A method, apparatus, and non-transitory computer-readable recording medium for generating an algebraic Spatially-Coupled Low-Density Parity-Check (SC LDPC) code are provided. The method includes selecting an LDPC block code over a finite field GF(q) with a girth of at least 6; constructing a parity-check matrix H from the selected LDPC block code; replicating H a user-definable number of times to form a two-dimensional array H.sub.rep; constructing a masking matrix W with a user-definable spatially-coupled pattern; and masking a sub-matrix of H.sub.rep using W to obtain a spatially-coupled parity-check matrix H.sub.SC, wherein a null space of H.sub.SC is the algebraic SC LDPC code.

Concepts and schemes pertaining to quasi-cyclic-low-density parity-check (QC-LDPC) coding are described. A processor of an apparatus may generate a QC-LDPC code having a plurality of codebooks embedded therein. The processor may select a codebook from the plurality of codebooks. The processor may also encode data using the selected codebook. Alternatively or additionally, the processor may generate the QC-LDPC code including at least one quasi-row orthogonal layer. Alternatively or additionally, the processor may generate the QC-LDPC code including a base matrix a portion of which forming a kernel matrix that corresponds to a code rate of at least a threshold value.

Embodiments of this application disclose a example polar code encoding methods, example polar code decoding methods, and example apparatuses thereof. One example method in embodiments of this application includes generating an input vector, where the input vector includes T subblocks, a first information bit of a first subblock is obtained by replicating a second information bit of a second subblock, the first subblock and the second subblock are subblocks of the T subblocks, a sequence number of the first subblock is after a sequence number of the second subblock, and T is an integer greater than or equal to 2. Polar encoding can then be performed on the input vector to obtain an encoded bit.

Aspects of the disclosure are directed to processing signals including data exhibiting characteristics that facilitate assessment of transmission errors. As may be implemented in accordance with one or more embodiments, parameters are generated based signal transmission characteristics and are indicative of a different types of signal characteristics, including an amount of error correction that has been carried out on the signal. Two or more of the parameters are selected based on properties of signal disturbance under different reception conditions for the signal, and a degree of disturbance in the signal is predicted based on the selected parameters and signal conditions for the respective parameters at which the signal cannot be corrected. An output generated with the signal is then controlled, based on the predicted degree of disturbance and a threshold degree of disturbance.

Systems, apparatuses, and methods for generating error correction codes (ECCs) with two check symbols are disclosed. In one embodiment, a system receives a data word of length N2 symbols, wherein N is a positive integer greater than 2, wherein each symbol has m bits, and wherein m is positive integer. The system generates a code word of length N symbols from the data word in accordance with a linear code defined by a parity check matrix. The parity check matrix is generated based on powers of , wherein is equal to raised to the (2.sup.m/41) power, is equal to a raised to the (2.sup.m/2+1) power, and is a primitive element of GF(2.sup.m). In another embodiment, the system receives a (N, N2) code word and decodes the code word by generating a syndrome S from the code word using the parity check matrix.

In an illustrative example, a method includes receiving data that includes a set of data symbols. The method further includes generating a set of parity symbols based on the set of data symbols using an erasure correcting code. The set of parity symbols includes at least a first parity symbol that is generated based on a first proper subset of the set of data symbols. The first parity symbol enables recovery of a data symbol of the first proper subset independently of a second proper subset of the set of data symbols.

A processor of an apparatus establishes a wireless communication link with at least one other apparatus via a transceiver of the apparatus. The processor wirelessly communicates with the other apparatus via the wireless communication link by: selecting a first shift-coefficient table from a plurality of shift-coefficient tables; generating a QC-LDPC code using a base matrix and at least a portion of the first shift-coefficient table; selecting a codebook from a plurality of codebooks embedded in the QC-LDPC code; storing the selected codebook in a memory associated with the processor; encoding data using the selected codebook to generate a plurality of modulation symbols of the data; and controlling the transceiver to multiplex, convert, filter, amplify and radiate the modulation symbols as electromagnetic waves through one or more antennas of the apparatus to transmit the modulation symbols of the data to the other apparatus via the wireless communication link.

Methods and devices are described for determining reliabilities of bit positions in a bit sequence for information bit allocation using polar codes. The reliabilities are calculated using a weighted summation over a binary expansion of each bit position, wherein the summation is weighted by an exponential factor that is selected based at least in part on the coding rate of the polar code. Information bits and frozen bits are allocated to the bit positions based on the determined reliabilities, and data is polar encoded as the information bits. The polar encoded data is then transmitted to a remote device.

The disclosure provides a non-orthogonal multiple access data transmission method and a transmission device using the same. The method includes: performing channel encoding for a plurality of data and a plurality of identifiers respectively corresponding to the plurality of data by using Raptor code so as to generate a Raptor codeword, wherein the plurality of identifiers respectively correspond to a plurality of receiving terminals; and modulating the Raptor codeword to generate a plurality of modulation symbols and broadcasting the plurality of modulation symbols.

A decoder for decoding a received set of blocks each including a plurality of data symbols and a plurality of parity symbols, wherein the received set of blocks is a subset of a complete set of blocks, the complete set of blocks including at least one erased block not included in the received set of blocks, the decoder including: a storage for a coding matrix which is the kronecker product of a totally non-singular matrix with an antidiagonal matrix; and a processor operable to determine data symbols of the at least one erased block using the encoding matrix.