33 results about "Bidiagonal matrix" patented technology

An apparatus and method for generating an encoding matrix for a low density parity check (LDPC) code having a dual-diagonal matrix as a parity check matrix are disclosed. The apparatus and method construct an information sub-matrix of the encoding matrix with a predetermined number of square matrixes according to a predetermined code rate such that each of the square matrixes has columns and rows with a weight of 1 and has a different offset value, combine the square matrixes with the dual-diagonal matrix, and perform inter-row permutation on the information sub-matrix.

An apparatus and method for encoding low-density parity check (LDPC) codes. The method for generating a low-density parity check code formed of an information-part matrix and a parity-part matrix comprises the steps of converting the information-part matrix into an array code structure and assigning a degree sequence to each submatrix column; extending a dual-diagonal matrix corresponding to the parity-part matrix such that an offset value between diagonals has a random value; lifting the normalized dual-diagonal matrix; determining an offset value for cyclic column shift for each submatrix of the lifted normalized dual-diagonal matrix; and determining a parity symbol corresponding to a column of the parity-part matrix.

A method is provided for puncturing a low density parity check (LDPC) code decoded by a parity check matrix that is expressed by a factor graph including a check node and a bit node, being connected to each other at an edge, and includes a parity part having a dual diagonal matrix with a single 3-weight column and the remaining columns being 2-weight columns. The method includes generating a puncturing pattern such that bits of the LDPC code are punctured in an order of a bit mapped to a column with a higher weight from among the columns constituting the parity part; and puncturing the LDPC code according to the generated puncturing pattern.

Disclosed is a method for puncturing a Low Density Parity Check (LDPC) code that is expressed by a factor graph having a check node and a variable node, connected to each other by an edge, and is decoded by a parity check matrix including a parity part having a single weight-3 column and a dual-diagonal matrix. The method includes selecting 1-step recoverable (1-SR) variable nodes with the highest quality including a variable node mapped to a weight-3 column, and setting a first puncturing priority group using the selected 1-SR variable nodes, selecting k-step recoverable (k-SR) variable nodes with the highest quality in the next step k taking into account the variable nodes selected in the current step, and setting a priority group for each individual step, puncturing an LDPC code mapped to a variable node belonging to a corresponding group according to priority of each group obtained in the preceding steps.

A high-speed quasi-cyclic low density parity check (QC-LDPC) coding apparatus for coding inputted information into a generator matrix having a dual diagonal matrix format includes: a parity bit generation unit configured to generate an arbitrary parity bit; a temporary parity bit generation unit configured to constitute the inputted information with circulants, and shift and combine the respective circulants at each row to generate a temporary parity bit; a corrected bit generation unit configured to generate corrected bits of parity bits by using an output of the temporary parity bit generation unit; and a parity bit correction unit configured to correct the temporary parity bit by reflecting an output of the corrected bit generation unit to the output of the temporary parity bit generation unit.

Methods, apparatuses, and systems are presented for performing data encoding involving receiving a sequence of data bits, encoding the sequence of data bits in accordance with a parity check matrix (H-matrix) to generate a sequence of encoded bits, wherein the H-matrix is capable of being partitioned into a first matrix and a second matrix, the first matrix being a dual-diagonal matrix, the second matrix comprising one or more vertically stacked sub-matrices, each sub-matrix consisting of a plurality of columns, each column having a column weight of no more than 1, wherein the second matrix is capable of being expressed as a product of a parity check matrix, an interleaver permutation matrix, and a repeat block matrix, and the interleaver permutation matrix satisfies a clash-free interleaver constraint, and outputting the sequence of encoded bits.

The invention discloses an encoding method of low bit-rate LDPC (Low Density Parity Check) code, including the following steps: step 1, matrixes H and H are respectively constructed, the H matrix is a diagonal matrix, H is an array matrix with q multiplied by 1 and consists of q end-around-shift permutation matrixes Q; the permutation matrix Q consists of b multiplied by b step permutation matrixes Q having row weight and line weight of 1, at most one element of 1 on each diagonal line and the rest elements of 0; step 2, an H matrix with the size of equal to bq multiplied b(q+1) is constructed; step 3, check vector c is constructed, c is equal to (p1, 1=1, 2, ..., M), p1 represents the value of any first check bit, and M is the length of check bit; step 4, according to the check vector c=(p1), the inputted information vector c is equal to (dj), and coded code word c=(cc) is obtained. In the method of the invention, an algebraic method used by end-around-shift value of Q permutation matrix leads belief propagation iterative decoding algorithm to be more easily realized in parallel; bidiagonal matrix structural characteristic of H matrix can encode low rate LDPC code in a recursion manner, and has linear time computing complexity. The simulation performance is superior to the performance of the existing low rate error correcting code, thereby being capable of reaching a signal noise ratio of 0.4 dB and having ratio compatibility.

