A general distributed source coding framework via block codes and their complements

© 2010 Dr. Xiaomin CaoDistributed Source Coding (DSC) is a practical coding technique for compression of correlated information sources which is suitable for sensor networks and video compression. Even though several DSC coding schemes have been proposed in the literature, connections between them are not clear. Moreover, the literature is not clear on extensions of these DSC schemes to more than two correlated sources. Also, the literature is not clear on how to achieve flexible compression rates per source. The aim of this thesis is to reveal the connections between DSC schemes by developing a general DSC framework for any number of sources which enables optimal compression, flexible code rates per source and a simplified coding structure. Before presenting our DSC scheme, we discuss linear block codes as sub spaces, and present the concept of “complementary code”. This concept is a key tool throughout this thesis. Our major contributions on DSC framework design are twofold. Firstly, we construct a generalized DSC scheme with conceptual simplicity via linear block codes and their complements, in which existing DSC schemes, as presented in the literature, are viewed as special cases. Not only does this framework allow for flexible non-asymmetric rates, but it also can be applied to any number of correlated information sources and achieve the optimal overall compression obtained by the asymmetric-rate DSC. In addition, our framework has flexibility in the choice of linear block codes: it enables practical DSC systems to be applied to any linear code and any corresponding complementary code with flexible code rates. Secondly, by utilizing the properties of complementarity, we simplify the DSC decoding algorithm into a combination of channel encoding, syndrome computation and syndrome-to-error- pattern decoding functions of linear codes and their complementary codes. Then, we interpret the framework in polynomial form since cyclic codes have simple hardware circuits in channel encoding and syndrome computation. By applying both cyclic codes and their cyclic complementary codes, our framework obtains hardware computational simplicity. This efficient coding algorithm is illustrated by a BCH code as well as a Reed-Solomon code. Finally, we investigate DSC systems which attempt to resolve the practical difficulties of compression rate initialization and modification. We take simultaneous error detection in the joint decoder as a rate adaptation trigger and build rate-adaptive DSC encoding schemes by cyclic codes and Complex Rotary codes, which exhibit computational efficiency. A part of the research results in this thesis has been published: X. Cao and M. Kuijper. A Distributed Source Coding framework for multiple sources. Information Theory and Its Applications, 2008. ISITA 2008, Dec. 2008. X. Cao and M. Kuijper. Distributed Source Coding with cyclic codes and their duals. International Conferences on Information, Communications and Signal Processing, Macau, Dec. 2009