Apparatus and method for encoding and decoding a block low density parity check code

A method for generating a block low density parity check (LDPC) code, comprising the steps of:

• receiving an information word vector;
• and
• generating a first parity vector such that a vector generated by multiplying a matrix generated by summing all rows of a fourth matrix for generating a first matrix included in a generation matrix, per block by a transpose vector of the information word vector as a vector generated by cyclic-shifting a transpose vector of the first parity vector by a predetermined value, the first matrix is generated by multiplying the fourth matrix, mapped to the information word vector of a parity check matrix corresponding to a length to be applied when generating the information word vector into a block LDPC code, by a predetermined fifth matrix;
• generating a second parity vector using back substitution by a third matrix mapped to the second parity vector in the generation matrix, the third matrix has a dual-diagonal structure, the third matrix is generated by multiplying a seventh matrix mapped to the second parity vector of the parity check matrix by the fifth matrix;
• and
• generating the block LDPC code by connecting the first parity vector and the second parity vector to the information word vector;
• wherein the generation matrix is generated by modifying the parity check matrix corresponding to the length to be applied when generating the information word vector into the block LDPC code,
• wherein the generation matrix represents a multiplication of a new matrix F and the parity check matrix, exponents of all non-zero permutation matrices corresponding to a last block of the generation matrix increased by am through a modulo-Ns operation, Ns is the number of rows or columns of a permutation matrix corresponding to each of partial blocks constituting the generation matrix, identity matrices are located along a diagonal line of the generation matrix except for a last part, and am are exponents of a permutation matrix located in the last part of a diagonal line in the generation matrix, and
• wherein the generation matrix includes a second matrix mapped to the first parity vector,
• the second matrix is generated by multiplying a sixth matrix mapped to the first parity vector of the parity check matrix by the fifth matrix.