Entropy of Highly Correlated Quantized Data

This paper considers the entropy of highly correlated quantized samples. Two results are shown. The first concerns sampling and identically scalar quantizing a stationary continuous-time random process over a finite interval. It is shown that if the process crosses a quantization threshold with positive probability, then the joint entropy of the quantized samples tends to infinity as the sampling rate goes to infinity. The second result provides an upper bound to the rate at which the joint entropy tends to infinity, in the case of an infinite-level uniform threshold scalar quantizer and a stationary Gaussian random process. Specifically, an asymptotic formula for the conditional entropy of one quantized sample conditioned on the previous quantized sample is derived. At high sampling rates, these results indicate a sharp contrast between the large encoding rate (in bits/sec) required by a lossy source code consisting of a fixed scalar quantizer and an ideal, sampling-rate-adapted lossless code, and the bounded encoding rate required by an ideal lossy source code operating at the same distortion

H2B: Heartbeat-based Secret Key Generation Using Piezo Vibration Sensors

We present Heartbeats-2-Bits (H2B), which is a system for securely pairing wearable devices by generating a shared secret key from the skin vibrations caused by heartbeat. This work is motivated by potential power saving opportunity arising from the fact that heartbeat intervals can be detected energy-efficiently using inexpensive and power-efficient piezo sensors, which obviates the need to employ complex heartbeat monitors such as Electrocardiogram or Photoplethysmogram. Indeed, our experiments show that piezo sensors can measure heartbeat intervals on many different body locations including chest, wrist, waist, neck and ankle. Unfortunately, we also discover that the heartbeat interval signal captured by piezo vibration sensors has low Signal-to-Noise Ratio (SNR) because they are not designed as precision heartbeat monitors, which becomes the key challenge for H2B. To overcome this problem, we first apply a quantile function-based quantization method to fully extract the useful entropy from the noisy piezo measurements. We then propose a novel Compressive Sensing-based reconciliation method to correct the high bit mismatch rates between the two independently generated keys caused by low SNR. We prototype H2B using off-the-shelf piezo sensors and evaluate its performance on a dataset collected from different body positions of 23 participants. Our results show that H2B has an overwhelming pairing success rate of 95.6%. We also analyze and demonstrate H2B's robustness against three types of attacks. Finally, our power measurements show that H2B is very power-efficient

Shake well before use: Authentication based on Accelerometer Data

Small, mobile devices without user interfaces, such as Bluetooth headsets, often need to communicate securely over wireless networks. Active attacks can only be prevented by authenticating wireless communication, which is problematic when devices do not have any a priori information about each other. We introduce a new method for device-to-device authentication by shaking devices together. This paper describes two protocols for combining cryptographic authentication techniques with known methods of accelerometer data analysis to the effect of generating authenticated, secret keys. The protocols differ in their design, one being more conservative from a security point of view, while the other allows more dynamic interactions. Three experiments are used to optimize and validate our proposed authentication method

Data Streams from the Low Frequency Instrument On-Board the Planck Satellite: Statistical Analysis and Compression Efficiency

The expected data rate produced by the Low Frequency Instrument (LFI) planned to fly on the ESA Planck mission in 2007, is over a factor 8 larger than the bandwidth allowed by the spacecraft transmission system to download the LFI data. We discuss the application of lossless compression to Planck/LFI data streams in order to reduce the overall data flow. We perform both theoretical analysis and experimental tests using realistically simulated data streams in order to fix the statistical properties of the signal and the maximal compression rate allowed by several lossless compression algorithms. We studied the influence of signal composition and of acquisition parameters on the compression rate Cr and develop a semiempirical formalism to account for it. The best performing compressor tested up to now is the arithmetic compression of order 1, designed for optimizing the compression of white noise like signals, which allows an overall compression rate = 2.65 +/- 0.02. We find that such result is not improved by other lossless compressors, being the signal almost white noise dominated. Lossless compression algorithms alone will not solve the bandwidth problem but needs to be combined with other techniques.Comment: May 3, 2000 release, 61 pages, 6 figures coded as eps, 9 tables (4 included as eps), LaTeX 2.09 + assms4.sty, style file included, submitted for the pubblication on PASP May 3, 200

Multiple-Description Coding by Dithered Delta-Sigma Quantization

We address the connection between the multiple-description (MD) problem and Delta-Sigma quantization. The inherent redundancy due to oversampling in Delta-Sigma quantization, and the simple linear-additive noise model resulting from dithered lattice quantization, allow us to construct a symmetric and time-invariant MD coding scheme. We show that the use of a noise shaping filter makes it possible to trade off central distortion for side distortion. Asymptotically as the dimension of the lattice vector quantizer and order of the noise shaping filter approach infinity, the entropy rate of the dithered Delta-Sigma quantization scheme approaches the symmetric two-channel MD rate-distortion function for a memoryless Gaussian source and MSE fidelity criterion, at any side-to-central distortion ratio and any resolution. In the optimal scheme, the infinite-order noise shaping filter must be minimum phase and have a piece-wise flat power spectrum with a single jump discontinuity. An important advantage of the proposed design is that it is symmetric in rate and distortion by construction, so the coding rates of the descriptions are identical and there is therefore no need for source splitting.Comment: Revised, restructured, significantly shortened and minor typos has been fixed. Accepted for publication in the IEEE Transactions on Information Theor