Any (n, k) block code, if the relationship between its information elements and supervision elements is linear, that is, can be described by a linear equation, it is called a linear block code.
The low-density parity check code (LDPC code) is essentially a linear block code that maps the information sequence into a transmission sequence, that is, a codeword sequence, through a generator matrix G. For the generator matrix G, there is a parity check matrix H completely equivalently, and all codeword sequences C constitute the null space of H, that is.
LDPC simulation system diagram The parity check matrix H of DLPC code is a sparse matrix. Relative to the length of rows and columns, the number of non-zero elements in each row and column of the check matrix (we are used to calling Row weight, column weight) are very small, which is why LDPC codes are called low-density codes. Due to the sparsity of the check matrix H and the different rules used in its construction, the coding bipartite graph (Taner graph) of different LDPC codes has different closed loop distributions. The closed loop in the bipartite graph is an important factor affecting the performance of the LDPC code. It causes the LDPC code to show completely different decoding performance under a type of iterative decoding algorithm similar to the Belief ProPagation algorithm.
When the row weight and column weight of H remain unchanged or as uniform as possible, we call such an LDPC code a regular LDPC code. On the contrary, if the column and row weights vary greatly, it is called a regular LDPC code. is a non-regular LDPc code. The research results show that the performance of correctly designed non-regular LDPC codes is better than that of regular LDPC. Depending on whether the elements in the check matrix H belong to GF(2) or GF(q)(q=2p), we can also divide the LDPC codes into binary domain or multivariate domain LDPC codes. Research shows that the performance of multivariate domain LDPC codes is better than that of binary domains.