Sergio D. Servetto

On the interdependence of routing and data compression in multi-hop sensor networks

Abstract We consider a problem of broadcast communication in sensor networks, in which samples of a random field are collected at each node, and the goal is for all nodes to obtain an estimate of the entire field within a prescribed distortion value. The main idea we explore in this paper is that of jointly compressing the data generated by different nodes as this information travels over multiple hops, to eliminate correlations in the representation of the sampled field. Our main contributions are: (a) we obtain, using simple network flow concepts, conditions on the rate/distortion function of the random field, so as to guarantee that any node can obtain the measurements collected at every other node in the network, quantized to within any prescribed distortion value; and (b) we construct a large class of physically-motivated stochastic models for sensor data, for which we are able to prove that the joint rate/distortion function of all the data generated by the whole network grows slower than the bounds found in (a). A truly novel aspect of our work is the tight coupling between routing and source coding, explicitly formulated in a simple and analytically tractable model – to the best of our knowledge, this connection had not been studied before.

Constrained random walks on random graphs: routing algorithms for large scale wireless sensor networks

We consider a routing problem in the context of large scale networks with uncontrolled dynamics. A case of uncontrolled dynamics that has been studied extensively is that of mobile nodes, as this is typically the case in cellular and mobile ad-hoc networks. In this paper however we study routing in the presence of a different type of dynamics: nodes do not move, but instead switch between active and inactive states at random times. Our interest in this case is motivated by the behavior of sensor nodes powered by renewable sources, such as solar cells or ambient vibrations. In this paper we formalize the corresponding routing problem as a problem of constructing suitably constrained random walks on random dynamic graphs. We argue that these random walks should be designed so that their resulting invariant distribution achieves a certain load balancing property, and we give simple distributed algorithms to compute the local parameters for the random walks that achieve the sought behavior. A truly novel feature of our formulation is that the algorithms we obtain are able to route messages along all possible routes between a source and a destination node, without performing explicit route discovery/repair computations, and without maintaining explicit state information about available routes at the nodes. To the best of our knowledge, these are the first algorithms that achieve true multipath routing (in a statistical sense), at the complexity of simple stateless operations.

Multiple description wavelet based image coding

We consider the problem of coding images for transmission over error-prone channels. The impairments we target are transient channel shutdowns, as would occur in a packet network when a packet is lost, or in a wireless system during a deep fade: when data is delivered it is assumed to be error-free, but some of the data may never reach the receiver. The proposed algorithms are based on a combination of multiple description scalar quantizers with techniques successfully applied to the construction of some of the most efficient subband coders. A given image is encoded into multiple independent packets of roughly equal length. When packets are lost, the quality of the approximation computed at the receiver depends only on the number of packets received, but does not depend on exactly which packets are actually received. When compared with previously reported results on the performance of robust image coders based on multiple descriptions, on standard test images, our coders attain similar PSNR values using typically about 50-60% of the bit rate required by these other state-of-the-art coders, while at the same time providing significantly more freedom in the mechanism for allocation of redundancy among descriptions.

Multiple-description vector quantization with lattice codebooks: design and analysis

The problem of designing a multiple-description vector quantizer with lattice codebook /spl Lambda/ is considered. A general solution is given to a labeling problem which plays a crucial role in the design of such quantizers. Numerical performance results are obtained for quantizers based on the lattices A/sub 2/ and Z/sup i/, i=1, 2, 4, 8, that make use of this labeling algorithm. The high-rate squared-error distortions for this family of L-dimensional vector quantizers are then analyzed for a memoryless source with probability density function (PDF) p and differential entropy h(p)</spl infin/. For any a /spl epsiv/ (0, 1) and rate pair (R, R), it is shown that the two-channel distortion d~/sub o/ and the channel 1 (or channel 2) distortion d~/sub s/ satisfy lim/sub R/spl rarr//spl infin//d~/sub o/2/sup 2R(1+a)/= 1/4 G(/spl Lambda/)2/sup 2h(p)/ and lim/sub R/spl rarr//spl infin//d~/sub s/2/sup 2R(1-a)/=G(S/sub L/)2/sup 2h(p)/ where G(/spl Lambda/) is the normalized second moment of a Voronoi cell of the lattice /spl Lambda/ and G(S/sub L/) is the normalized second moment of a sphere in L dimensions.

