Systems, devices, and methods for encoding information bits for storage, including encoding information bits and balance bits to obtain a first bit chunk of a first arrangement; permuting the first bit chunk to obtain a second bit chunk of a second arrangement; encoding the second bit chunk to obtain a third bit chunk of the second arrangement; permuting a first portion of the third bit chunk to obtain a fourth bit chunk of the first arrangement, and encoding the fourth bit chunk to obtain a fifth bit chunk of the first arrangement; permuting a second portion of the third bit chunk, and adjusting the balance bits based on the fifth bit chunk and the permutated second portion of the third bit chunk; adjusting the first arrangement based on the adjusted balance bits, and obtaining a codeword based on the adjusted first arrangement; and transmitting the codeword to a storage device.

There is provided a method for generating a burst error correction code. The method comprises: setting a mother code; defining a syndrome set corresponding to each burst error pattern for at least two burst error patterns to be corrected based on the mother code; shortening a column of a PCM (parity check matrix) of the mother code so that the defined syndrome sets are relatively prime; and designing an error correction code for the each burst error pattern based on an optimal generator polynomial maximizing a length of the shortened code within a range of a length of a parity bit of the mother code or a syndrome vector included in the syndrome set that is relatively prime.

A method for channel-coding information bits using a code generation matrix including 32 rows and A columns corresponding to length of the information bits includes, channel-coding the information bits having “A” length using basis sequences having 32-bit length corresponding to columns of the code generation matrix, and outputting the channel-coded result as an output sequence. If “A” is higher than 10, the code generation matrix is generated when (A−10) additional basis sequences were added as column-directional sequences to a first or second matrix. The first matrix is a TFCI code generation matrix composed of 32 rows and 10 columns used for TFCI coding. The second matrix is made when at least one of an inter-row location or an inter-column location of the first matrix was changed. The additional basis sequences satisfy a value 10 of a minimum Hamming distance.

An error correction and fault tolerance method and system for an array of disks is presented. The array comprises k+5 disks, where k disks store user data and 5 disks store computed parity. The present invention further comprises a method and a system for reconstituting the original content of each of the k+5 disks, when up to 5 disks have been lost, wherein the number of disks at unknown locations is E and the number of disks wherein the location of the disks is known is Z. All combinations of faulty disks wherein Z+2×E≤4 are reconstituted. Some combinations of faulty disks wherein Z+2×E≥5 are either reconstituted, or errors are limited to a small list.

An encoding method and apparatus, a decoding method and apparatus, and a device are provided. The encoding method includes obtaining K to-be-encoded bits (S301), where K is a positive integer; determining a first generator matrix, where the first generator matrix includes at least two sub-blocks distributed based on a preset position relationship, and the sub-block includes a plurality of first generator matrix cores (S302); generating a second generator matrix based on the first generator matrix, where the second generator matrix includes T sub-blocks, and a position relationship between two adjacent sub-blocks of the T sub-blocks is determined based on the preset position relationship (S303), where T is a positive integer; and polar encoding the K to-be-encoded bits based on the second generator matrix (S304), to obtain encoded bits. This reduces encoding/decoding complexity.

An apparatus is described. The apparatus includes a memory chip. The memory chip has an error correction code (ECC) encoder logic circuit and an ECC decoder logic circuit. The ECC decoder logic circuit is to place an additional one or more errors that result from incorrect error correction applied to a read code word into a same block of multiple blocks of the read code word's raw data bit portion where original errors in the read code word existed before the read code word was decoded by the ECC decoder logic circuit.

Methods, apparatuses and systems are provided for constructing and modulating polar codes. Such procedures may involve identifying nonuniform channel conditions, selecting a modulation order, configuring a plurality of component codes and incremental ratios for Unequal Error Protection (UEP), identifying initial code construction parameters for each component code, calculating modified code construction parameters based on the incremental ratios for UEP, and encoding the component polar codes according to the modified construction parameters. Each component code may be comprised of a plurality of input bits. The initial and modified code construction parameters may include a number of unfrozen and frozen input bits, and identifying a number of unfrozen and frozen input bits may involve calculating and comparing reliability values for each bit. Calculating and comparing reliability values for each bit may involve applying a Polarization Weight (PW)-based method.

A method for the redundant transmission of data by means of light-based communication may include a data stream to be transmitted that is converted into symbols. This data stream is converted from bipolar symbols into multiple partial data streams having e.g. unipolar-positive symbols. The partial data streams are converted into multiple semi-redundant signals that are then transmitted to the receiver via multiple light-based channels. In the receiver, the received signals are converted back again analogously to when they were sent, in order to obtain the original data stream again.

An apparatus is described. The apparatus includes a memory chip. The memory chip has an error correction code (ECC) encoder logic circuit and an ECC decoder logic circuit. The ECC decoder logic circuit is to place an additional one or more errors that result from incorrect error correction applied to a read code word into a same block of multiple blocks of the read code word's raw data bit portion where original errors in the read code word existed before the read code word was decoded by the ECC decoder logic circuit.

A method for channel-coding information bits using a code generation matrix including 32 rows and A columns corresponding to length of the information bits includes, channel-coding the information bits having “A” length using basis sequences having 32-bit length corresponding to columns of the code generation matrix, and outputting the channel-coded result as an output sequence. If “A” is higher than 10, the code generation matrix is generated when (A-10) additional basis sequences were added as column-directional sequences to a first or second matrix. The first matrix is a TFCI code generation matrix composed of 32 rows and 10 columns used for TFCI coding. The second matrix is made when at least one of an inter-row location or an inter-column location of the first matrix was changed. The additional basis sequences satisfy a value 10 of a minimum Hamming distance.