The invention discloses a method for generating an LDPC (Low Density Parity Check) code check matrix and an LDPC code coding method based on the check matrix. The method for generating the LDPC code check matrix comprises the steps of firstly constructing an index matrix and then constructing the check matrix by using the index matrix and specifically comprises the steps of: extending each element axy in the index matrix into a 2<m>-order (0,1) square matrix, namely a formula shown in a drawing, and then forming the check matrix; and constructing an equation shown in a drawing, wherein the element of each square matrix in the position of a formula shown in a drawing is 1, the other elements are all 0, and i is equal to 1, 2, 3 or 2<m>. Furthermore, a combination of the check matrix generated by using the method and a dual-diagonal matrix is provided. The invention further provides the LDPC code coding method adopting the check matrix generated by adopting any of the methods. The methods have the advantages of easiness in design, low coding complexity, small storage space and excellent performance.

The invention provides a method and a device for the singular value and feature value composition of a matrix on a processing system. The method for singular value composition includes: the matrix is converted into a bidiagonal matrix, and a sandwich matrix which needs to be converted into a singular vector matrix is obtained at the same time; submatrixes of which the elements are not zero are found out and converted in an iterative way on the vice diagonals in the bidiagonal matrix so that the bidiagonal matrix can be converged into a diagonal matrix and the sandwich matrix can be converted into the singular vector matrix; in each iterative step: Givens rotation parameter groups generated in the QR iterative processes of the submatrixes and the positions of the left boundary and the right boundary of the corresponding submatrixes which need to use the Givens rotation parameter groups in the sandwich matrix are accumulated in a memory; and when the number of the accumulated Givens rotation parameter groups reaches the preset threshold value, the Givens rotation parameter groups are utilized to carry out the Givens rotation of the sandwich matrix, wherein the threshold value is an integer which is higher than or equal to 2.

A method of and an apparatus for generating a block-based low density parity check (LDPC) matrix, where calculation of an inverse matrix is not necessary and back-substitution is possible over the entire matrix area, and a recording medium having recorded thereon code for implementing the method. An area of the LDPC matrix is vertically divided based on respective lengths of first and second parity bit vectors and, a block-based matrix is generated such that a double diagonal matrix is arranged in an upper portion of an area corresponding to the second parity bit vector among areas into which the LDPC matrix is vertically divided., The area of the LDPC matrix is horizontally divided based on a position of the double diagonal matrix, and block-based matrices are generated in the divided areas of the LDPC matrix, to satisfy a condition that column weights (Wc) are uniform.

The invention discloses a method for generating LDPC codes. The method comprises the following steps that: step one, the size of a check matrix of the LDPC codes is set, wherein the check matrix is divided into an information portion and a check portion, wherein the check portion is obtained through dual diagonal matrix interweaving; step two, the information portion is divided into a plurality of sub information matrixes, wherein each sub information matrix comprise a plurality of circulatory arrays, and the column degree of each sub information matrix is determined, wherein the column degree is the number of non-zero circulatory arrays contained in the sub information matrix; step three, the positions of the non-zero circulatory arrays of each sub information matrix are determined; and step four, the offset of the non-zero circulatory arrays of each sub information matrix is determined. According to the method of the invention, on the one hand, the minimum distance of the codes is decreased through adopting an interweaving method, and on the other hand, optimal degree distribution and optimal circulatory matrix distribution can be researched by means of tools.

The present invention provides a low-complexity geometric mean value decomposition precoding implementation method based on bidiagonalization. The method comprises the following steps: (1) calculatinga conjugate transpose of a channel matrix and own product; (2) based on a given Hermitian matrix bidiagonalization method, changing the channel matrix into a bidiagonal matrix through Givens rotation; (3) based on a given geometric mean value decomposition method, changing the bidiagonal matrix into an upper triangular matrix where the diagonal elements all equal to the geometric mean value of the channel matrix eigenvalues through Givens rotation; (4) constructing a precoding matrix with the geometric mean value decomposed, that is, the product of all Givens right rotation matrices. The technical scheme can determine the number of iterations, and uses the Hermitian matrix for solutions further to reduce the implementation complexity and reduce the use of the CORDIC (Coordinate Rotation Digital Computer) module. The method utilizes the properties of the Hermitian matrix to effectively reduce the implementation complexity of geometric mean value decomposition precoding based on bidiagonalization.