A method and apparatus for efficient data decoding is described. Data is encoded by an LDPC encoder using a G matrix. An LDPC decoder uses a modified H matrix to decode encoded blocks of data, the modified H matrix having at least two columns of its circulants swapped with each other. The encoded blocks of data are stored, decoded and reconstructed in an order that considers the circulants in the columns that have been swapped.

The present disclosure relates to low-density parity-check (LDPC) encoding methods and apparatus. One example method includes obtaining k information bits to be sent to a receive end, performing LDPC encoding on the 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 the receive end.

A transmitter is provided. The transmitter includes: an outer encoder configured to encode input bits to generate outer-encoded bits including the input bits and parity bits; a zero padder configured to constitute Low Density Parity Check (LDPC) information bits including the outer-encoded bits and zero bits; and an LDPC encoder configured to encode the LDPC information bits, wherein the LDPC information bits are divided into a plurality of bit groups, and wherein the zero padder pads zero bits to at least some of the plurality of bit groups, each of which is formed of a same number of bits, to constitute the LDPC information bits based on a predetermined shortening pattern which provides that the some of the plurality of bit groups are not sequentially disposed in the LDPC information bits.

A transmitter is provided. The transmitter includes: an outer encoder configured to encode input bits to generate outer-encoded bits including the input bits and parity bits; a zero padder configured to constitute Low Density Parity Check (LDPC) information bits including the outer-encoded bits and zero bits; and an LDPC encoder configured to encode the LDPC information bits, wherein the LDPC information bits are divided into a plurality of bit groups, and wherein the zero padder pads zero bits to at least some of the plurality of bit groups, each of which is formed of a same number of bits, to constitute the LDPC information bits based on a predetermined shortening pattern which provides that the some of the plurality of bit groups are not sequentially disposed in the LDPC information bits.

Various aspects of systems for generating parity bits for encoding based on a portion of a generator matrix are disclosed. In one aspect, a generator matrix includes a sub-block including a first set of elements circularly shifted from an identity matrix by a first amount, and a second set of elements circularly shifted from the identity matrix by a second amount. Bit permutation circuitry generates first bits according to input bits and the first amount. Each of the first bits is provided as input to a corresponding XOR device of XOR devices. Each of a set of storage registers stores an output of the corresponding XOR device. The bit permutation circuitry generates second bits according to the input bits and the second amount. The XOR devices perform bit-wise XOR operations on the stored outputs and the generated second bits, to provide a portion of the parity bits.

A transmitter is provided. The transmitter includes: an outer encoder configured to encode input bits to generate outer-encoded bits including the input bits and parity bits; a zero padder configured to constitute Low Density Parity Check (LDPC) information bits including the outer-encoded bits and zero bits; and an LDPC encoder configured to encode the LDPC information bits, wherein the LDPC information bits are divided into a plurality of bit groups, and wherein the zero padder pads zero bits to at least some of the plurality of bit groups, each of which is formed of a same number of bits, to constitute the LDPC information bits based on a predetermined shortening pattern which provides that the some of the plurality of bit groups are not sequentially disposed in the LDPC information bits.

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).

A method of characterizing a distribution of a maximum number of errors that first cause uncorrectable error correction code failure for hard low density parity check codes includes selecting a low density parity check code, generating encoded data with the low density parity check code and writing the encoded data to a number of memory blocks, reading the encoded data from the number of memory blocks and determining any pages having a first uncorrectable error correction code failure, determining a number of raw bit errors for each page having a first uncorrectable error correction code failure, incrementing an error count value corresponding to each of the numbers of raw bit errors determined, and repeating the generating, reading, determining, and incrementing steps for a predetermined range of values of a predetermined reliability statistic of the memory blocks.

A transmitter is provided. The transmitter includes: an outer encoder configured to encode input bits to generate outer-encoded bits including the input bits and parity bits; a zero padder configured to constitute Low Density Parity Check (LDPC) information bits including the outer-encoded bits and zero bits; and an LDPC encoder configured to encode the LDPC information bits, wherein the LDPC information bits are divided into a plurality of bit groups, and wherein the zero padder pads zero bits to at least some of the plurality of bit groups, each of which is formed of a same number of bits, to constitute the LDPC information bits based on a predetermined shortening pattern which provides that the some of the plurality of bit groups are not sequentially disposed in the LDPC information bits.

A low-density parity-check (LDPC) decoder performs check node computations as N different segments of the check nodes which have connections only to a codeword segment of length C/N bits as well as check nodes that have connections across the entire codeword of length C. The decoder can include a controller or other compute hardware to decode the codeword, including to perform computations for separate segments of C/N bits of the codeword. The system can perform computations including adjustment of the decode computations based on an expected error rate for selected segments of the codeword.