Compressive Oversampling for Robust Data Transmission in Sensor Networks

1. Compressive Oversampling for Robust Data Transmission in Sensor Networks Infocom 2010

2. Outline • Introduction • Problem Formulation • Compressive Sensing for Erasure Coding • Channel Coding Overview • Compressive Sensing Fundamentals • Handling Data Losses Compressively • Evaluation Results • Conclusions

3. 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

4. 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.

5. 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

6. Conventional and Proposed Approaches

7. 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

8. 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

9. 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 :

10. Compressive Sensing Fundamentals • Compressive Sensing • is original signal • is K-sparse under • , measurement matrix • Reconstruct signal by linear program

11. 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

12. 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

13. 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

14. Evaluation Results

15. Evaluation Results

16. Evaluation Results

17. Evaluation Results

18. 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

19. CSEC Implementation Costs

20. 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