A check-matrix generating method includes a quasi-cyclic matrix generating step of generating a regular quasi-cyclic matrix in which cyclic permutation matrices are arranged in a row direction and a column direction and specific regularity is given to the cyclic permutation matrices; a mask-matrix generating step of generating a mask matrix capable of supporting a plurality of encoding rates, for making the regular quasi-cyclic matrix into irregular; a masking step of converting a specific cyclic permutation matrix in the regular quasi-cyclic matrix into a zero-matrix using a mask matrix corresponding to a specific encoding rate to generate an irregular masking quasi-cyclic matrix; and a check-matrix generating step of generating an irregular parity check matrix with an LDGM (low-density generation matrix) structure in which the masking quasi-cyclic matrix and a matrix in which the cyclic permutation matrices are arranged in a staircase manner are arranged in a predetermined location.