Modern Error Control Codes and Applications to Distributed Source Coding

Multicast;Rateless codes;Wyner-Ziv limit;Reiger bound;Error control coding;Wavelet two-dimensionl codes;Lossy distributed source coding;Slepian-Wolf limit;Distributed source coding

Sartipi, Mina ; Electrical and Computer Engineering

University:Georgia Institute of Technology

Department:Electrical and Computer Engineering

关键词: Multicast;    Rateless codes;    Wyner-Ziv limit;    Reiger bound;    Error control coding;    Wavelet two-dimensionl codes;    Lossy distributed source coding;    Slepian-Wolf limit;    Distributed source coding;   

Others  :  https://smartech.gatech.edu/bitstream/1853/19795/1/sartipi_mina_200612_phd.pdf

美国|英语

来源: SMARTech Repository

【 摘 要 】

This dissertation first studies two-dimensional wavelet codes (TDWCs). TDWCsare 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 N₁ X N₂ satisfy the Reiger bound with equality forburst erasures of dimensions N₁ X N₂/2 and N₁/2 X N₂, where GCD(N₁,N₂) = 2. Examplesof TDWC are provided that recover any rectangular burst erasure of area N₁N₂/2. Theselattice-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 codingproblem 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 thesource coding considerably. LDPC codes are used for lossless and lossy distributed sourcecoding, 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 simplifiedto non-uniform LDPC code and semi-random punctured LDPC codes for a system of twoand three correlated sources, respectively. We also investigate distributed source coding atany arbitrary rate on the Slepian-Wolf rate region. This problem is simplified to designinga rate-compatible LDPC code that has unequal error protection property. This dissertationfinally studies the distributed source coding problem for applications whose wireless channel is an erasure channel with unknown erasure probability. For these application, ratelesscodes are better candidates than LDPC codes. Non-uniform rateless codes and improveddecoding algorithm are proposed for this purpose. We introduce a reliable, rate-optimal,and energy-efficient multicast algorithm that uses distributed source coding and ratelesscoding. The proposed multicast algorithm performs very close to network coding, while ithas lower complexity and higher adaptability.