Download or read book Construction and Decoding of Codes on Finite Fields and Finite Geometries written by Li Zhang and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this doctoral dissertation, two constructions of binary low-density parity-check (LDPC) codes with quasi-cyclic (QC) structures are presented. A general construction of RC-constrained arrays of circulant permutation matrices is introduced, then two specific construction methods based on Latin squares and cyclic subgroups are presented. Array masking is also proposed to improve the waterfall-region performance of the QC-LDPC codes. Also, by analyzing the parity check matrices of these codes, combinatorial expressions for their ranks and dimensions are derived. Experimental results show that, with iterative decoding algorithms, the constructed codes perform very well over both the additive white Gaussian noise (AWGN) and the binary erasure channels (BEC). Also presented in this dissertation are constructions of QC-LDPC codes based on two special classes of balanced incomplete block designs (BIBDs) derived by Bose. Codes are constructed for both the AWGN channel and the binary burst erasure channel (BBEC). Experimental results show that the codes constructed perform well not only over these two types of channels but also over the BEC. Finally, a two stage iterative decoding is presented to decode a class of cyclic Euclidean geometry codes. By exploiting the inherent geometry structure of the codes and avoiding the degrading effect of short cycles, the proposed algorithm provides good decoding performance of the codes.