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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Review: Genetic Algorithm (GA) Approach and Centralized Algorithm

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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

Temporal Distribution

Age-mixed subpopulation management: Replaces worst k - 1 individuals.

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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

Optimization under Different Packet Delay Metrics

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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