GOALS
NEW INSIGHTS
• Converse results for the canonical problem are
generalized to multi-node networks.
Extend this methodology to
various source coding
problems.
• Derive new bounds and find
network topologies for which they
are tight.
• Different demand models(e.g.
distortion)
Strategies intended for small problems, joint with network codes, can solve complex networks
Feedback and Network Coding
Effros and Bakshi
STATUS QUO
ACHIEVEMENT DESCRIPTION
MAIN ACHIEVEMENT:
- Butterfly network
- Source coding with coded side information
- Multiterminal source coding
In today’s networks, bulk of
transmission from sources to sinks
• Remote sources have often lesser power
available than sinks
IMPACT
In several examples networks, the capacity with
feedback is strictly bigger than that without feedback
HOW IT WORKS:
• Feedback is studied mostly in the context of
channel knowledge, not source knowledge
Receiver sends back everything it knows to the
transmitter nodes.
Increase in capacity is
potentially unbounded.
Power consumption by remote
sources can be decreased by
employing feedback from the
central receivers.
e.g.
- Sum rate required is only H(X)
NEW INSIGHTS
ASSUMPTIONS AND LIMITATIONS:
Feedback increases the capacity
region.
• Feedback links are assumed to have infinite
capacity
• Sources nodes are assumed to have sufficient
processing power
By knowing what the receiver
already knows from other sources,
source nodes can avoid
unnecessary transmission.
Feedback increases the capacity of networks
NEXT-PHASE GOALS
- Encoder 2 knows X after the feedback.
Cost of feedback?.
• Feedback links may not always
be “free”
Multicast Capacity Region of a Large Wireless Network
Urs Niesen Piyush Gupta Devavrat Shah
MAIN ACHIEVEMENT:
Characterization of n  2 dim. multicast region
• Easily computable in terms of 2n `weighted cuts’
• Under Gaussian fading channel model
n
Very little known about multicast
capacity region of wireless
network of n nodes
n
• It is n  2 dimensional
• Lack of fundamental understanding
of co-operative relay schemes
IMPACT
STATUS QUO
ACHIEVEMENT
•Optimal two-layer network
co-operative scheme for any
traffic demand built on multihop and hierarchical scheme
•Geometry of capacity region:
it is nice and round
• Realize `tree’ network using co-operative relay
built on multi-hop and hierarchical (virtual MAC
and BC) depending upon channel characteristics
• Use this as multicast `tree’
Equivalence relation
• Wireless network = “treestructure”
• This decides optimal structure
for network-wide co-operation
Converse
• Establish tightness of 2n cuts, each of them
corresponds to a `node’ of tree
ASSUMPTIONS AND LIMITATIONS:
• Random node placement
NEXT-PHASE GOALS
NEW INSIGHTS
HOW IT WORKS:
Achievability
Multicast capacity scaling
• Arbitrary node placement
Complete characterization of multicast capacity region: separation of NET and PHY layer
Information Theory for Mobile Ad-Hoc Networks (ITMANET):
The FLoWS Project
Thrust 3
What is the state of the art and
MAIN RESULT:
what are its limitations?
Notes from Austin: MW routing inflexible,
and does not easily incorporate multiaccess capacity region in wireless.
Workload relaxation techniques:
Tremendous value for policy
synthesis based on dynamic hotspots in the network
Numerical findings: With many flows, the rate
region appears smooth even in a static
interference model
Impact: Network cut
is no longer a useful
concept
Infinite complexity leads to simple solution:
Dynamics of 720 queues
Half space relaxation
provides:
• Lower bound on
performance and
KEY NEW INSIGHTS:
• Extend to wireless? YES
Geometric picture is very
different. Interpretation: The
number of resources is infinite
• Structure of optimal solution
to relaxation is very simple,
even for very complex networks
• New application of relaxation:
Q-learning and TD-learning for
routing and power control
• Tools for policy synthesis
HOW IT WORKS:
Step 1: Estimate capacity region near estimated
allocation rate vector
Step 2: Construct ellipsoidal, and half-space
relaxations
Step 3: Optimal policy for relaxation, and
interpret for original network
END-OF-PHASE GOAL
ACHIEVEMENT DESCRIPTION
Can these techniques be
extended to wireless models?
NEW INSIGHTS
W. Chen & S. Meyn
COMMUNITY CHALLENGE
STATUS QUO
Relaxation Techniques for Net Opt
• Implementation –
Consensus algorithms &
Information distribution
• Adaptation –
Reinforcement learning
techniques
• Integration with Network
Coding projects: Code
around network hot-spots
• Un-consummated union
challenge: Integrate coding
and resource allocation
• Generally, solutions to
complex decision problems
should offer insight
Algorithms for dynamic routing: Visualization and Optimization
Stochastic resource allocation
Boyd and Akuiyibo
Current resource allocation
research focus on iterative
methods.
