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.

The disclosure relates to devices and methods implementing polar codes. For instance, the disclosure relates to an an encoder for encoding data, wherein the encoder comprises a processor configured to encode the data using a (n, k, d) parent polar code C into codewords c.sub.0.sup.n-1=u.sub.0.sup.n-1A subject to the constraints u.sub.0.sup.n-1V.sup.T=0, wherein u.sub.0.sup.n-1 denotes the data, wherein $A={\left(\begin{array}{cc}1& 0\\ 1& 1\end{array}\right)}^{.Math.m},$
wherein F.sup..Math.m denotes the m-times Kronecker product of the matrix F with itself and wherein the constraint matrix V comprises in addition to the constraint matrix V.sub.0 of the parent polar code the constraint matrix V.sub.1 of a first helper code C.sub.1 and the constraint matrix V.sub.2 of a second helper code C.sub.2.

A method for constructing parity-check concatenated polar codes and an apparatus therefor are disclosed. According to an embodiment of the inventive concept, a method for constructing a polar code includes receiving a code length, a message length, and channel information, generating an information set and a parity set of polar codes based on the received code length, the received message length, and the received channel information, and generating a parity node including the information set of elements based on the generated information set and the generated parity set.

The invention discloses a method for transmitting additional information using linear block codes, which comprises the following steps: when encoding: a linear block code C with a code length of n and an information bit length of k is used as a payload code, to embed an additional information sequence v of length m by superposition coding and resulting into a codeword c of length n. When decoding, firstly decode the additional information according to the received sequence y: select an additional information sequence with the largest characteristic metric function value as the decode output. Then perform payload information sequence decoding: remove the interference of superposition sequence from the received sequence y, and then use the basic linear block code C decoder to decode. The present invention can transmit a small amount of additional information at a low frame error rate while causing a negligible effect on payload information decoding without additionally increasing transmission energy and bandwidth overhead.

A method includes generating an extended result from a first operation circuitry having a result register bit width greater than a bus width associated with a residue check path of a second operation circuitry associated with a floating point unit. An extended result residue less a first portion residue of the extended result received from the residue check path is stored as a first partial result residue. The first partial result residue is compared with a first result residue of the second operation circuitry. The extended result residue less both the first partial result residue and a second portion residue of the extended result received from the residue check path as a second partial result residue is compared with a second result residue of the second operation circuitry.

An H.sub.C of a code B is first transformed into an H.sup.B. A parity bit of the code B is obtained by performing an operation on the H.sup.B and an information bit of the code B. The parity bit is used to perform RS coding on a code A, to obtain a parity bit of the code A. A check code of a GEL code is obtained by performing an operation on the parity bits of the code B and the code A. Finally, a single bit parity check bit is added. The code A is defined in a finite field GF (2.sup.l1), the code B is defined in a finite field GF (2.sup.l2), and l.sub.1 and l.sub.2 are positive integers. A success rate of decoding the code A in the first row can be improved using this method.

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.

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.

Systems and methods related to data encoders that can perform error detection or correction. The encoders and decoders may minimize the addition of errors due to aliasing in error correction codes by implementing operators associated with reduced aliasing parity generating or reduced aliasing error checking matrices.

A method for determining features of an error correcting code system, comprising independent error correcting codes and a polarization module, allowing transmitting a binary input vector on block fading sub-channels, the independent error correcting codes generating components of the binary input vector and a channel polarization being applied to the binary input vector by the polarization module. The method comprises: obtaining characteristics of the block fading sub-channels; and, determining features of said error correcting code system, comprising, for each error correcting code, a rate of said error correcting code, adapted to the obtained characteristics and minimizing a function of a probability that an instantaneous equivalent channel capacity of the block fading sub-channels is below a transmission rate transmitted on the block fading sub-channels.