Modern Error Control Codes and Applications to Distributed Source Coding
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This dissertation first studies two-dimensional wavelet codes (TDWCs). TDWCs are introduced as a solution to the problem of designing a 2-D code that has low decoding- complexity and has the maximum erasure-correcting property for rectangular burst erasures. The half-rate TDWCs of dimensions N<sub>1</sub> X N<sub>2</sub> satisfy the Reiger bound with equality for burst erasures of dimensions N<sub>1</sub> X N<sub>2</sub>/2 and N<sub>1</sub>/2 X N<sub>2</sub>, where GCD(N<sub>1</sub>,N<sub>2</sub>) = 2. Examples of TDWC are provided that recover any rectangular burst erasure of area N<sub>1</sub>N<sub>2</sub>/2. These lattice-cyclic codes can recover burst erasures with a simple and efficient ML decoding. This work then studies the problem of distributed source coding for two and three correlated signals using channel codes. We propose to model the distributed source coding problem with a set of parallel channel that simplifies the distributed source coding to de- signing non-uniform channel codes. This design criterion improves the performance of the source coding considerably. LDPC codes are used for lossless and lossy distributed source coding, when the correlation parameter is known or unknown at the time of code design. We show that distributed source coding at the corner point using LDPC codes is simplified to non-uniform LDPC code and semi-random punctured LDPC codes for a system of two and three correlated sources, respectively. We also investigate distributed source coding at any arbitrary rate on the Slepian-Wolf rate region. This problem is simplified to designing a rate-compatible LDPC code that has unequal error protection property. This dissertation finally studies the distributed source coding problem for applications whose wireless channel is an erasure channel with unknown erasure probability. For these application, rateless codes are better candidates than LDPC codes. Non-uniform rateless codes and improved decoding algorithm are proposed for this purpose. We introduce a reliable, rate-optimal, and energy-efficient multicast algorithm that uses distributed source coding and rateless coding. The proposed multicast algorithm performs very close to network coding, while it has lower complexity and higher adaptability.