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ENCODING SCHEME, AND A DECODING SCHEME USING A SERIES OF LDPC CODES BASED ON FINITE INVERSIVE SPACES
ENCODING SCHEME, AND A DECODING SCHEME USING A SERIES OF LDPC CODES BASED ON FINITE INVERSIVE SPACES
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机译:基于有限逆空间的编码方案以及使用一系列LDPC码的编码方案
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摘要
There is disclosed a method of creating an LDPC code that is defined by a parity-check matrix H. The parity-check matrix H is derived from a (0,1)-geometry which is induced by a finite inversive space. This inversive space has an order q where every circle in the inversive space contains exactly q+1 points, q is preferably even, and most preferably equal to 2. Where the inversive space has a dimension n. Where the (0,1)-geometry is formed as a derived geometric structure based on pencils of degree m≦n in the inversive space. The method includes construction of a binary K by N matrix H labelled by K circles and N pencils of the inversive space, wherein the (i, j)-entry of the matrix is 1 if circle i belongs to pencil j, and 0 otherwise. If the degree of the pencil is given by 2 then the parity-check matrix H needs to be transposed, i.e. HT is used instead of H. A method of transmitting a message, a coder, a decoder and a data transmission system using such codes are also disclosed.
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机译:公开了一种创建由奇偶校验矩阵H定义的LDPC码的方法。奇偶校验矩阵H是从由有限逆空间引起的(0,1)几何导出的。该可逆空间具有阶数q,其中,可逆空间中的每个圆正好包含q + 1个点,q优选为偶数,最优选等于2。其中可逆空间的尺寸为n。其中,(0,1)几何形状是基于逆空间中m≤n的铅笔的派生几何结构而形成的。该方法包括通过由K个圆和逆空间的N个铅笔标记的N个矩阵H构造二进制K,其中如果圆i属于铅笔j,则矩阵的(i,j)项为1,否则为0。如果铅笔的度数为2,则需要转置奇偶校验矩阵H,即使用H T Sup>代替H。发送消息的方法,编码器,解码器还公开了使用这种代码的数据传输系统。
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