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 present disclosure provides a code generator for generating an {N′, K′} code for encoding and/or decoding data transmitted in a communication channel from an {N, K} code, wherein N and N′ are code lengths, K and K′ are code dimensions. The code generator is configured to shorten the {N, K} code to obtain an intermediate code, and to extend the intermediate code to obtain the {N′, K′} code. The present disclosure also provides a corresponding code construction method. Further, the present disclosure provides a device for encoding and/or decoding data transmitted in a communication channel, the device being configured to encode and/or decode the data based on an {N′, K′} code generated from the {N, K} code.

Methods, systems, and apparatus for producing CCZ states and T states. In one aspect, a method for distilling a CCZ state includes preparing multiple target qubits, ancilla qubits and stabilizer qubits in a zero state, performing an X gate for each stabilizer qubit on multiple ancilla qubits or multiple ancilla qubits and one of the target qubits using the stabilizer qubit as a control, measuring the stabilizer qubits, performing, on each of the ancilla qubits, a Z.sup.1/4 gate and a Hadamard gate, measuring each of the ancilla qubits, performing, conditioned on each measured ancilla qubit state, a NOT operation on a selected stabilizer qubit, or a NOT operation on the selected stabilizer qubit and a Z gate on one or more respective target qubits, performing, on each target qubit and conditioned on a measured state of a respective stabilizer qubit, a Z gate on the target qubit, and performing an X gate on each of the target qubits.

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 N×N, wherein the transformation matrix G.sub.N is based on a first matrix G.sub.N, of size N.sub.r×N, and on a second matrix G.sub.N.sub.d of size N.sub.d×N.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, . . . N−1, of the vector corresponding to an information bit if i∈I, I being a set of K information bit indices, and u.sub.i=0, if i∈F, F being a set of N−K frozen bit indices.

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.

A method for supporting a rate-compatible non-binary LDPC code, performed by a wireless device, according to the present embodiment, comprises the steps of: acquiring a kernel part comprising a plurality of first check nodes and a plurality of first variable nodes, the kernel part having a predetermined first code rate applied thereto, and the level of each of the plurality of first variable nodes included in the kernel part being set to 2; and generating, on the basis of the kernel part, a protograph having a second code rate, when a change from the first code rate to the second code rate is required.

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.

A data error correction method, apparatus, device, and readable storage medium are disclosed. The method includes: acquiring target data to be error-corrected; performing error correction on the target data using an error-correcting code to obtain first data; judging whether the performing of the error correction on the target data is successful; responsive to the performing of the error correction on the target data being not successful, correcting the target data using a target neural network to obtain second data, determining the second data as the target data, and continuing to perform the error correction on the target data again; and responsive to the performing of the error correction on the target data being successful, determining the first data as the error-corrected target data.

A method for supporting a rate-compatible non-binary LDPC code, performed by a wireless device, according to the present embodiment, comprises the steps of: acquiring a kernel part comprising a plurality of first check nodes and a plurality of first variable nodes, the kernel part having a predetermined first code rate applied thereto, and the level of each of the plurality of first variable nodes included in the kernel part being set to 2; and generating, on the basis of the kernel part, a protograph having a second code rate, when a change from the first code rate to the second code rate is required.

A method includes generating, by processing circuitry of a communications device, a partitioned complementary sequence based on information bits for transmission. The partitioned complementary sequence may include zero-valued elements. The method may include encoding a plurality of symbols on a plurality of orthogonal subcarriers using the partitioned complementary sequence. The encoding may include mapping additional information bits on subcarriers associated with the zero-valued elements of the partitioned complementary sequence. Additionally, the method may include controlling a radio of the communications device to transmit the plurality of symbols on the plurality of orthogonal subcarriers via an antenna of the communications device.