Some embodiments are directed to an electronic cryptographic device arranged to determine a cryptographic key. The cryptographic device can include a physically unclonable function (PUF) arranged to produce a first noisy bit string during the enrollment phase and a second noisy bit string during the reconstruction phase, and a statistical unit arranged to execute a statistical test for verifying correct functioning of the physical unclonable function. The statistical test computes a statistical parameter for the physical unclonable function using helper data. The statistical test determines correct functioning if the statistical parameter satisfies a criterion of the statistical test.

Provided are methods and systems for storing data using locally repairable multiple encoding. A data storage method may include generating n N×M encoding matrices, each including an M×M first matrix, an 1×M second matrix in which all of elements have a value of 1, and an M×M third matrix that is a symmetric matrix in which respective columns are configured by changing a sequence of elements from an element set; arranging the encoding matrices into a plurality of groups; generating a data block through the first matrix, a local parity block through the second matrix, and a global parity block through the third matrix by encoding source data of a first group with a first encoding matrix among the encoding matrices arranged into the first group; and merging the global parity block with a global parity block of a second encoding matrix that is different than the first encoding matrix.

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.

Methods, apparatuses, and systems related to a data storage are described. Data targeted for storage is communicated to a memory device along with a scramble key. The scramble key is used to encode the target data, and the encoded data is stored at the memory device. For read operations, the encoded data is provided instead of the target data, and the target data is recovered outside of the memory device according to the scramble key.

An apparatus (100) for providing an joint error correction code (140) for a combined data frame (254) comprising first data (112) of a first data channel and second data (122) of a second data channel comprises a first error code generator (110) configured to provide, based on a linear code, information on a first error correction code (114a, 114b) using the first data (112). The apparatus further comprises a second error code generator (120) configured to provide, based on the linear code, information on a second error correction code (124) using the second data (122). The apparatus is configured to provide the joint error correction code (140) using the information on the first error correction code (114a, 114b) and the information on the second error correction code (124).

The present disclosure includes apparatuses and methods for ECC operation associated with memory. One example apparatus comprises a controller configured to perform an error correction code (ECC) operation on a codeword stored in the memory, wherein the codeword includes a first number of ECC bits and the first number of ECC bits are generated based on an encoding matrix, wherein each row of the encoding matrix has an odd number of bits having a binary value of 1.

Systems and methods are disclosed for providing H-ARQ transmissions in respect of a set of horizontal code blocks are combined in a code. Retransmissions contain vertical parity check blocks which are determined from verticals from the set of horizontal code blocks. Once all the vertical parity check blocks have been transmitted, a new set may be determined after performing interleaving upon either the content of the horizontal code blocks, in the case of non-systematic horizontal code blocks, or over the content of encoder input bits in the place of systematic horizontal code blocks. The interleaving may be bitwise or bit subset-wise. The retransmissions do not contain any of the original bits. In the decoder, soft decisions are produced, and nothing needs to be discarded; decoding will typically improve with each retransmission.

The present technology relates to an error correction circuit. According to the present technology, an error correction circuit performing error correction encoding on a plurality of messages to be stored in a memory device includes a first error correction encoder and a second error correction encoder. The first error correction encoder generates a plurality of codewords by performing first error correcting encoding on each of the plurality of messages. The second error correction encoder performs a second error correction encoding operation by performing an exclusive OR operation on symbols of an identical column layer within the codewords. The second error correction encoder determines a data unit as a target of the second error correction encoding operation based on a use period of the memory device.

A data storage device is disclosed comprising a non-volatile storage medium (NVSM). A first block of data is channel encoded into first channel data based on a channel code constraint, and the first channel data is error correction encoded to generate first redundancy bits. A second block of data is channel encoded into second channel data based on the channel code constraint and the first redundancy bits, and the first channel data and the second channel data are error correction encode to generate second redundancy bits. A third block of data is channel encoded into third channel data based on the channel code constraint and the second redundancy bits. The first, second and third channel data and the first and second redundancy bits are stored in the NVSM.

An FEC codec module is provided. Code elements, i.e., code words of forward error correction code, are added to the data code stream of each transmission link through the codec module, so that accurate error determination and automatic error correction may be realized at the receiving end. The interleaving process is performed on multi-link data to prevent the occurrence of continuous burst errors in the data link in a transmission process, and the error correction capability of FEC is utilized to improve the data transmission efficiency and anti-interference ability of the system.