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Xiaojie Zhang(University of California, San Diego), “LDPC Codes -- Structural Analysis and Decoding Techniques”, Advisor: Prof. Paul H. Siegel, 2012
Low-density parity-check (LDPC) codes have been the focus of much research over the past decade. However, the error floor phenomenon observed in MP decoding, which manifests itself as an abrupt change in the slope of the error-rate curve, has hindered the adoption of LDPC codes and MP decoders in some applications requiring very low error rates. As an alternative to MP decoding, linear programming (LP) decoding is an approximation to maximum-likelihood decoding by relaxing the optimal decoding problem into a linear optimization problem.
In this dissertation, the author first designed an efficient exhaustive search algorithm to find all small error-prone substructures, some of which are commonly blamed for certain decoding failures of MP decoding. Then, the author investigated the cause of error floors in LDPC codes from the perspective of the MP decoder implementation, and proposed a quantization method for fixed-point implementation of MP decoding which significantly improves the error-floor performance by overcoming the limitations of standard quantization rules. For LP decoding, the author improved the error-correcting capability of LP decoding by using an effective algorithm to generate additional redundant parity-check constraints which eliminate certain undesired solutions to LP decoding problem. The author further proposed an efficient message-passing algorithm to solve the LP decoding problem.
For details, please contact the author or visit the thesis page.
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