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5G-NR LDPC code encoding
After the base matrix is updated and expanded, the coding can be carried out. The source information sequence is input into the encoder for coding to obtain the coding sequence, and the coding result is expressed as c = [SP]. Among them, S = (s 1, s 2 ,..., sk) represents an information bit sequence of length k, P = (p 1, p 2 ,..., pm) represents a check bit sequence of length m, and they obey n = m + k, n is the length of the codeword, the base matrix H b is a matrix of mb × nb, and the core matrix is a matrix of mc × nc.
The information bit sequence S is divided into a group according to each Z bits, and can be divided into kb = nb-mb groups in total, and the grouped bit sequence is denoted as s = [s(0), s(1),..., s (kb -1)]; Similarly, the same operation is performed on the parity bit sequence P, which can be divided into mb groups in total, denoted as p=[p(0), p(1),..., p(mb -1) )], the check bit is divided into 2 parts P = [P 1 P 2 ], where P 1 = [p (0) T, p (1) T ,..., p(mc -1)T ], denoted as mc group, P 2 = [p (mc )T, p (mc +1 )T ,..., p (mb -1)T ], denoted as mb-mc group.
The figure below is an example of a 5G NR BGn2 base matrix:
The check matrix obtained by the expansion of the base matrix is H. Using H * c T (transpose of the C matrix) = 0, the following formula is obtained by expansion:
Among them, H i (i = A, D, O, E, F, I) represents the sub-matrix of the check matrix, HA and HD form the core matrix, where HD is a quasi-double diagonal matrix, HO is a matrix of all 0s, and HI is the identity matrix, then you can get:
To get the check bit, you need to calculate P1 And P2 are two parts:
1) P 1 is calculated iteratively by using the special structure of the quasi-double diagonal matrix HD;
2) P 2 is calculated by P 1 and the identity matrix HI.
The evaluation process of P1 is as follows:
(1) Initialization. After expanding the above formula and accumulating, we get:
idx(0 ＜ idx ＜ mc -1) represents the row number coordinates of the non-negative elements in the remaining elements after removing the first and last two rows in the first column of the sub-matrix HD, Then p(0) is as follows:
(2) Iteration. According to the HD structure, the following expression can be obtained:
After P 1 is obtained, the previous formula can be expanded to obtain the P2 part:
Find the check bit sequence P = [P 1 P 2 ], combine it with the information bit, and get c = [SP] .
5G-NR LDPC code punching, shortening and expansion
In order to ensure the realization of arbitrary code length and code rate, 5G-NR LDPC code adopts information bit puncturing, information bit shortening and check bit puncturing technology.
When the code word c is obtained, it is punctured and shortened. The number of punctured and shortened bits is shown in the following table.
