An LDPC parity check matrix, includes a systematic portion having a plurality of systematic elements having a value, the value each systematic element determining a cyclic shift to be applied to rows of an identity submatrix corresponding to that element; and a parity portion having a plurality of panty elements having a value, the value of each parity element determining a cyclic shift to be applied to rows of an identity submatrix corresponding to that element; wherein the weights of each column of a group of columns of the parity portion is the same. The LDPC parity check matrix may be used for data access, communication and storage, and may be used, for example for communications among a plurality of network nodes.

An encoding apparatus is provided. The encoding includes a low density parity check (LDPC) encoder which performs LDPC encoding on input bits based on a parity-check matrix to generate an LDPC codeword formed of 64,800 bits, in which the parity-check matrix includes an information word sub-matrix and a parity sub-matrix, the information word sub-matrix is formed of a group of a plurality of column blocks each including 360 columns, and the parity-check matrix and the information word sub-matrix are defined by various tables which represent positions of value one (1) present in every 360-th column.

Certain aspects of the present disclosure generally relate to techniques for compactly describing lifted low-density parity-check (LDPC) codes. A method by a transmitting device generally includes selecting a first lifting size value and a first set of lifting values; generating a first lifted LDPC code by applying the first set of lifting values to interconnect edges in copies of a parity check matrix (PCM) having a first number of variable nodes and a second number of check nodes; determining a second set of lifting values for generating a second lifted LDPC code for a second lifting size value based on the first lifted PCM and the first set of lifting values; encoding a set of information bits based the first lifted LDPC code or the second lifted LDPC code to produce a code word; and transmitting the code word.

The present disclosure relates to a pre-5th-Generation (5G) or 5G communication system to be provided for supporting higher data rates Beyond 4th-Generation (4G) communication system such as Long Term Evolution (LTE). A channel encoding method in a communication or broadcasting system includes identifying an input bit size, determining a block size (Z), determining an LDPC sequence for LDPC encoding, and performing the LDPC encoding based on the LDPC sequence and the block size.

A low density parity check (LDPC) encoder, an LDPC decoder, and an LDPC encoding method are disclosed. The LDPC encoder includes first memory, second memory, and a processor. The first memory stores an LDPC codeword having a length of 16200 and a code rate of 3/15. The second memory is initialized to 0. The processor generates the LDPC codeword corresponding to information bits by performing accumulation with respect to the second memory using a sequence corresponding to a parity check matrix (PCM).

The present disclosure relates to low-density parity-check (LDPC) encoding methods and apparatus. One example method includes encoding k information bits by using a submatrix of ((n−k)/Z+j) rows and (n/Z+j) columns at an upper left corner of a check matrix H based on a first transmission code rate R satisfying R=k/(n+j×Z), obtaining a first codeword including the k information bits and (n−k+j×Z) redundant bits, and sending the first codeword to a receive end.

A system for generating a parity check matrix for low-density parity-check (LDPC) codes includes a memory and a processing circuitry that retrieves a base matrix from the memory. The base matrix represents sets of valid and invalid positions for a set of circulant matrices. The processing circuitry determines a value for each valid position based on a heuristic function. The value for each valid position indicates a corresponding circulant matrix of the set of circulant matrices. The processing circuitry replaces each valid position with the corresponding circulant matrix based on the determined value, and each invalid position with a null matrix, to generate the parity check matrix. The parity check matrix thus generated has a high girth and equal distribution of cycles within the parity check matrix.

Methods and system for error correction based on rate adaptive LDPC codes with flexible column weights in the parity check matrices are described. Data is encoded according to a first encoding parity check matrix of a first Low Density Parity Check (LDPC) code to obtain a first codeword with first parities. The first codeword is encoded according to a second encoding parity check matrix of a second LDPC code to obtain second parities. The first codeword is received. Responsive to failure of error correction of the first codeword based on the first parities, the second parities are received. The first codeword is corrected based on the second parities and a decoding parity check matrix of a rate adaptive LDPC code that is constructed by vertically concatenating the second encoding parity check matrix and the first encoding parity check matrix and adding an all-zero sub-matrix to complete its dimensions.

Methods and apparatuses for generating optimized LDPC codes are proposed. One of the methods is a method for generating an optimized LDPC code for an asymmetric transmission channel. The method includes receiving an initial LDPC code for the asymmetric transmission channel. Further, the method includes performing a density evolution threshold optimization for the initial LDPC code in order to obtain the optimized LDPC code for the asymmetric transmission channel. A uniformly mixed symmetric channel density for the asymmetric transmission channel is used in the density evolution threshold optimization.

The present technology relates to a data processing device and a data processing method, which are capable of securing excellent communication quality in data transmission using an LDPC code. In group-wise interleave, an LDPC code in which a code length N is 16200 bits and an encoding rate r is 6/15, 8/15, or 10/15 is interleaved in units of bit groups of 360 bits. In group-wise deinterleave, a sequence of the LDPC code that has undergone the group-wise interleave is restored to an original sequence. For example, the present technology can be applied to a technique of performing data transmission using an LDPC code.