The present disclosure provides a method for optimizing a protograph-based LDPC code over an underwater acoustic (UAW) channel. The traditional protograph-based LDPC code over an UAW channel does not consider performance in an error floor region. The method first determines parameters such as a protograph-based LDPC code length, a basic protograph, a target decoding threshold, a threshold adjustment factor, and an ACE check parameter. The protograph is optimized, and the method constructs a parity check matrix by using a UAW channel-based PEG/ACE hybrid algorithm, performs ACE check on the parity check matrix, and calculates a decoding threshold for the matrix passing the check. If the decoding threshold is within a range of an iterative decoding threshold, the parity check matrix is a final optimized matrix. Otherwise, the method continues to optimize the protograph until a parity check matrix passing the check is obtained.

The present disclosure provides a method for optimizing a protograph-based LDPC code over an underwater acoustic (UAW) channel. The traditional protograph-based LDPC code over an UAW channel does not consider performance in an error floor region. The method first determines parameters such as a protograph-based LDPC code length, a basic protograph, a target decoding threshold, a threshold adjustment factor, and an ACE check parameter. The protograph is optimized, and the method constructs a parity check matrix by using a UAW channel-based PEG/ACE hybrid algorithm, performs ACE check on the parity check matrix, and calculates a decoding threshold for the matrix passing the check. If the decoding threshold is within a range of an iterative decoding threshold, the parity check matrix is a final optimized matrix. Otherwise, the method continues to optimize the protograph until a parity check matrix passing the check is obtained.

Provided is a system and method for determining a generalized Low-Density Parity-Check (LDPC) code for forward error correction channel coding that has a repeat-accumulate code structure.

A data transmitting method using an LDPC code as an error correction code is provided. The method includes providing a parity check matrix of LDPC code, wherein the size of the parity check matrix is (m1+m2)×(n1+n2); in a sending side, encoding an input data of K bits with a encoder to generate a first block code of (n1+n2) bits, according to the parity check matrix; through a transmitting channel, sending n1 bits of the first block code from the sending side to a receiving side, wherein n2 bits of the first block code are not transmitted; and receiving the n1 bits of the first block code in the receiving side, and using the parity check matrix to perform a decoding algorithm to the received first block code to iterative decodes a second block code of (n1+n2) bits with a decoder. Furthermore, a data decoding method thereof is also provided.

A method for quasi-cyclic low-density parity-check (QC-LDPC) encoding and decoding of a data packet by a lifted matrix is provided, the method comprising: lifting the QC-LDPC code for maximal code length N.sub.max and maximal circulant size Z.sub.upper of the base matrix; generating a plurality of optimal values r.sub.i for a plurality of circulants Z.sub.1, Z.sub.2, . . . , Z.sub.upper based on the QC-LDPC code lifted for maximal length N.sub.max, 0r.sub.iZ.sub.upper1; saving the generated plurality of optimal values r.sub.i corresponding to the plurality of circulants Z.sub.1, Z.sub.2, . . . , Z.sub.upper and a matrix for the QC-LDPC code lifted for maximal length N.sub.max in the memory; receiving a current circulant Z.sub.current from the plurality of circulants Z.sub.1, Z.sub.2, . . . , Z.sub.upper; selecting a current optimal value r.sub.current from the plurality of optimal values r.sub.i stored in the memory corresponding to the current circulant Z.sub.current; and lifting the base matrix based on the current optimal value r.sub.current.

The method for shuffled decoding of LDPC codes includes calculating check-variable mutual information which is mutual information of a message propagating from a plurality of check nodes to a plurality of variable nodes by a check-variable mutual information calculating unit, calculating variable-check mutual information which is mutual information of a message propagating from the plurality of variable nodes to the plurality of check nodes connected to the plurality of variable nodes based on the check-variable mutual information by a variable-check mutual information calculating unit, and Calculating the entire mutual information which is a sum of variable-check mutual information for each of the plurality of variable nodes and determines an operation order of a variable node having the largest entire mutual information among the plurality of variable nodes to be next, by an operation order determining unit.

A decoder circuit includes an input to receive a first codeword encoded based on a quasi-cyclic low-density parity-check (QC LDPC) code and a plurality of memory banks to store the received codeword. Each column of the received codeword is assigned to one of the plurality of memory banks based at least in part on an order of the plurality of columns in the received codeword. A first reordering stage is to change the memory bank assignment for one or more of the plurality of columns by reordering the columns in the received codeword. An LDPC decoder is to decode the reordered codeword stored in the plurality of memory banks based at least in part on the QC LDPC code. A second reordering stage is to output the decoded codeword from the plurality of memory banks based at least in part on an order of the columns in the first codeword.

Provided is an encoder, a decoder, a computer-readable medium and methods of forward error correction channel encoding/decoding within a HARQ scheme, based on a generalized quasi-cyclic low-density parity-check code comprising a Cordaro-Wagner component code.

Provided is a system and method for determining a generalized LDPC code for forward error correction channel coding that has a repeat-accumulate code structure.

According to one embodiment, a memory system comprises an encoder that encodes by a graph code and a data holding unit that holds data to be used in encoding. A check matrix of the graph code includes first to sixth submatrices, and the encoder produces a first vector obtained by multiplying an information word and the first submatrix, produces a second vector obtained by multiplying the information word and the third submatrix, produces a third vector obtained by multiplying the first vector and the fifth submatrix inverted in sign, produces a fourth vector obtained by adding the third vector and the second vector, produces a first parity obtained by multiplying the fourth vector and the data, produces a fifth vector obtained by multiplying the first parity and the second submatrix inverted in sign, and produces a second parity obtained by adding the fifth vector and the first vector.