Method of constructing parity-check matrix of ldpc code and encoding method and encoding apparatus based on the method

An encoding method of the LDPC code, comprising the following steps of:

• dividing the parity-check matrix H into two submatrixes H=[Hm Hp], wherein Hm is a submatrix with size of M×(N−M) and Hp is a submatrix with size of M×M, and computing Hp−1 and Hp−1 Hm, wherein the parity-check matrix H is constructed by the following steps of:
• constructing a MB×NB base matrix B for an LDPC code with code rate R and code length N, MB=M/K, NB=N/K, M=N (1−R), K is the expansion factor of the base matrix, Kεφ, and φ is the set of the common factors of M and N, selecting the number of ‘1’ in each row and each column of the base matrix B, so that the row weight distribution and the column weight distribution of B meet a preset node degree distribution, selecting the position of ‘1’ in each row and each column in the base matrix B, so that the MB×MB submatrix composed of the right MB columns of B is full rank, expanding the base matrix B into a parity-check matrix H with size of M×N, replacing ‘0’ in the base matrix B with a K×K all-‘0’ matrix Z, replacing ‘1’ in the base matrix B with a K×K dimensional circulant permutation matrix P, wherein the row number i and the column number j of ‘1’ in P meet j=(i+k) mod k, k is the offset of the circulant permutation matrix, and mod indicates the modulo operation, and selecting an offset for each K×K circulant permutation matrix P;
• computing the 1×M parity-check sequence p=m(Hp−1 Hm)T according to the input 1×(N−M) information sequence m;
• and combining the information sequence m with the parity-check sequence p into the 1×N code word sequence c=[m p], and outputting the same.

An encoding apparatus of the LDPC code, comprising an encoding matrix storing module, a parity-check sequence computing module and a code word sequence generating module, wherein

• the encoding matrix storing module is used for storing the structure of the encoding matrix, dividing the parity-check matrix H with size of M×N into two submatrixes H=[Hm Hp], wherein Hm is a submatrix with size of M×(N−M) and Hp is a submatrix with size of M×M, the encoding matrix storing module is used for storing the structure of the matrix Hp−1 Hm, wherein the Hp−1 Hm has the block circulant structure and can be stored in the form of block, and the parity-check matrix H is constructed by the following steps of:
• constructing a MB×NB base matrix B for an LDPC code with code rate R and code length N, wherein MB=M/K, NB=N/K, M=N (1−R), K is the expansion factor of the base matrix, Kεφ, and φ is the set of the common factors of M and N, selecting the number of ‘1’ in each row and each column of the base matrix B, so that the row weight distribution and the column weight distribution of B meet a preset node degree distribution, selecting the position of ‘1’ in each row and each column in the base matrix B, so that the MB×MB submatrix composed of the right MB columns of B is full rank, expanding the base matrix B into a parity-check matrix H with size of M×N, replacing ‘0’ in the base matrix B with a K×K all-‘0’ matrix Z, replacing ‘1’ in the base matrix B with a K×K circulant permutation matrix P, wherein the row number i and the column number j of ‘1’ in P meet j=(i+k) mod k, k is the offset of the circulant permutation matrix, mod indicates the modulo operation, and selecting an offset for each K×K circulant permutation matrix P;
• the parity-check sequence computing module is used for multiplying the input information sequence m by the matrix (Hp−1 Hm)T to obtain the parity-check sequence p;
• and
• the code word sequence generating module is used for combining the information sequence m with the parity-check sequence p into the code word sequence c, and outputting the same.