Post on 22-Dec-2015
transcript
How to Turn on The Coding in MANETs
Chris Ng, Minkyu Kim, Muriel Medard,
Wonsik Kim, Una-May O’Reilly, Varun Aggarwal,
Chang Wook Ahn, Michelle Effros
DAWN Presentation at UCSCOctober 14, 2008
Introduction
Coding improves performance in networks: E.g., increased throughput, achieves multicast capacity.
However, coding may lead to increased costs: E.g., node complexity, computation overhead, coding delay.
We treat the amount of coding as a parameter to be optimized in the network:
I. MANET with network coding: we minimize the number of coding nodes while maintaining multicast capacity.
II. Packet erasure channel: we optimize packet coding parameters jointly with physical layer parameters under different delay metrics.
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Network Coding in MANETs
Network coding achieves multicast capacity.
Only need a small number of coding nodes in the network:
The other nodes only need to perform traditional routing.
Either z or w needs to code in the example.
Use a genetic algorithm (GA) approach to find the minimum set of coding nodes.
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Distributed GA Algorithm in MANETs
MANETs: Network topology given by
an acyclic hypergraph. Hyperarcs to model the
wireless broadcast medium. Potential packet loss.
Distributed algorithm: No central coordination in
MANETs. Algorithm exploits spatial and
temporal distribution. Genetic operations done
independently at local nodes.
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Distributed GA Algorithm
Fitness evaluation is done in three steps: 1) forward (source to sink); 2) backward (sinks to source); 3) fitness
calculation (at the source).6
Simulation Results: Number of Coding Nodes
Random topology: 10x10 square. Radius of connectivity: 3. Rate is the multicast
capacity. GA population size: 200.
Experiment results: Network coding is not
needed in most cases. Number of coding nodes
necessary is small. Location of coding nodes:
flexible.
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Temporal Distribution and Packet Losses
With temporal distribution: k = 5 subpopulations,
migration every 5 generations. Faster convergence, standard
deviation is significantly reduced.
Packet losses: Erasure rates: 1% to 5%. Algorithm finds the optimal
solution, but requires more generations.
Temporal distribution provides resilience to packet losses.
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Generations required to find the knownoptimal solution:
With packet erasures:
30 trials of algorithm
50 trials of algorithm
Minimizing Packet Coding Delay
Reliable communications over unreliable wireless channels.
Physical layer: channel coding. Erasure channel: coding across packets.
Fundamental tradeoff in coding. Long coding blocks are more effective in mitigating channel
variations. But introduce larger decoding delay.
End-to-end performance depends on parameters across networks layers:
Delay sensitivity, packet coding strategy, transmission SNR target, power allocation among users.
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End-to-end Performance Metrics
Physical layer link performance: Instantaneous rate and outage probability. Cannot resolve system-level design choices: Higher rate with
greater outage probability, or vice versa?
To optimize end-to-end performance, need to additionally consider:i. User decoding delay requirements.
ii. How and when the transmitter learns about the outage event.
iii. Retransmission or coding strategy that recovers the outage data loss.
Cross-layer model to jointly optimize packet level and physical layer parameters.
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Packet Erasure Channel
Packet erasure channel with delayed acknowledgment feedback.
In-order packet delivery; erasure probability q. ACK/NACK feedback after D time slots.
Linear packet coding: Transmitter may combine (encode) source packets to form a
coded packet. Coded packet is a linear combination of the source packets. Receiver knows the transmitter’s coding scheme.
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Packet Delay Cost Function
Inter-decoding times:
Delay cost function: Normalized p-norm of the expected inter-decoding times:
Larger p: more sensitive to delay between decoding times.
When p=1; expected completion time:
When p=∞; per-packet delay:
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Block-by-Block Packet Coding
Transmitter sends linearly independent coded packets. Over a block size of k packets until receives ACK.
Tradeoff between completion time and per-packet delay: Optimize block size k based on delay sensitivity p:
15Completion Time Completion Time
Per
-Pac
ket D
elay
Per
-Pac
ket D
elay
Wireless Erasure Channel
Fading wireless channel: With additive white Gaussian noise:
Packet erasure induced by small-scale channel fading.
Shadowing: G can be accurately estimated. Fading: F is a random variable; transmitter knows only its
distribution.
Transmission outage leads to packet erasure. Transmitter picks SNR target s. Outage/erasure probability: q = Pr{ realized SNR < s }.
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Wireless Packet Network
Multiuser wireless erasure channels:
M users in the network:
Transmission from each user interferes with one another.
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Optimal Transmit Power Allocation
Need to optimize power allocation among users. Transmit at maximum power is not necessarily optimal due to
interference. Power constraint for each user: Interference is treated as noise. Signal to interference-plus-noise ratio (SINR) at receiver i :
Outage probability: qi = Pr{ realized Si < target si }. Power allocation among the users are coupled in the outage
probability constraints on the SINRs:
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Cross-Layer Optimization
Minimize global cost function:
J(d) jointly convex in d1,…,dM. Convexity of J(d) penalizes overlong user delays.
Independent Rayleigh fading channels:
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Convex Optimization Problem
Minimizing the global cost function can be formulated as a convex optimization problem.
Transformation similar to the single-user channel optimization previously considered.
We assume The optimization
formulation is otherwise valid for all ranges of SINR.
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Convexity of the Feasibility Regions
In a wireless network (when interference is treated as noise), the feasible rate region is not convex.
However, the corresponding feasible delay region is convex. Delay performance metrics:
Allows joint optimization over physical layer and packet level parameters.21
Rate Region Delay Region
Conclusions
Coding improves performance, but may lead to increased overheads.
Optimize the “amount” coding in a network, performance metrics based on:
Multicast capacity, number of coding nodes. Different delay sensitivity of the user applications.
When to “turn on” coding: Can be identified through a spatially and temporally distributed
algorithm. May depend on other parameters such as feedback, and physical
layer operating conditions.
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