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và nhận Anten Nhiều Trong các môi trường với một ăng-ten truyền đơn tại các trạm cơ sở và nhiều nhận các ăng-ten ở mỗi điện thoại di động, mã hóa chồng chất và nhận beamforming với hủy bỏ sự can thiệp là chiến lược tối ưu và tối đa hóa các SINRs nhận kết quả đầu ra bộ lọc. | FORWARD ERROR CORRECTION CODING 165 area whose width g has to be minimized is allowed while the rest of the matrix is sparse. With this approach a codeword is split into three parts the information part d and two parity parts denoted by q and p that is b7 d7 q7 pr holds. The encoding process now consists of two steps. First the coefficients of q are determined by k q1 Hi n-k-g 1 di 3.147a i 1 and k k j-1 qj 5 Hi n-k-g j di 5 Hi n-k-g j qi-k 3.147b i 1 i k 1 with 2 j g. Their calculation is based on the nonsparse part of H. Next the bits of p can be determined according to k k g P1 52 Hi 1 di 52 Hi 1 qi-k 3.148a i 1 i k 1 and k k g j k g-1 pj 5 . Hi j di 5 . Hi j qi-k 52 Hi j Pi-k-g 3.148b i 1 i k 1 i k g 1 with 2 j n - k - g. Richardson and Urbanke 2001 showed that the modification of the parity check matrix leads to a low-complexity encoding process and shows nearly no performance loss. 3.7.2 Graphical Description Graphs are a very illustrative way of describing LDPC codes. We will see later that the graphical representation allows an easy explanation of the decoding process for LDPC codes. Generally graphs consist of vertices nodes and edges connecting the vertices Lin and Costello 2004 Tanner 1981 . The number of connections of a node is called its degree. Principally cyclic and acyclic graphs can be distinguished when the latter type does not possess any cycles or loops. The girth of a graph denotes the length of its shortest cycle. Generally loops cannot be totally avoided. However at least short cycles of length four should be avoided because they lead to poor distance properties and thus asymptotically weak codes. Finally a bipartite graph consists of two disjoint subsets of vertices where edges only connect vertices of different subsets but no vertices of the same subset. These bipartite graphs will now be used to illustrate LDPC codes graphically. Actually graphs are graphical illustrations of parity check matrices. Remember that the J columns of H .