Constructive approaches for network source coding

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Network source coding refers to data compression in network scenarios, i.e., where there is more than one transmitter, or more than one receiver, or both. Traditional data compression techniques, devised for the situation where a single source is to be reconstructed at a single destination, are suboptimal for the complex network scenarios that have emerged lately, and thus, may lead to a waste of bandwidth resources. Therefore, the investigation of techniques for network source coding are of great interest. Their study from an information theoretical point of view establishes fundamental limits of performance, but such results are based on random coding arguments, which are nonconstructive. For practical use, constructive approaches are needed. This research will develop novel and efficient constructive network source coding schemes for several network scenarios, as follows: 1) robust distributed compression of correlated sources; 2) networks with one transmitter and more receivers with side information; 3) Slepian-Wolf coding over broadcast channels. The general approach will be to devise coding schemes based on vector quantizers (VQ) with structured codebooks. Specifically, we will employ VQs with lattice codebooks and shape-gain VQs with uniform shape codebooks. We will draw inspiration from the random coding schemes used to derive the achievable rate-distortion regions, where available, or from constructions used in related problems. We will analyze the asymptotical performance under the high rate assumption and, based on this analysis, design asymptotically optimal schemes. Additionally, in the case of shape-gain VQs, we will design algorithms to optimize the codes for finite rates. This research aims at designing network source coding schemes which use the available bandwidth more efficiently and provide a guarantee on the quality of service. By accomplishing this goal our research will lay the foundation of novel technologies, which have the potential of making their way in the development of future standards related to multimedia networking. The implementation of such technologies will present an economic opportunity to Canadian information technology companies, and will ultimately be of benefit to consumers of internet services. On the theoretical side, the proposed research will advance the knowledge and understanding in the area of network source code design and analysis. The techniques and insights developed will be also applicable to other more complex network source coding problems which may arise in the future. An important component of this research will be the training of highly qualified personnel. Several graduate students will be engaged in this research and will be trained in multimedia coding and communications, information theory and optimization. This training will prepare them for an engineering or academic career in the information technology sector.