A Distributed Framework for Correlated Data Gathering in Sensor Networks Kevin Yuen, Ben Liang, Baochun Li IEEE Transactions on Vehicular Technology 2008.

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A Distributed Framework for Correlated Data Gathering in Sensor

Networks

Kevin Yuen, Ben Liang, Baochun Li

IEEE Transactions on Vehicular Technology 2008

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Outline

IntroductionProblem FormulationLocalized Slepian-Wolf CodingDistributed Solution: A Price-Based FrameworkImplementation IssuesPerformance Evaluation

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Introduction

Recent technological advances have enabled the production of low-cost sensors.

Usually sensors are densely deployed in sensor networks. (Overlapping sensing ranges)

Find a transmission structure to minimize total energy

This framework should be compatiblee.g. multi-sink, distributed solution, asynchronous network settings, sink mobility, duty schedules

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Problem Formulation

Model the WSN as a directed graph G=(V,E)V = Assign every node i with rate Transmission range and exists if Each link(i,j) has a weight represents the flow rate of link(i,j)

We can minimize the optimization objective by adjusting and

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Problem Formulation

Use rate distortion theory to analyze the problem

Let S be a spatially correlated random Gaussian vector

Σ𝑖𝑗=𝑊𝑑𝑖𝑗

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Problem Formulation

Goal : Minimize transmission energy

ConstraintsFlow Conservation

Channel Contention

Rate Admissibility

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Problem Formulation

The constraints and the correlated data-gathering problem can be modeled as an exponential-constraint linear programming formulation

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Localized Splepian-Wolf Coding

Disadvantages of the optimization formulationsDifficult to solveRequire global knowledge of the correlation structure

Use Slepian-Wolf coding to relax the rate admissibility constraints such that only local correlation information is required.Each sensor node i should encode its data at a rate equal to

the conditioned entropyConsider the data correlation with one-hop neighbors in

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Localized Splepian-Wolf Coding

Supports multiple sinks:a subset of sensors within the neighborhood of

sensor that are closer to sensor ’s sink

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Distributed Solution:A Price-Based

Framework

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Lagrangian Dualization(1/2)

Goal: allocate the limited capacity of the wireless shared medium

Price-based resource allocationEach wireless link is a basic resource unitA price can reflect the relation between the traffic load of

the link and its bandwidth capacity

Relax the channel contention constraints with Lagrangian dualization

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Lagrangian Dualization(2/2)

The weight of each link is equal to the sum of its energy and capacity cost.

energy capacity cost

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Subgradient Algorithm

An efficient iterative algorithm to solve the Lagrangian dual problem.

Solve the Lagrangian sub problem by finding the shortest path from each sensor node to its nearest sink node with current Lagrangian multiplier during each iteration

Update the Lagrangian multiplier

𝛽𝑖𝑗 [𝑘+1 ]

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Distributed Algorithm(1/2)

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Distributed Algorithm(2/2)

The algorithm requires 3 control packetsFlow rates of all links within the clusterPrices for all clusters that are inherent to itThe identities of other sensor nodes in its neighborhood

and their distance to destination sink node

90sensors,10sinks,Transmission rage=30m

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Asynchronous Network Model

Synchronous network modelEvery node simultaneously execute at every time instanceIt is expensive to synchronize local clocks across the

entire networkPartial-asynchronous network model

The time between consecutive updates is bounded by BAt time t, instead of the most recent information, a node

may receive a sequence of recent updatesCompute the average of the sequence of updates from

time to

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Implementation Issues

Primal RecoveryGuarantee to generate feasible primal solutionThe network must remain static

: step size : the weights of convex combination

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Implementation Issues

Capacity ReservationThe rate allocation generated by subgradient algorithm

often violate the channel contention constraintsGenerate feasible solutions by reserving a suitable

amount of capacity (e.g. 10%)

Handling Network DynamicsNodes retrieve up-to-date topology in their neighborhood

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Performance Evaluation

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Simulation Environments

Implement with C++Experiments are performed on the random

topology with 90 sensor nodes and 10 sink nodesTransmission range & interference range are 30mThe capacity of wireless shared medium is 150

bitsCorrelation parameter Per node distortion

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Converge Speed

Chose 10% as sink nodesThe algorithm is executed in synchronous

environment with 500 iterations

Primal Sub gradient

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Impact of Asynchronous Network Settings

• Run 500 iterations with different time bounds B = 1,5,10,25

• The convergence speed is associated with the time bound B.

Primal

Sub gradient

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Effect of Data Correlation

Compare the effect of data correlation between synchronous and independent environment.

D = 0.001, 0.01 and 0.1W = 0.9 to 0.9999

Implementation I : localImplementation II: global

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Adapta

tion to

Sin

k M

obility

Adaptation to Duty Schedules

Model duty schedules as a 2-state Markov chain and are state transition probabilitiesSet the simulation environment for 300s

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𝜶𝜷

=𝟓 𝜶+𝜷=𝟎 .𝟎𝟏