Coding sub-channel selection involves, in an embodiment, determining, from sub-channels that are defined by a code and that have associated reliabilities for input bits at input bit positions, a first number of the sub-channels to carry bits that are to be encoded. A second number of the sub-channels, greater than the first number, are selected. The second number of sub-channels are selected to provide exactly the first number sub-channels to be available to carry the bits that are to be encoded.

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.

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 device for generating a multi-kernel polar code x.sub.N of length N and dimension K on the basis of a first transformation matrix G.sub.N of size NN that defines a first multi-kernel polar code includes a processor configured to generate a second transformation matrix G.sub.N of size NN by permuting the order of at least two columns of a sub-matrix of the first transformation matrix G.sub.N, and generate the multi-kernel polar code x.sub.N an the basis of x.sub.N=u.sub.N.Math.G.sub.N, wherein u.sub.N=(u.sub.0, . . . , u.sub.N1) is a vector of size N, with the elements u.sub.i, i=0, . . . N1, corresponding to an information bit if il, l being a set of K information bit indices, and u.sub.i=0, if iF, F being a set of NK frozen bit indices.

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.

The embodiments herein provide a system and method for generating a catalog of graphs that acts as a source for creating error correcting codes. A D3 chord index notation is used to describe the graphs. A list of (3, g) Hamiltonian graphs for even girth g is created to satisfy the condition 6g16. Each of the lists is infinite and is used for creating LDPC codes of high quality.

The present disclosure relates to a device for generating a polar code x.sub.N of length N and dimension K on the basis of a transformation matrix G.sub.N of size NN, wherein the transformation matrix G.sub.N is based on a first matrix G.sub.N, of size N.sub.rN, and on a second matrix G.sub.N.sub.d of size N.sub.dN.sub.d, wherein N=N.sub.r.Math.N.sub.d, and wherein the polar code x.sub.N is given by x.sub.N=u.sub.N.Math.G.sub.N, wherein u.sub.N=(u.sub.0, . . . u.sub.N-1) is a vector of size N, an element u.sub.i, i=0, . . . N1, of the vector corresponding to an information bit if iI, I being a set of K information bit indices, and u.sub.i=0, if iF, F being a set of NK frozen bit indices.

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.

This application provides a polar code encoding method and apparatus. The method includes: obtaining, by a sending device, a sequence corresponding to a required mother code length; obtaining, by the sending device, a to-be-encoded bit; and performing, by the sending device, polar code encoding on the to-be-encoded bit by using the sequence corresponding to the required mother code length, to obtain an encoded bit, where the sequence is generated based on a basic sequence, and a length of the basic sequence is less than the mother code length.

A communication device includes: an encoder that encodes an input vector to output a codeword using a generator matrix of polar code; a memory that stores a frozen set including frozen bit indices and a non-frozen set including non-frozen bit indices; and a controller that is configured to: a) select at least one check bit index from the frozen set in descending order of row weights of the generator matrix and in descending order of index reliabilities of the input vector; b) select at least one non-frozen bit index from the non-frozen set to compute at least one check bit from at least one bit of information bits at the at least one non-frozen bit index; and c) put the at least one check bit at the at least one check bit index.