This dissertation is mainly focused on the analysis, design and optimization of Low-density parity-check (LDPC) codes over channels with large alphabet sets and the applications on compressed sensing (CS) and flash memories. Compared to belief-propagation (BP) decoding, verification-based (VB) decoding has significantly lower complexity and near optimal performance when the channel alphabet set is large. We analyze the verification-based decoding of LDPC codes over the q-ary symmetric channel (q-SC) and propose the list-message-passing (LMP) decoding which off ers a good tradeoff between complexity and decoding threshold. We prove that LDPC codes with LMP decoding achieve the capacity of the q-SC when q and the block length go to infinity. CS is a newly emerging area which is closely related to coding theory and information theory. CS deals with the sparse signal recovery problem with small number of linear measurements. One big challenge in CS literature is to reduce the number of measurements required to reconstruct the sparse signal. In this dissertation, we show that LDPC codes with verification-based decoding can be applied to CS system with surprisingly good performance and low complexity. We also discuss modulation codes and error correcting codes (ECC’s) design for flash memories. We design asymptotically optimal modulation codes and discuss their improvement by using the idea from load-balancing theory. We also design LDPC codes over integer rings and fields with large alphabet sets for flash memories.

Thesis (M.S.)--West Virginia University, 2001. / Title from document title page. Document formatted into pages; contains vi, 68 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 67-68).

Thesis (Ph. D.)--University of Texas at Austin, 2001. / Vita. Includes bibliographical references. Available also from UMI/Dissertation Abstracts International.

Thesis (M.S. in Electrical Engineering)--Naval Postgraduate School, March 2004. / Thesis advisor(s): Murali Tummala, Roberto Cristi. Includes bibliographical references (p. 133-134). Also available online.

Thesis (M. Phil.)--University of Hong Kong, 2010. / Includes bibliographical references (leaves 59-61). Also available in print.

Thesis (Ph. D.)--School of Electrical and Computer Engineering, Georgia Institute of Technology, 2004. Directed by Yucel Altunbasak. / Vita. Includes bibliographical references (leaves 141-146).

Thesis (M.S.)--West Virginia University, 2001. / Title from document title page. Document formatted into pages; contains xi, 113 p. : ill. (some col.). Vita. Includes abstract. Includes bibliographical references (p. 110-112).

Thesis (Ph. D.)--Hong Kong University of Science and Technology, 2003. / Includes bibliographical references (leaves 136-144). Also available in electronic version. Access restricted to campus users.

Includes bibliographical references (p. 64-67).

Thesis (Ph. D.)--University of California, San Diego, 2003. / Vita. Includes bibliographical references.