… Each symbol is checked by a small number of parity checks, and each parity check includes
a … Step 2: Perform semi-Gaussian elimination on the permuted parity-check matrix from left to …

… -Density Parity-Check (LDPC) codes based on Tensor product of matrices. In this paper,
first a general construction method of regular LDPC codes exploiting permutation matrices is …

… It proves that each circulant in this array is either a circulant permutation matrix (CPM) or
a zero matrix (ZM). A CPM is a permutation matrix for which each row is the cyclic-shift of the …

… [\begin {array}{cc} 1 & 0 \\ 1 & 1 \end {array}\right ]\) and B N is the bit-reversal permutation
matrix. The popular decoding algorithms of polar codes are SC algorithm and BP algorithm. …

We present a tutorial overview of low-density parity-check (LDPC) codes. As the name suggests,
LDPC codes are block codes defined by a parity-check matrix that is sparse. They were …

… in the base matrix A can be eliminated in the parity check matrix H of QC-LDPC coeds by
selecting the shift value P ij of the cyclic permutation matrix. In particular, if the girth of base …

… permutation matrices, like in the original McEliece cryptosystem, can be restored by using
codes with increased parity-check matrix … the density of the parity-check matrices of the private …

… to construct a good parity-check matrix for specified rate and … graph associated to the
paritycheck matrix had a very negative effect … We will use Ik for the N 2N circulant permutation …

… as reversible, the weights of parity check matrix can be converted into the weights of the
original parity check matrix (3, 6) to complete the parity check matrix that can be encoded. Code …

… We arrange the four 7r-rotation permutation matrices as shown to cre ate the Ha sub-matrix
for a rate | code..................................................... 73 5.3 This is the basic configuration of the Hd …