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 10 4 random instances of a length 256 sparse signal and computing how often CS erasure coding results in exact recovery

14. Evaluation Results

18. 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 a university building

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