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

One-bit Distributed Sensing and Coding for Field Estimation in Sensor Networks

This paper formulates and studies a general distributed field reconstruction problem using a dense network of noisy one-bit randomized scalar quantizers in the presence of additive observation noise of unknown distribution. A constructive quantization, coding, and field reconstruction scheme is developed and an upper-bound to the associated mean squared error (MSE) at any point and any snapshot is derived in terms of the local spatio-temporal smoothness properties of the underlying field. It is shown that when the noise, sensor placement pattern, and the sensor schedule satisfy certain weak technical requirements, it is possible to drive the MSE to zero with increasing sensor density at points of field continuity while ensuring that the per-sensor bitrate and sensing-related network overhead rate simultaneously go to zero. The proposed scheme achieves the order-optimal MSE versus sensor density scaling behavior for the class of spatially constant spatio-temporal fields.Comment: Fixed typos, otherwise same as V2. 27 pages (in one column review format), 4 figures. Submitted to IEEE Transactions on Signal Processing. Current version is updated for journal submission: revised author list, modified formulation and framework. Previous version appeared in Proceedings of Allerton Conference On Communication, Control, and Computing 200

High-resolution distributed sampling of bandlimited fields with low-precision sensors

The problem of sampling a discrete-time sequence of spatially bandlimited fields with a bounded dynamic range, in a distributed, communication-constrained, processing environment is addressed. A central unit, having access to the data gathered by a dense network of fixed-precision sensors, operating under stringent inter-node communication constraints, is required to reconstruct the field snapshots to maximum accuracy. Both deterministic and stochastic field models are considered. For stochastic fields, results are established in the almost-sure sense. The feasibility of having a flexible tradeoff between the oversampling rate (sensor density) and the analog-to-digital converter (ADC) precision, while achieving an exponential accuracy in the number of bits per Nyquist-interval per snapshot is demonstrated. This exposes an underlying ``conservation of bits'' principle: the bit-budget per Nyquist-interval per snapshot (the rate) can be distributed along the amplitude axis (sensor-precision) and space (sensor density) in an almost arbitrary discrete-valued manner, while retaining the same (exponential) distortion-rate characteristics. Achievable information scaling laws for field reconstruction over a bounded region are also derived: With N one-bit sensors per Nyquist-interval, $\Theta(\log N)$ Nyquist-intervals, and total network bitrate $R_{net} = \Theta((\log N)^2)$ (per-sensor bitrate $\Theta((\log N)/N)$), the maximum pointwise distortion goes to zero as $D = O((\log N)^2/N)$ or $D = O(R_{net} 2^{-\beta \sqrt{R_{net}}})$. This is shown to be possible with only nearest-neighbor communication, distributed coding, and appropriate interpolation algorithms. For a fixed, nonzero target distortion, the number of fixed-precision sensors and the network rate needed is always finite.Comment: 17 pages, 6 figures; paper withdrawn from IEEE Transactions on Signal Processing and re-submitted to the IEEE Transactions on Information Theor

Analysis for Scalable Coding of Quality-Adjustable Sensor Data

학위논문 (박사)-- 서울대학교 대학원 : 전기·컴퓨터공학부, 2014. 2. 신현식.Machine-generated data such as sensor data now comprise major portion of available information. This thesis addresses two important problems: storing of massive sensor data collection and efficient sensing. We first propose a quality-adjustable sensor data archiving, which compresses entire collection of sensor data efficiently without compromising key features. Considering the data aging aspect of sensor data, we make our archiving scheme capable of controlling data fidelity to exploit less frequent data access of user. This flexibility on quality adjustability leads to more efficient usage of storage space. In order to store data from various sensor types in cost-effective way, we study the optimal storage configuration strategy using analytical models that capture characteristics of our scheme. This strategy helps storing sensor data blocks with the optimal configurations that maximizes data fidelity of various sensor data under given storage space. Next, we consider efficient sensing schemes and propose a quality-adjustable sensing scheme. We adopt compressive sensing (CS) that is well suited for resource-limited sensors because of its low computational complexity. We enhance quality adjustability intrinsic to CS with quantization and especially temporal downsampling. Our sensing architecture provides more rate-distortion operating points than previous schemes, which enables sensors to adapt data quality in more efficient way considering overall performance. Moreover, the proposed temporal downsampling improves coding efficiency that is a drawback of CS. At the same time, the downsampling further reduces computational complexity of sensing devices, along with sparse random matrix. As a result, our quality-adjustable sensing can deliver gains to a wide variety of resource-constrained sensing techniques.Abstract i Contents iii List of Figures vi List of Tables x Chapter 1 Introduction 1 1.1 Motivation 1 1.2 Spatio-Temporal Correlation in Sensor Data 3 1.3 Quality Adjustability of Sensor Data 7 1.4 Research Contributions 9 1.5 Thesis Organization 11 Chapter 2 Archiving of Sensor Data 12 2.1 Encoding Sensor Data Collection 12 2.1.1 Archiving Architecture 13 2.1.2 Data Conversion 16 2.2 Compression Ratio Comparison 20 2.3 Quality-Adjustable Archiving Model 25 2.3.1 Data Fidelity Model: Rate 25 2.3.2 Data Fidelity Model: Distortion 28 2.4 QP-Rate-Distortion Model 36 2.5 Optimal Rate Allocation 40 2.5.1 Rate Allocation Strategy 40 2.5.2 Optimal Storage Configuration 41 2.5.3 Experimental Results 44 Chapter 3 Scalable Management of Storage 46 3.1 Scalable Quality Management 46 3.1.1 Archiving Architecture 47 3.1.2 Compression Ratio Comparison 49 3.2 Enhancing Quality Adjustability 51 3.2.1 Data Fidelity Model: Rate 52 3.2.2 Data Fidelity Model: Distortion 55 3.3 Optimal Rate Allocation 59 3.3.1 Rate Allocation Strategy 60 3.3.2 Optimal Storage Configuration 63 3.3.3 Experimental Results 71 Chapter 4 Quality-Adjustable Sensing 73 4.1 Compressive Sensing 73 4.1.1 Compressive Sensing Problem 74 4.1.2 General Signal Recovery 76 4.1.3 Noisy Signal Recovery 76 4.2 Quality Adjustability in Sensing Environment 77 4.2.1 Quantization and Temporal Downsampling 79 4.2.2 Optimization with Error Model 85 4.3 Low-Complexity Sensing 88 4.3.1 Sparse Random Matrix 89 4.3.2 Resource Savings 92 Chapter 5 Conclusions 96 5.1 Summary 96 5.2 Future Research Directions 98 Bibliography 100 Abstract in Korean 109Docto

