As the demand of error-free data transmission and storage increases, error control becomes increasingly important in data communication and storage systems. Today very sophisticated error control mechanisms are being used in a broad range of communication and data storage systems to achieve reliable data transmission and storage, such as wireless, satellite, optical, digital video broadcast, network communications, hard disc drives, compact disks, and many others. This research is to devise methods for constructing good error control codes and developing efficient error control mechanisms that have great potential to achieve error-free information transmission and data storage for the future generation of data communication and storage systems. This research investigates several very promising algebraic methods for systematic construction of binary and q-ary high performance and efficiently encodable quasi-cyclic (QC) LDPC codes for AWGN, random erasure, erasure-burst and error-burst channels. Specical subjects investigated include: (1) a united approach based on nite fields for constructing binary and q-ary QC-LDPC codes; (2) a masking technique that adjusts column and row weights of the parity-check matrices of the constructed codes to yield performance close to Shannon limit; (3) construction of codes for both random and burst erasure channels that yield good performance when decoded iteratively; and (4) a new simple algorithm for decoding cyclic codes, including LDPC codes, over error-burst channel. Preliminary results are impressive. The q-ary LDPC codes constructed significantly outperform comparable RS codes decoded with any existing algebraic soft-decision decoding algorithm.
