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.

Aspects of the disclosure are directed to processing signals including data exhibiting characteristics that facilitate assessment of transmission errors. As may be implemented in accordance with one or more embodiments, parameters are generated based signal transmission characteristics and are indicative of a different types of signal characteristics, including an amount of error correction that has been carried out on the signal. Two or more of the parameters are selected based on properties of signal disturbance under different reception conditions for the signal, and a degree of disturbance in the signal is predicted based on the selected parameters and signal conditions for the respective parameters at which the signal cannot be corrected. An output generated with the signal is then controlled, based on the predicted degree of disturbance and a threshold degree of disturbance.

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.

Methods, systems, and devices for wireless communications are described. An encoder of a wireless device may receive a number of information bits and a block size for transmission. If the block size is not a power of two, the encoder may round the block size up to the nearest power of 2, generate a larger codeword, and puncture the excess bits. The punctured bits may affect a rate of polarization when generating a polar code, and sub-blocks with a high number of punctured bits may produce too few sufficiently polarized channels. The encoder may implement a capacity backoff when polar coding to identify a greater number of polarized channels. The encoder may assign information bits to sufficiently polarized channels of the greater number of polarized channels.

Methods and apparatus deduplicate and erasure code a message in a data storage system. One example apparatus includes a first chunking circuit that generates a set of data chunks from a message, an outer precoding circuit that generates a set of precoded data chunks and a set of parity symbols from the set of data chunks, a second chunking circuit that generates a set of chunked parity symbols from the set of parity symbols, a deduplication circuit that generates a set of deduplicated data chunks by deduplicating the set of precoded chunks or the set of chunked parity symbols, an unequal error protection (UEP) circuit that generates an encoded message from the set of deduplicated data chunks, and a storage circuit that controls the data storage system to store the set of deduplicated data chunks, the set of parity symbols, or the encoded message.

Methods and apparatus deduplicate and erasure code a message in a data storage system. One example apparatus includes a first chunking circuit that generates a set of data chunks from a message, an outer precoding circuit that generates a set of precoded data chunks and a set of parity symbols from the set of data chunks, a second chunking circuit that generates a set of chunked parity symbols from the set of parity symbols, a deduplication circuit that generates a set of deduplicated data chunks by deduplicating the set of precoded chunks or the set of chunked parity symbols, an unequal error protection (UEP) circuit that generates an encoded message from the set of deduplicated data chunks, and a storage circuit that controls the data storage system to store the set of deduplicated data chunks, the set of parity symbols, or the encoded message.

The disclosure provides a non-orthogonal multiple access data transmission method and a transmission device using the same. The method includes: performing channel encoding for a plurality of data and a plurality of identifiers respectively corresponding to the plurality of data by using Raptor code so as to generate a Raptor codeword, wherein the plurality of identifiers respectively correspond to a plurality of receiving terminals; and modulating the Raptor codeword to generate a plurality of modulation symbols and broadcasting the plurality of modulation symbols.

An encoding apparatus includes a processor a non-transitory computer-readable storage medium storing a program for encoding data x of dimension k into a codeword c of length n. The program includes instructions to encode the data x using a C(n, k, d) code. The code C(n,k,d) has a length n and a minimum distance d, n=2.sup.m.sup.1+ . . . +2.sup.m.sup.s, m.sub.h, h=1, . . . , s, is an integer, on the basis of c=uA, where u.sub.i=x.sub.j.sub.i, 0j.sub.i<k1, if i.Math.F, F is a set of nk frozen bit indices of the code C(n,k,d), and u.sub.i=.sub.s=0.sup.i1.sub..sub.i.sub.,su.sub.s, if iF, is a constraint matrix given by a solution of .sup.T=0, .sub.i is an index of a row of the matrix , having a last non-zero element in column i, and is a precoding matrix and A is a matrix defined by

[00001]$A_{m_h}={\left(\begin{array}{cc}1& 0\\ 1& 1\end{array}\right)}^{.Math.m_h},$

and Q.sup..Math.m denotes the m-times Kronecker product of a matrix Q with itself.

A construction method for a (n,n(n1),n1) permutation group code based on coset partition is provided. The presented (n,n(n1),n1) permutation group code has an error-correcting capability of d1 and features a strong anti-interference capability for channel interferences comprising multi-frequency interferences and signal fading. As n is a prime, for a permutation code family with a minimum distance of n1 and a code set size of n(n1), the invention provides a method of calculating n1 orbit leader permutation codewords by O.sub.n={o.sub.1}.sub.=1.sup.n-1(mod n) and enumerating residual codewords of the code set by P.sub.n=C.sub.nO.sub.n={(l.sub.1).sup.n-1O.sub.n}={(r.sub.n).sup.n-1O.sub.n}. Besides, a generator of the code set thereof is provided. The (n,n(n1),n1) permutation group code of the invention is an algebraic-structured code, n1 codewords of the orbit leader array can be obtained simply by adder and (mod n) calculator rather than multiplication of positive integers. Composition operations of the cyclic subgroup C.sub.n acting on all permutations o.sub. of the orbit leader permutation array O.sub.n are replaced by well-defined cyclic shift composite operation functions (l.sub.1).sup.n-1 and (r.sub.n).sup.n-1 so that the action of the cyclic group acting on permutations is realized by a group of cyclic shift registers.

The present disclosure relates to encoding method and devices. One example method includes determining N to-be-encoded bits, where the N to-be-encoded bits include information bits and frozen bits, obtaining a first polarization weight vector including polarization weights of N polarized channels, where the N to-be-encoded bits correspond to the N polarized channels, determining positions of the information bits based on the first polarization weight vector, and performing polar encoding on the N to-be-encoded bits to obtain polar-encoded bits.