Structure And Typical Applications Of The Algebraic Structure Of Ldpc Codes

Low density parity check (LDPC) codes are shown to be one class of Shannon limit approaching codes. With advantages of high encoding gain, low decoding complexity and flexible code rates, etc., the research of these codes has become a hot spot of coding academia. Meanwhile, the project of the beyond third generation (B3G) mobile communication system has gradually entered the initial phase of being materialized. In order to satisfy the needs, espacially under a variety of different services and the high data rate requirement, the search of highly efficient channel codes has definitely become highlighted in the B3G-system. However, the most conmmonly used efficient channel codes such as Turbo Product Codes (TPC) and Turbo Codes are virtually falling short of meeting these requirements. While for the sake of good performance and the universal application potentials, the LDPC codes have been increasingly recoganized recently.However, the long codes of random-generated LDPC are unfortunately sufferd from a defect of high encoding complexity; especially the storage of generator matrix is considerably large during the encoding process. Therefore, by way of making LDPC become realizable in the applications, it's particularly important to search families of LDPC codes which may possess some algebraic structural properties.In this paper, we firstly introduce the algorithms of two main approaches that can be utilized to generate LDPC parity matrices with algebraic constructures. And base on these algorithms, it's convenient to construct LDPC codes which are either cyclic or quasi-cyclic. In chapter 3, we propose the methods for finding the generator matrix of a quasi-cyclic LDPC in"systematic form"from its parity-check matrix and its corresponding encoding schemes. These quasi-cyclic LDPC can not only reduce the storage of LDPC generator matrix, but also decrease the encoding complexity efficiently, which is of great significance for the applications. Furthermore, simulations show that well-designed quasi-cyclic LDPC can perform as well as those random-generated LDPC codes. And in the last section of chapter3, we present a"quasi-cyclic LDPC based"code division scheme, which can be possibly applied to the adaptive coding.Because of the time variation of wireless channel, getting the exact channel estimation and good synchronization is difficult for the receiver, so that the differential system could be an attractive choice. However, on the other hand, compared with coherent detection, differential detection comes with an evident loss of performance. In order to make up this gap, this paper presents a differential detection scheme that serial concatenate a LDPC code to form a iterative detection cycle. Moreover, under different channel conditions, simulations show that this scheme can improve the differential system performance considerably, of which may be meritorious to the applications.