A method and associated apparatus is disclosed for processing data by means of an error code, wherein the error code has an H-matrix with n columns and m rows, wherein the columns of the H-matrix are different, wherein component-by-component XOR sums of adjacent columns of the H-matrix are different from one another and from all columns of the H-matrix and wherein component-by-component XOR sums of nonadjacent columns of the H-matrix are different from all columns of the H-matrix and from all component-by-component XOR sums of adjacent columns of the H-matrix.

The present disclosure relates to a 5.sup.th generation (5G) or pre-5G communication system for supporting a data transmission rate higher than that of a post-4.sup.th generation (4G) communication system such as Long Term Evolution (LTE). The present disclosure is for decoding a polar code in a communication system. An operation method of a reception device comprises the steps of: receiving data encoded by means of a polar code and comprising a plurality of bits; confirming one or more bits which do not require a decoding operation among the plurality of bits; and decoding at least some of the bits remaining after excluding the one or more bits.

Certain aspects of the present disclosure generally relate to wireless communications and, more particularly, to methods and apparatus for rate-matching a stream of bits encoded using polar codes. An exemplary method generally includes encoding K information bits using a polar code with a mother code length, N, to generate a stream of encoded bits storing a portion of the encoded bits in a circular buffer of size N reordering P blocks of the circular buffer according to row weights of a Hadamard matrix J interlacing the encoded bits of the blocks having a same row weight selecting, based on the row weights, a subset of the encoded bits in the blocks to modify modifying the selected subset of the encoded bits and transmitting the encoded bits in the P blocks, subsequent to modifying the selected subset of the encoded bits, via transmission resources.

Certain aspects of the present disclosure generally relate to techniques for encoding and decoding bits of information using cyclic redundancy check (CRC) concatenated polar encoding and decoding. The CRC concatenated polar encoding techniques may avoid transmission of dummy bits. A method generally includes obtaining the bits of information to be transmitted. The method includes performing CRC outer encoding of the bits of information using an even-weighted generator polynomial to produce CRC encoded bits. The method includes performing polar inner encoding of the CRC encoded bits to generate a codeword. The method includes discarding a first code bit at a beginning of the codeword. The shortened codeword is transmitted over a wireless medium. In another method, bit-level scrambling is performed on the CRC encoded bits before the polar encoding to avoid generating a dummy bit. In another method, only odd-weighted generator polynomials are selected to avoid generating the dummy bit.

Certain aspects of the present disclosure generally relate to techniques for encoding and decoding bits of information using cyclic redundancy check (CRC) concatenated polar encoding and decoding. The CRC concatenated polar encoding techniques may avoid transmission of dummy bits. A method generally includes obtaining the bits of information to be transmitted. The method includes performing CRC outer encoding of the bits of information using an even-weighted generator polynomial to produce CRC encoded bits. The method includes performing polar inner encoding of the CRC encoded bits to generate a codeword. The method includes discarding a first code bit at a beginning of the codeword. The shortened codeword is transmitted over a wireless medium. In another method, bit-level scrambling is performed on the CRC encoded bits before the polar encoding to avoid generating a dummy bit. In another method, only odd-weighted generator polynomials are selected to avoid generating the dummy bit.

Certain aspects of the present disclosure generally relate to techniques for encoding and decoding bits of information using cyclic redundancy check (CRC) concatenated polar encoding and decoding. A method generally includes obtaining the bits of information to be transmitted. The method includes performing CRC outer encoding of the bits of information using an even-weighted generator polynomial to produce CRC encoded bits. The method includes performing polar inner encoding of the CRC encoded bits to generate a codeword. The method includes discarding a first code bit at a beginning of the codeword. The shortened codeword is transmitted over a wireless medium. In another method, bit-level scrambling is performed on the CRC encoded bits before the polar encoding to. In another method, only odd-weighted generator polynomials are selected.

The present disclosure relates to data transmission methods. One example method includes obtaining K information bits, determining to-be-encoded bits, where the to-be-encoded bits include (K+P) bits, the (K+P) bits include the K information bits and P check bits, the K information bits correspond to K polarization channels, the P check bits include T first-type check bits, all the T first-type check bits are PC bits, and reliability of a polarization channel corresponding to each of the T first-type check bits is greater than a minimum value of reliability of the K polarization channels, and performing polar coding on the to-be-encoded bits to obtain encoded bits, where the (K+P) bits are in a one-to-one correspondence with (K+P) rows in a generator matrix of the encoded bits, a maximum row weight corresponding to the T first-type check bits is less than or equal to W.sub.2.

Encoding bits with a Q-ary linear error correction code defined over a binary-extension Galois field GF(2k), defined by a quasi-cyclic parity-check matrix comprising: first, second and third circulant sub-matrices comprising respective circulants respectively having first, second and third shifts and defined by first, second and third parameters belonging to the Galois field GF(2k), the second shift equal to a difference between a number of rows of each circulant and the first shift. A first set of parity-check bits is determined according to a fourth circulant having a shift equal to a difference between the number of rows and the first and third shifts and defined by the multiplicative inverse of a product between the first and third parameters, and to the second and third circulant sub-matrices. A second set of parity-check bits is determined according to the first set of parity-check bits and the first and second circulant sub-matrices.

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).

A method for encoding information bits with a Q-ary linear error correction code defined over a binary-extension Galois field GF(2.sup.k), and defined by a quasi-cyclic parity-check matrix comprising: first, second and third circulant sub-matrices respectively comprising first, second and third circulants respectively having first, second and third shifts and being defined respectively by first, second and third parameters belonging to the Galois field GF(2.sup.k), said second parameter being the inverse of the first parameter, and the second shift being equal to a difference between a number of rows of each circulant and the first shift. The method comprises determining: a first set of parity-check bits according to a fourth circulant having a fourth shift equal to a difference between said number of rows and said first and third shifts and being defined by the multiplicative inverse of a fourth parameter given by a product between the first and third parameters, and to the second and third circulant sub-matrices, and a second set of parity-check bits according to the determined first set of parity-check bits and said first and second circulant sub-matrices.