A data storage device has a controller that is configured to generate SECDED codes based on a plurality (at least 2) of codes, where each of the constituent codes is a cyclic code over a finite field of size 2.sup.m for some integer m. Any 2 constituent codes are associated with 2.sup.m1 and 2.sup.m2, where m1 and m2 are coprime (i.e., gcd(m1,m2)=1) where gcd is the greatest common divisor. In such a case, it is possible to generate a cyclic code of length (2.sup.m1−1)*(2.sup.m2−1), which will be a long code, but enjoy the complexity, in encoding and decoding, of the small fields of the constituent codes.

Methods, systems, and devices for wireless communication are described for mutual information based polar code construction. A wireless device may receive a codeword over a wireless channel, the codeword encoded using a polar code. The wireless device may identify a set of bit locations of the polar code corresponding to information bits of an encoded information bit vector. The set of bit locations may be determined based at least in part on a reliability order of the bit locations of the polar code, and the reliability order may be determined based at least in part on a recursive model that includes at least one mutual information transfer function that is applied at each polarization stage of multiple polarization stages of the polar code. The wireless device may decode the received codeword to obtain the information bit vector at the set of bit locations.

A number K of N sub-channels that are defined by a code and that have associated reliabilities for input bits at N input bit positions, are to be selected to carry bits that are to be encoded. A localization area that includes multiple sub-channels and is located below fewer than K of the N sub-channels in a partial order of the N sub-channels is determined based on one or more coding parameters. The fewer than K sub-channels of the N sub-channels above the localization area in the partial order are selected, and a number of sub-channels from those in the localization area are also selected. The selected fewer than K sub-channels and the number of sub-channels selected from those in the localization area together include K sub-channels to carry the bits that are to be encoded.

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 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.

The present disclosure relates to a pre-5.sup.t-Generation (5G) or 5G communication system to be provided for supporting higher data rates Beyond 4.sup.th-Generation (4G) communication system such as Long Term Evolution (LTE). A method for operating a transmitting stage in a wireless communication system includes generating a signal by encoding an input bit sequence according to polar code determined from a linear code, and transmitting the signal to a receiving stage. The input bit sequence includes a second frozen bit which is determined based on a first frozen bit and an information bit. The first frozen bit and the information bit precede the second frozen bit in the input bit sequence.

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.

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 (A10) 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.

A method for generating a polar code c.sub.N of length N and dimension K, on the basis of a generator matrix G.sub.N of size NN, is provided. The method includes generating a distance spectrum vector d.sub.T.sub.p=(d.sub.T.sub.p(1), . . . , d.sub.T.sub.p(p)) of size p of the kernel T.sub.p, wherein d.sub.T.sub.p(h), h=1, . . . , p, corresponds to a maximum value among all possible minimum distances of all possible polar codes of size p and dimension h generated on the basis of the kernel T.sub.p. The method also includes generating a distance spectrum vector d.sub.G.sub.N of size N of the generator matrix G.sub.N on the basis of the distance spectrum vector d.sub.T.sub.p, determining the set of K information bit indices I on the basis of the distance spectrum vector d.sub.G.sub.N, and generating the polar code c.sub.N on the basis of the set of K information bit indices I.

A polar code construction method, apparatus, electronic device, and readable storage medium, applied to the field of wireless communication technology to reduce the complexity of polar code construction. The method comprises: calculating a weight spectrum corresponding to a polarized channel of a polar code with code length 2N based on the weight spectrum corresponding to the polarized channel with code length N, and MacWilliams identities; calculating, for each polarized channel, a union bound on the error probability of the polarized channel under the condition of additive white Gaussian noise based on the weight spectrum corresponding to the polarized channel and a union bound formula; determining the error probability threshold values based on the union bounds and a measurement method; sorting the error probability threshold values of all the polarized channels in ascending order, and selecting the polarized channels corresponding to the K smallest error probability threshold values.

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.