| Summary: | 碩士 === 國立中央大學 === 通訊工程研究所 === 95 === LDPC code used by the advanced communication standard of the next generation is an error control code. Its error correction ability may approach the Shannon’s theoretical value. With the MP algorithm, it can decode received samples in high speed from transmitter. Good LDPC codes that have been found are largely computer generated, especially long codes, and their encoding is very complex owing to the lack of structure. Kou, Lin, Fossorier [13] introduced the first algebraic and systematic construction of LDPC codes based on finite geometries. The large classes of finite-geometry LDPC codes have relatively good minimum distances, and their Tanner graphs do not contain short cycles. Consequently, their encoding is simple and can be implemented with linear shift registers. Based on the above construction method on finite geometries[13], we append more restrictions on finite geometries to construct LDPC codes using the non-degenerated quadratic surfaces on three-dimensional projective geometry. Owing some special properties on quadratic surfaces, some parameters of LDPC can be proven mathematically.
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