Energy efficient and latency aware adaptive compression in wireless sensor networks

Wireless sensor networks are composed of a few to several thousand sensors deployed over an area or on specific objects to sense data and report that data back to a sink either directly or through a series of hops across other sensor nodes. There are many applications for wireless sensor networks including environment monitoring, wildlife tracking, security, structural heath monitoring, troop tracking, and many others. The sensors communicate wirelessly and are typically very small in size and powered by batteries. Wireless sensor networks are thus often constrained in bandwidth, processor speed, and power. Also, many wireless sensor network applications have a very low tolerance for latency and need to transmit the data in real time. Data compression is a useful tool for minimizing the bandwidth and power required to transmit data from the sensor nodes to the sink; however, compression algorithms often add a significant amount of latency or require a great deal of additional processing. The following papers define and analyze multiple approaches for achieving effective compression while reducing latency and power consumption far below what would be required to process and transmit the data uncompressed. The algorithms target many different types of sensor applications from lossless compression on a single sensor to error tolerant, collaborative compression across an entire network of sensors to compression of XML data on sensors. Extensive analysis over many different real-life data sets and comparison of several existing compression methods show significant contribution to efficient wireless sensor communication --Abstract, page iv

Data compression and computational efficiency

In this thesis we seek to make advances towards the goal of effective learned compression. This entails using machine learning models as the core constituent of compression algorithms, rather than hand-crafted components. To that end, we first describe a new method for lossless compression. This method allows a class of existing machine learning models – latent variable models – to be turned into lossless compressors. Thus many future advancements in the field of latent variable modelling can be leveraged in the field of lossless compression. We demonstrate a proof-of-concept of this method on image compression. Further, we show that it can scale to very large models, and image compression problems which closely resemble the real-world use cases that we seek to tackle. The use of the above compression method relies on executing a latent variable model. Since these models can be large in size and slow to run, we consider how to mitigate these computational costs. We show that by implementing much of the models using binary precision parameters, rather than floating-point precision, we can still achieve reasonable modelling performance but requiring a fraction of the storage space and execution time. Lastly, we consider how learned compression can be applied to 3D scene data - a data medium increasing in prevalence, and which can require a significant amount of space. A recently developed class of machine learning models - scene representation functions - has demonstrated good results on modelling such 3D scene data. We show that by compressing these representation functions themselves we can achieve good scene reconstruction with a very small model size

AdamRTP: Adaptive multi-flow real-time multimedia transport protocol for Wireless Sensor Networks

Real-time multimedia applications are time sensitive and require extra resources from the network, e.g. large bandwidth and big memory. However, Wireless Sensor Networks (WSNs) suffer from limited resources such as computational, storage, and bandwidth capabilities. Therefore, sending real-time multimedia applications over WSNs can be very challenging. For this reason, we propose an Adaptive Multi-flow Real-time Multimedia Transport Protocol (AdamRTP) that has the ability to ease the process of transmitting real-time multimedia over WSNs by splitting the multimedia source stream into smaller independent flows using an MDC-aware encoder, then sending each flow to the destination using joint/disjoint path. AdamRTP uses dynamic adaptation techniques, e.g. number of flows and rate adaptation. Simulations experiments demonstrate that AdamRTP enhances the Quality of Service (QoS) of transmission. Also, we showed that in an ideal WSN, using multi-flows consumes less power than using a single flow and extends the life-time of the network