长 目< + = Figure 4.8.4 Normal graph of a regular LDPC code withd=3 andd=6. 4.8.2 Encoding of LDPC Codes 如前所述，LDC码是一种线性分组码，其编码可以按照一般线性分组码的编码原 理进行，即首先通过Gauss-Jordan消去法将给定的校验矩阵H变换为如下形式： H=[P I-] where P is a (nk)xk binary matrix and is the identity matrix of size n-k.Then the generator matrix in systematic form is obtained G=「LP] Thus.the encoding of the code defined by H can be performed via c=uG=u uPT] (4.4) Example 4.8.3:Consider the encoding of the length-10 rate-1/2 LDPC code [Johnson,pp.15] 「1101100100 0110111000 H=0001000111 1100011010 0010010101 First,we put H into row-echelon form(ie.so that in any two successive rows that do no consist entirely of zeros,the leading 1 in the lower row occurs further to the right than the leading I in the higher row). The matrix H is put into this form by applying elementary row operations in GF(2). 6 6 Figure 4.8.4 Normal graph of a regular LDPC code with dv = 3 and dc = 6. 4.8.2 Encoding of LDPC Codes 如前所述，LDPC码是一种线性分组码，其编码可以按照一般线性分组码的编码原 理进行，即首先通过Gauss-Jordan消去法将给定的校验矩阵H变换为如下形式： H PI = [ n k − ] where P is a ( ) nk k − × binary matrix and In-k is the identity matrix of size n-k. Then the generator matrix in systematic form is obtained T k = ⎡ ⎤ GIP ⎣ ⎦ Thus, the encoding of the code defined by H can be performed via T = = ⎡ ⎤ ⎣ ⎦ c uG u uP (4.4) Example 4.8.3: Consider the encoding of the length-10 rate-1/2 LDPC code [Johnson, pp.15] 1101100100 0110111000 0001000111 1100011010 0010010101 ⎡ ⎤ ⎢ ⎥ = ⎣ ⎦ H First, we put H into row-echelon form (i.e. so that in any two successive rows that do not consist entirely of zeros, the leading 1 in the lower row occurs further to the right than the leading 1 in the higher row). The matrix H is put into this form by applying elementary row operations in GF(2)