Compressive Oversampling for Robust Data Transmission in Sensor Networks

Infocom 2010

Outline

• Introduction– Problem Formulation

• Compressive Sensing for Erasure Coding– Channel Coding Overview– Compressive Sensing Fundamentals– Handling Data Losses Compressively

• Evaluation Results• Conclusions

Introduction

• Data loss in wireless sensing applications is inevitable– Transmission medium impediments– Faulty sensors

• To cope with channel disturbances,– Retransmission

• Inefficient in many scenarios, e.g., acoustic links

– Forward error correction schemes (Reed-Solomon , LT , convolutional codes)• Computational complexity or bandwidth overhead

Introduction

• Why compressive sensing?– Reconstruction algorithms for compressively sampled

data exploit randomness • The stochastic nature of wireless link losses do not hamper

the performance of reconstruction algorithms at the decoder

• Proposed Compressive Sensing Erasure Coding (CSEC)– CSEC is achieved by nominal oversampling in an

incoherent measurement basis. • Cheaper than conventional erasure coding that is applied

over the entire data set from scratch.

Introduction

• CSEC is not intended as a replacement for traditional physical layer channel codes

• It is neither as general-purpose– It cannot be used for arbitrary non-sparse data

• Nor is the decoding as computationally efficient

Conventional and Proposed Approaches

Compressive Sensing for Erasure Coding

• The problem is to address is acquiring a length n signal vector f at a sensor node and communicating a length k measurement vector z such that f can be recovered accurately at a base station one or more wireless hops away

Channel Coding Overview

• Consider a simple sense-and-send scenario where we send the sensed signal to a base station over an unreliable communication channel, and

• Channel coding increases the average transmission rate by adding redundancy

nf R

z f k n

k n

, k nz f R

Channel Coding Overview

• Define the received measurement vector of length , where is the number of erasures

• Recovering the original signal from the received data is then a decoding operation of the form :

zk k e e

1

ˆ

T T

f C z

z Cz

X X X X

Compressive Sensing Fundamentals

• Compressive Sensing– is original signal– is K-sparse under – ,

measurement matrix – Reconstruct signal by linear program

Nx R

, x S S N N

M Ny x S My R

1ˆ arg min s.t.

NS R

S S y S

Handling Data Losses Compressively

• We argue that compressive sensing not only concentrates but also spreads information across the m measurements acquired

• Based on this observation, we propose an efficient strategy for improving the robustness of data transmissions– the sensing matrix Φ with e additional rows

generated in the same way as the first m rows

Handling Data Losses Compressively

• These extra rows constitute extra measurements, which, under channel erasures will ensure that sufficient information is available at the receiver

• If incoherent measurements are acquired through “compressive oversampling” and e erasures occur in the channel

• The CS recovery performance will equal that of the original sensing matrix with a pristine channel with high probability

k m e

Evaluation Results

• Realistic wireless channels exhibit bursty behavior• To estimate the effect of CSEC performance with

bursty channels, we use the popular Gilbert-Elliott (GE) model

• We do this by performing a Monte-Carlo simulation over 104 random instances of a length 256 sparse signal and computing how often CS erasure coding results in exact recovery

Evaluation Results

Evaluation Results

Evaluation Results

Evaluation Results

Evaluation Results

• using a wireless network trace from the CRAWDAD database

• We selected used sensor nodes with an IEEE 802.15.4 radio transceiver placed about 12m apart between two different floors of auniversitybuilding

CSEC Implementation Costs

Conclusion

• We have explored the application of Compressive Sensing to handling data loss from erasure channels by viewing it as a low encoding-cost, proactive, erasure correction scheme

• We showed that oversampling is much less expensive than competing erasure coding methods and performs just as well

• This makes it an attractive choice for low-power embedded sensing where forward erasure correction is needed