These automatically adapt to
changing data assuming they
are held constant.
MAIN RESULT:
Explicit optimal control laws for resource
allocation in a system with quadratic cost,
linear dynamics, and random linear
constraints.
Target value, x =6
IMPACT
STATUS QUO
ACHIEVEMENT DESCRIPTION
averaging input algorithm
Stochastic allocation
of competing network
resources i.e.,
bandwidth, power,
flow rates, etc.
Simple control laws
(linear coefficients can
be computed ahead of
time).
NEW INSIGHTS
optimal trajectory
Formulate as stochastic
control problem
•Resource limits are random
•Allocate resources based on
availability and system state
ASSUMPTIONS AND LIMITATIONS:
• Assumes that the first and second moments of
the resources are known
• Utility is quadratic; dynamics must be linear
NEXT-PHASE GOALS
greedy algorithm trajectory
Utility maximizing
estimation techniques
• Decentralized solutions
Optimal dynamic resource allocation with heterogeneous flows
A Distributed Newton Method for Network Optimization
Jadbabaie and Ozdaglar
MAIN ACHIEVEMENT:
• We developed a Newton method that solves network
optimization problems in a distributed manner.
All existing distributed optimization
methods rely on dual decomposition
and subgradient (first order)
algorithms
• We provide convergence and rate of convergence
guarantees for the proposed method.
• Simulation experiments on a series of randomly
generated graphs suggest superiority of the distributed
Newton method over dual subgradient methods.
IMPACT
STATUS QUO
ACHIEVEMENT DESCRIPTION
• These algorithms easy to distribute
• However, they can be quite slow to
converge limiting their use in rapidly
changing dynamic wireless networks.
HOW IT WORKS:
NEW INSIGHTS
• Constrained Newton method
• Dual Newton step found by solving a discrete Poisson
equation involving the graph Laplacian.
Combine Newton (second order)
methods with consensus policies to
distribute the computations
associated with the dual Newton step
• Using a consensus-based local averaging scheme, this
can be done using only local information.
ASSUMPTIONS AND LIMITATIONS:
• Solves minimum cost network flow problems
• Extension to network utility maximization
NEXT-PHASE GOALS
Significant performance
improvements with the
distributed Newton method
compared to standard
subgradient methods.
Second order methods for
distributed network
optimization
•Suggests an extensive research
agenda for the investigation of
these methods in decentralized
environments
Distributed Second Order Methods with Convergence Guarantees
Distributed Scheduling and Equilibrium Dynamics in Wireless Networks
with Correlated Fading Channels (Candogan, Menache, Ozdaglar, Parrilo)
STATUS QUO
FLOWS ACHIEVEMENT
• Game-theoretic analysis of a distributed approach to
scheduling that adapts to dynamically varying channel
conditions.
• Game-theoretic scheduling models allow
the flexibility to incorporate different user
objectives and arrive at an efficient
operating point in a distributed manner.
• Correlated channel states are more
realistic than existing models as they
incorporate joint fading effects.
• Simple convergent distributed dynamics and
equilibrium characterization.
• Efficiency loss analysis suggests that finer state
quantization can improve equilibrium performance.
IMPACT
Achievements
• Robust system design in the
presence of non-cooperative
users utilizing the desirable
properties of potential games.
How it works:
• Design incentives for the mobiles to project the game
onto an (exact) potential game with desirable properties
(such as convergence of simple dynamics)
Equilibrium
Combine tools from optimization
and game theory
$
$
NEW INSIGHTS
Example: Collision
Channel with two
users. The resulting
game is an ordinal
potential game with
two equilibria
• Improved bounds on equilibrium performance can be
obtained as a function of a technology related system
parameter.
(TX, I) & (I, TX)
Assumptions and limitations:
•Potential games allow establishing
existence and uniqueness of
equilibrium, and convergence of
simple distributed algorithms.
• Full correlation across individual channel state
processes.
• Fixed number of users and an uplink scenario.
NEXT-PHASE GOALS
$
Local components (buildings)
• Partial channel state correlation
• Projection of general games to
ordinal potential games
• Convergence of dynamics with
asynchronous updates
• Multi-hop network topologies
A potential game approach for distributed scheduling in wireless networks
A Game Theoretic Approach to Network Coding
Marden and Effros
STATUS QUO
ACHIEVEMENT DESCRIPTION
MAIN ACHIEVEMENT:
IMPACT
Introduced game theory as a distributed tractable
mechanism to obtain good network performance
Global Objective: Efficiently use
network using network coding
Approach: Centralized solutions.
