Efficient Analysis, Design and Decoding of Low-density Parity-check Codes [microform]

Download or read book Efficient Analysis, Design and Decoding of Low-density Parity-check Codes [microform] written by Masoud Ardakani and published by Library and Archives Canada = Bibliothèque et Archives Canada. This book was released on 2004 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation presents new methods for the analysis, design and decoding of low-density parity-check (LDPC) codes. We start by studying the simplest class of decoders: the binary message-passing (BMP) decoders. We show that the optimum BMP decoder must satisfy certain symmetry and isotropy conditions, and prove that Gallager's Algorithm B is the optimum BMP algorithm. We use a generalization of extrinsic information transfer (EXIT) charts to formulate a linear program that leads to the design of highly efficient irregular LDPC codes for the BMP decoder. We extend this approach to the design of irregular LDPC codes for the additive white Gaussian noise channel. We introduce a "semi-Gaussian" approximation that very accurately predicts the behaviour of the decoder and permits code design over a wider range of rates and code parameters than in previous approaches. We then study the EXIT chart properties of the highest rate LDPC code which guarantees a certain convergence behaviour. We also introduce and analyze gear-shift decoding in which the decoder is permitted to select the decoding rule from among a predefined set. We show that this flexibility can give rise to significant reductions in decoding complexity. Finally, we show that binary LDPC codes can be combined with quadrature amplitude modulation to achieve near-capacity performance in a multitone system over frequency selective Gaussian channels.