Image coding based on a morphological representation of wavelet data

In this paper, an experimental study of the statistical properties of wavelet coefficients of image data is presented, as well as the design of two different morphology-based image coding algorithms that make use of these statistics. A salient feature of the proposed methods is that, by a simple change of quantizers, the same basic algorithm yields high performance embedded or fixed rate coders. Another important feature is that the shape information of morphological sets used in this coder is encoded implicitly by the values of wavelet coefficients, thus avoiding the use of explicit and rate expensive shape descriptors. These proposed algorithms, while achieving nearly the same objective performance of state-of-the-art zerotree based methods, are able to produce reconstructions of a somewhat superior perceptual quality, due to a property of joint compression and noise reduction they exhibit.

Multiple description lattice vector quantization

We consider the problem of designing a lattice-based multiple description vector quantizer for a two-channel diversity system. The design of such a quantizer can be reduced to the problem of assigning pair labels to points of a vector quantizer codebook. A general labeling procedure based on the structure of the lattice is presented, along with detailed results for the hexagonal lattice: algorithms, asymptotic performance, and numerical simulations. Asymptotically, when compared with the lattice Z, the resulting quantizer achieves the standard second-moment gain of the hexagonal lattice for the central distortion, and, surprisingly, achieves the two-dimensional sphere gain for the side distortion.

Broadcast Channels With Cooperating Decoders

We consider the problem of communicating over the general discrete memoryless broadcast channel (DMBC) with partially cooperating receivers. In our setup, receivers are able to exchange messages over noiseless conference links of finite capacities, prior to decoding the messages sent from the transmitter. In this paper, we formulate the general problem of broadcast with cooperation. We first find the capacity region for the case where the BC is physically degraded. Then, we give achievability results for the general broadcast channel, for both the two independent messages case and the single common message case

Multiple-description wavelet based image coding

We consider the problem of image coding for communication systems that use diversity to overcome channel impairments. We focus on the special case in which there are two channels of equal capacity between a transmitter and a receiver. Our designs are based on a combination of techniques successfully applied to the construction of some of the most efficient wavelet based image coding algorithms, with multiple description scalar quantizers (MDSQs). For a given image, we produce two bitstreams, to be transmitted over each channel. Should one of the channels fail, each individual description guarantees a minimum image quality specified by the user. However, if both descriptions arrive at destination, they are combined to produce a higher quality image than that achievable based on individual descriptions. We formulate a discrete optimization problem, whose solution gives parameters of the proposed encoder yielding optimal performance in an operational sense. Simulation results are presented.

On the scalability of cooperative time synchronization in pulse-connected networks

The problem of time synchronization in dense wireless networks is considered. Well-established synchronization techniques suffer from an inherent scalability problem in that synchronization errors grow with an increasing number of hops across the network. In this work, a model for communication in wireless networks is first developed, and then the model is used to define a new time synchronization mechanism. A salient feature of the proposed method is that, in the regime of asymptotically dense networks, it can average out all random errors and maintain global synchronization in the sense that all nodes in the multihop network can see identical timing signals. This is irrespective of the distance separating any two nodes.

Lattice quantization with side information

We consider the design of lattice vector quantizers for the problem of coding Gaussian sources with uncoded side information available only at the decoder. The design of such quantizers can be reduced to the problem of finding an appropriate sublattice of a given lattice codebook. We study the performance of the resulting quantizers in the limit as the encoding rate becomes high, and we evaluate these asymptotics for three lattices of interest: the hexagonal lattice A/sub 2/, the Gosset lattice E/sub 8/, and the Leech lattice /spl Lambda//sub 24/. We also verify these asymptotics numerically, via computer simulations based on the lattice A/sub 2/. Surprisingly, the lattice E/sub 8/ achieves the best performance of all cases considered.