(e.g., opportunistic coding) Fix paths,
use coding opportunities if available
Approach provides guarantees
independent of network
structure.
Guarantees existence of an
equilibrium that achieves a
system cost of at most 50%
higher than the optimal.
This offers an improvement over
opportunistic coding.
NEW INSIGHTS
• Model interactions as a non-cooperative game
- players (unicast flows)
- actions (available paths)
• Assign each player a “cost” function
• Analyze efficiency of equilibrium behavior
What about distributed solutions?
What if flows were allowed to select
path in response to local “cost”?
Goal: Let users create coding
opportunities to improve efficiency
ASSUMPTIONS AND LIMITATIONS:
• Limited form of network coding (reverse carpool)
• Players have knowledge of available paths
• Players equilibrate faster than network changes
NEXT-PHASE GOALS
HOW IT WORKS:
Understand the potential
of game theory in
network coding problems
Establish desirable distributed
learning algorithms with good
convergence rates
Extend game theoretic approach
to more general network coding
problems
Game theory is an applicable tool for distributed optimization in network coding
Oblivious equilibrium for stochastic games with concave utility
S. Adlakha, R. Johari, G. Weintraub, A. Goldsmith
In prior work, we developed a general
stochastic game model to tractably
capture interactions of many devices.
Our results provide a general
framework to study the interaction of
multiple devices.
Current state or
current action
Consider stochastic games per-period utility and state
dynamics that are increasing, concave, submodular.
Then in a large system, each node can find
approximately optimal policies by treating the state of
other nodes as constant.
IMPACT
Many cognitive radio models do not
account for reaction of other devices
to a single device’s action.
Current state or
current action
Next state
MAIN RESULT:
Utility
STATUS QUO
ACHIEVEMENT DESCRIPTION
Further, our results:
• unify existing models for which
such limits were known
• and provide simple exogeneous
conditions that can be checked to
ensure the main result holds
HOW IT WORKS:
# of other
devices with
given state
Under our assumptions, no single node is overly
influential )
we can replace other nodes’ states by their mean.
So the optimal policies decouple between nodes.
NEW INSIGHTS
State of other devices
ASSUMPTIONS AND LIMITATIONS:
Action of device i
In principle, tracking state of other
devices is complex.
We approximate state of other
devices via a mean field limit.
This result holds under much more general technical
assumptions than our early results on the problem.
A key modeling limitation, however, is that the limit
requires all nodes to interact with each other.
Thus the results apply only to dense networks.
NEXT-PHASE GOALS
State
State of device i
We will apply our results to a model
of interfering transmissions among
energy-constrained devices.
Our main goal is to develop a
related model that applies when a
single node interacts with a small
number of other nodes each
period.
Real environments are reactive and non-stationary;
this requires new game-theoretic models of interaction
Fluid limits for gossip processes
V. Manshadi and R. Johari
…
Gossip is a simple model for
communication between nodes:
at random times, each node contacts a
neighbor and relays its information.
Prior work has studied the time until all
nodes acquire the information.
Two versions of this model: a “micro”
model and a “macro” model.
…
IMPACT
MAIN RESULT:
…
STATUS QUO
ACHIEVEMENT DESCRIPTION
We consider a random graph model where each node
has d neighbors, and we consider a limit where the
number of nodes N approaches infinity.
We prove that the (random) sample path of the
micro model converges to the (deterministic) path
of the corresponding macro model.
Micro and macro models of gossip
processes have been
available for several decades.
Unifying these will allow us to
translate macro-level control
insights to micro-level system
designs.
HOW IT WORKS:
N(t)
“Micro”
Time t
Time t
The micro model tracks exactly which
nodes have the information.
The macro model is a mean field limit:
what fraction of nodes have learned
the information?
We connect these two models.
Nodes that
currently do not
have the info
We approximately characterize how
information flows in the micro model between
the sets of informed and uninformed nodes.
This approximation is exact as N ! infinity.
ASSUMPTIONS AND LIMITATIONS:
Our results currently only apply under specific
topological assumptions.
NEXT-PHASE GOALS
NEW INSIGHTS
N(t)
“Macro”
Nodes that
currently have
the info
Several goals:
(1) Extend fluid analysis to
include heterogeneous
random graphs.
(2) Get finer understanding of
behavior when initial number
of informed nodes is
constant as N ! infinity.
(3) Extend the model to include
link failures.
