An inter-die double data rate (DDR) data transfer scheme is provided. In particular, the data transfer scheme utilizes an error correction code (ECC) encoding scheme that exploits the DDR property that a single microbump defect can only yield four possible error scenarios. A specialized single error correcting, double error detecting, and double adjacent error correcting (SEC-DED-DAEC) encoding scheme that imposes at least four parity check matrix constraints may be used. Configured and operated in this way, a fewer number of parity check bits are required to detect data bit errors associated with a single defective microbump.

A system, method and apparatus for encoding and decoding data in a distributed data storage and retrieval system. Data destined for storage is converted into information vectors, and the information vectors are multiplied by a binary encoder matrix to form systematic codewords. The binary encoder matrix is formed as a binary representation of an encoding matrix, the encoding matrix matrix comprising an identity matrix and a special Cauchy matrix, where each element in encoding matrix is an element of an extension field.

An encoding circuit includes: a polar encoding unit capable of encoding a polar code of N bits; a frozen bit adding unit that generates a first sequence by adding frozen bits to an input signal; and a bit arrangement changing unit that: generates a second sequence of N bits by arranging the first sequence in the second sequence according to an arrangement rule dependent on a ratio of N.sub.t bits, being a code length of a polar code to be encoded and being N bits or less, and N bits, and setting bit values at bit positions other than positions where the first sequence is arranged in the second sequence to zero when N.sub.t bits are less than N bits; and inputs the second sequence to the polar encoding unit. A code word of N.sub.t bits is generated by thinning processing based on a result of encoding the second sequence.

A system for decoding a transmission include a client device configured to receives a superposition via one or more communication links. The superposition may correspond to a transmission encoded into a plurality of fragments. The system may determine a coefficient for each fragment contained in the superposition and initialize a decoding process. The decoding process may facilitate determining a value of each fragment based on the identified coefficient of each fragment in the superposition. Advantageously, the system, through use of a the one or more communication links, may be configured to decode the transmission to derive information transmitted from a data source quickly and reliably.

Systems and methods are provided for decoding data read from non-volatile storage devices. A method that may include decoding a first codeword read from a storage location of a non-volatile storage device using a first decoder without soft information, determining that the first decoder has failed to decode the first codeword, decoding the first codeword using a second decoder without soft information, determining that the second decoder has succeeded in decoding the first codeword, generating soft information associated with the storage location using decoding information generated by the second decoder and decoding a subsequent codeword from the storage location using the soft information associated with the storage location. The second decoder may be more powerful than the first decoder.

What is proposed is a solution for processing errors in a sequence of bits, wherein the sequence of bits, in the error-free case, forms a codeword of an error code, wherein the error code is based on an H-matrix or is able to be determined thereby, wherein an error syndrome is determined for the sequence of bits, wherein a link is determined between components of the error syndrome and parts of the H-matrix, and wherein two adjacent bits in the sequence of bits are corrected if the link adopts a predefined value.

Devices and methods may be used to append a scalable (1) of parity bits in a data packet that scales with a number of data bits in a payload of the data packet. The parity bits may be generated utilizing a table of entries. In some examples, each entry in the table corresponds to a number of the data bits to be included in the payload; and each column of the table may be used to generate a corresponding parity bit of the one or more parity bits.

Devices and methods may be used to append a scalable (1) of parity bits in a data packet that scales with a number of data bits in a payload of the data packet. The parity bits may be generated utilizing a table of entries. In some examples, each entry in the table corresponds to a number of the data bits to be included in the payload; and each column of the table may be used to generate a corresponding parity bit of the one or more parity bits.

A system for decoding a transmission include a client device configured to receives a superposition via one or more communication links. The superposition may correspond to a transmission encoded into a plurality of fragments. The system may determine a coefficient for each fragment contained in the superposition and initialize a decoding process. The decoding process may facilitate determining a value of each fragment based on the identified coefficient of each fragment in the superposition. Advantageously, the system, through use of a the one or more communication links, may be configured to decode the transmission to derive information transmitted from a data source quickly and reliably.

A decoding device and a decoding method which relate to: receiving a codeword; estimating a number of errors included in the received codeword; and decoding the codeword based on the estimated number of errors using at least one of a first parity check matrix and a second parity check matrix, wherein the first parity check matrix corresponds to a first low-density parity check (LDPC) code, and the second parity check matrix corresponds to a second LDPC code, and wherein the first parity check matrix is based on a first code type, and the second parity check matrix is based on a second code type different from the first code type.