A storage network operates by: issuing a read threshold number of read slice requests to storage units of a set of storage units, where the read threshold number of read slice requests identifies a read threshold number of encoded slices of a set of encoded slices corresponding to a data segment; when one or more other encoded data slices of the read threshold number of encoded slices is not received within a time threshold, facilitating receiving a decode threshold number of encoded slices of the set of encoded slices; decoding the decode threshold number of encoded slices to produce recovered encoded data slices, wherein a number of the recovered encoded data slices corresponds to the read threshold number minus a number of the encoded slices received within the time threshold; and outputting the recovered encoded data slices and the encoded slices of the read threshold number of encoded slices received within the time threshold.

A method of reading from a storage medium to recover a group of information sectors, each comprising a respective information payload. The medium stores redundancy data comprising a plurality of separate redundancy codes for the group, each code being a linear sum of terms, each term in the sum being the information payload from a different respective one of the information sectors in the group weighted by a respective coefficient of a set of coefficients for the redundancy code. The method comprises, after the redundancy data has already been stored on the medium: identifying a set of k′ information sectors to be recovered; selecting k′ of the redundancy codes; determining a square matrix E of the k′ information sectors by the k′ sets of coefficients of the selected codes; determining a matrix D being a matrix inverse of E; and recovering the k′ information payloads from the inverse matrix D.

A system and method for distributing data over a plurality of remote storage nodes. Data are split into segments and each segment is encoded into a number of codeword chunks. None of the codeword chunks contains any of the segments. Each codeword chunk is packaged with at least one encoding parameter and identifier, and metadata are generated for at least one file and for related segments of the at least one file. The metadata contains information to reconstruct from the segments, and information for reconstructing from corresponding packages. Further, metadata are encoded into package(s), and correspond to a respective security level and a protection against storage node failure. A plurality of packages are assigned to remote storage nodes to optimize workload distribution. Each package is transmitted to at least one respective storage node as a function iteratively accessing and retrieving the packages of metadata and file data.

A system for software error-correcting code (ECC) protection or compression of original data using ECC data in a first memory is provided. The system includes a processing core for executing computer instructions and accessing data from a main memory, and a non-volatile storage medium for storing the computer instructions. The software ECC protection or compression includes: a data matrix for holding the original data in the first memory; a check matrix for holding the ECC data in the first memory; an encoding matrix for holding first factors in the main memory, the first factors being for encoding the original data into the ECC data; and a thread for executing on the processing core. The thread includes a Galois Field multiplier for multiplying entries of the data matrix by an entry of the encoding matrix, and a sequencer for ordering operations using the Galois Field multiplier to generate the ECC data.

One coding method of a plurality of coding methods including at least a first coding method and a second coding method is selected, an information sequence is encoded by using the selected coding method, and an encoded sequence obtained by performing predetermined processing on the information sequence is modulated and transmitted. The first coding method is a coding method having a first coding rate, for generating a first encoded sequence by performing puncturing processing on a generated first codeword by using a first parity check matrix. The second coding method is a coding method having a second coding rate, for generating a second encoded sequence by performing puncturing processing on a generated second codeword by using a second parity check matrix that is different from the first parity check matrix, the second coding rate after the puncturing process being different from the first coding rate.

Embodiment techniques map parity bits to sub-channels based on their row weights. In one example, an embodiment technique includes polar encoding, with an encoder of the device, information bits and at least one parity bit using the polar code to obtain encoded data, and transmitting the encoded data to another device. The polar code comprises a plurality of sub-channels. The at least one parity bit being placed in at least one of the plurality of sub-channels. The at least one sub-channel is selected from the plurality of sub-channels based on a weight parameter.

A method of data recovery for a distributed storage system is a method of recovering multiple failed nodes concurrently with the minimum feasible bandwidth when failed nodes exist in a distributed storage system. By means of selecting assistant nodes, obtaining helper data sub-blocks through computing the selected assistant nodes, then computing a repair matrix and finally multiple the repair matrix and the helper data sub-blocks, the missing data blocks are reconstructed; or the missing data blocks are reconstructed by decoding. The method is applicable to data recovery in the case of any number of failed nodes and any reasonable combinations of coding parameters. The data recovery herein can reach the theoretical lower limit of the minimum recovery bandwidth.

Disclosed are systems, methods, and software for generating spatially-coupled low-density parity-check (SC-LDPC) codes. A method for generating SC-LDPC codes includes generating one or more quasi-cyclic low-density parity-check (QC-LDPC) codes, and also includes assigning at least one of the generated one or more QC-LDPC codes as one or more template codes. The method further includes copying at least a portion of the one or more template codes to introduce irregularity. The method also includes shifting one or more template codes on a sub-block basis to generate at least one SC-LDPC code. As compared to known LDPC code generation modalities, the disclosed invention provides a simplified technique for implementation in streamlined hardware which has more general applicability across both present, and anticipated, communication systems, including those adapted for use with optical communications, wireless communications, and 5G as well as future 6G.

A transmitting apparatus and a receiving apparatus are provided. The transmitting apparatus includes: an encoder configured to generate a low density parity check (LDPC) codeword by performing LDPC encoding; an interleaver configured to interleave the LDPC codeword; and a modulator configured to modulate the interleaved LDPC codeword according to a modulation method to generate a modulation symbol. The interleaver is formed of a plurality of columns each including a plurality of rows and includes a block interleaver configured to divide each of the plurality of columns into a first part and a second part and interleave the LDPC codeword, the number of rows constituting each column divided into the first part is determined differently depending upon the modulation method, wherein the number of rows constituting each column divided into the second part is determined depending upon the number of rows constituting each column divided into the first part.

The present invention related to a 5G or pre-5G communication system to be provided to support a higher data transmission rate since 4G communication systems like LTE. The present invention relates to a method and an apparatus for encoding a channel in a communication or broadcasting system supporting parity-check matrices having various sizes are provided. The method for encoding a channel includes determining a block size of the parity-check matrix; reading a sequence for generating the parity-check matrix, and transforming the sequence by applying a previously defined operation to the sequence based on the determined block size.