The simplicity of macroscopic models for information gossip
can be combined with the accuracy of microscopic stochastic models
Information Theory for Mobile Ad-Hoc Networks (ITMANET):
The FLoWS Project
Thrusts 1,2,&3
Queuing analysis for coded networks with feedback
J. Sundararajan, D. Shah, M. Médard, M. Mitzenmacher, J. Barros
Packets can be dropped from
queue only upon confirmation
of decoding
• This means the queue sizes will be
unnecessarily long
MAIN ACHIEVEMENT:
 Propose novel ACK mechanism that allows
nodes to manage queue occupancy effectively
• In particular, as load factor ρ
approaches capacity, queue grows
quadratically as a function of 1/(1- ρ)
2
1
k
N
 Characterize expected queue size at each node
HOW IT WORKS:
Consequences.
 Queue size now grows linearly
with 1/(1- ρ)
IMPACT
STATUS QUO
ACHIEVEMENT DESCRIPTION
Unseen
Decoded
p1 p2 p3 p4 p5 p6 p7 p8
1
1
1
1
1
Key insight.
λ x (Time for receiver’s
ACK to propagate from
source to node k)
λ
x
(Time between node (i-1) seeing pkt and node i seeing pkt)
Almost as if there is link-by-link feedback…
ASSUMPTIONS AND LIMITATIONS:
 Perfect and delay-free feedback used in analysis,
though not critical for the approach
 Field size assumed to be very large
NEXT-PHASE GOALS
NEW INSIGHTS
Coefficient vectors of
received linear
combinations, after
Gaussian elimination
Number of seen packets = Rank of matrix
 With drop-when-decoded, the
busy period of the virtual queue
contributes to the physical queue
size calculation
 Responding to ACK of the
degrees of freedom ensures only
queuing delay of virtual queues
contributes to physical queue size
0 0 0
0 0 0
-------------------
 Analysis also applies when only
some nodes do re-encoding
 ACK of degrees of freedom
allows traditional queuing
results to be applied easily in
scenarios with network coding
Acknowledge “seen” packets
Seen
 Reduces the amount of storage
needed at intermediate nodes
for performing re-encoding
Rx
Tx
Rx
Extend queue management
protocol to more general
(wireless) scenarios
• Multipath routing with coding
• Multicast traffic pattern
The proposed approach to queue management will play a key role in interfacing TCP with
network coding, especially when intermediate nodes re-encode
Scheduling for Network Coded Multicast
Medard, Traskov, Heindlmaier, Koetter
No systematic approach to
multi-access for network coding.
MAIN ACHIEVEMENT:
Hyperarc scheduling outperforms well-known
scheduling techniques.
IMPACT
STATUS QUO
ACHIEVEMENT DESCRIPTION
• Shows that the
performance of well-known
scheduling techniques is
very poor.
• Suggests a largely
improved bandwidth
efficiency.
• New notion of scheduling
conflicts, when network
coding is used.
NEW INSIGHTS
HOW IT WORKS:
• Valid network configurations can be identified as
stable sets in the conflict graph.
• Jointly solve subgraph selection and scheduling
problem.
• Graphical model for conflicts
between hyperarcs.
• Distributed algorithm.
ASSUMPTIONS AND LIMITATIONS:
• Do not try to minimize the
number of collisions per se.
• Convergence speed of algorithm.
• Scaling with the size of the network.
NEXT-PHASE GOALS
Current scheduling techniques use
the bandwidth very inefficiently.
• Extension to INTER-session
network coding.
• Investigations on
performance/complexity tradeoffs.
Scheduling matched to the network coding subgraph largely improves performance.
Interference-Mitigating Mobility Strategies in
MANETs: Naini and Moulin
ACHIEVEMENT DESCRIPTION
Identifying the two-fold role of
relays as:
MANETs : Focus has been
mainly on mutual interlinking
and cooperation of nodes
with randomized mobility in
the backdrop. Lack of results
on interference-mitigating
mobility strategies.
Derived optimal interference-mitigating strategies
for receiver node in a network with fixed relays
IMPACT
STATUS QUO
MAIN RESULT:
• being part of the sourcereceiver link
• conveying information about
interferer’s signal
Optimal mobility patterns
could be used to gain insight
into
• Optimal relay placement
• Positioning of nodes in
coexistent interfering
networks.
•Mobility should be seen as a
resource to actively avoid
interference from other nodes.
•Optimal mobility strategies can
be established for nodes in
noncooperative scenarios
• Saddle point strategies are feasible for the
receiver and interferer.
ASSUMPTIONS AND LIMITATIONS:
• Greedy mobility strategy is assumed
• Nodes know neighboring nodes location and
transmission power
• Surrogate capacity cost function is used
NEXT-PHASE GOALS
NEW INSIGHTS
• Cut-set bound on capacity used as the
cost-function.
Allow for relay mobility
Include multi-hop relaying
Extension to non-greedy and
multi-objective cost function.
Exploit mobility to dynamically enlarge capacity regions