This application relates to the field of wireless communications technologies, and discloses a polar code encoding method and apparatus, to improve accuracy of reliability calculation and ordering for polarized channels. The method includes: obtaining a first sequence used to encode K to-be-encoded bits, where the first sequence includes sequence numbers of N polarized channels, the sequence numbers of the N polarized channels are arranged in the first sequence based on reliability of the N polarized channels, K is a positive integer, N is a mother code length of a polar code, N is a positive integer power of 2, and KN; selecting sequence numbers of K polarized channels from the first sequence in descending order of reliability; and placing the to-be-encoded bits based on the selected sequence numbers of the K polarized channels, and performing polar code encoding on the to-be-encoded bits.

A distributed storage system can use a high rate MSR erasure code to repair multiple nodes when multiple node failures occur. An encoder constructs m r-ary trees to determine the symbol arrays for the parity nodes. These symbol arrays are used to generate the parity data according to parity definitions or parity equations. The m r-ary trees are also used to identify a set of recovery rows across helper nodes for repairing a systematic node. When failed systematic nodes correspond to different ones of the m r-ary trees, a decoder may select additional recovery rows. The decoder selects additional recovery rows when the parity definitions do not provide a sufficient number of independent linear equations to solve the unknown symbols of the failed nodes. The decoder can select recovery rows contiguous to the already identified recovery rows for access efficiency.

Input bits are encoded into codewords that include coded bits. Encoding involves applying a first set of polar encoding matrices G.sub.Y of prime number dimension Y to the input bits to produce output bits, and applying a second set of polar encoding matrices G.sub.Z of prime number dimension Z to the output bits to produce the codeword. One or both of G.sub.X and G.sub.Y could be non-2-by-2. Such kernel design and other aspects of code construction, including reliabilities and selection of sub-channels for code construction, non-CRC-aided error correction, and code shortening and puncturing, are discussed in further detail herein.

A method comprises: obtaining a coded bit sequence by performing PC-polar coding on information bits based on first constructor parameters; and sending the coded bit sequence. A check equation of the first constructor parameters includes a first element representing a check-required information bit position and a second element representing a check bit position, the first element corresponds to a first vector (V1) in a generator matrix for PC-polar codes, the second element corresponds to a second vector (V2) in the generator matrix, and if a first Hamming weight (HW1) of V1 is the same as a second Hamming weight (HW2) of V2, then a third Hamming weight (HW3) of an addition modulo 2 vector is greater than HW1 and greater than HW2, or if HW1 is different from HW2, then HW3 is greater than a smaller one of the HW1 and HW2.

A distributed storage system can use a high rate MSR erasure code to repair multiple nodes when multiple node failures occur. An encoder constructs m r-ary trees to determine the symbol arrays for the parity nodes. These symbol arrays are used to generate the parity data according to parity definitions or parity equations. The m r-ary trees are also used to identify a set of recovery rows across helper nodes for repairing a systematic node. When failed systematic nodes correspond to different ones of the m r-ary trees, a decoder may select additional recovery rows. The decoder selects additional recovery rows when the parity definitions do not provide a sufficient number of independent linear equations to solve the unknown symbols of the failed nodes. The decoder can select recovery rows contiguous to the already identified recovery rows for access efficiency.

The disclosure relates to a communication method and system for converging a 5th-Generation (5G) communication system for supporting higher data rates beyond a 4th-Generation (4G) system with a technology for Internet of Things (IoT). The disclosure may be applied to intelligent services based on the 5G communication technology and the IoT-related technology, such as smart home, smart building, smart city, smart car, connected car, health care, digital education, smart retail, security and safety services. The disclosure relates to encoding and decoding by using a polar code in a wireless communication system, and an operation method of a transmission-end apparatus includes determining segmentation and the number of segments, based on parameters associated with encoding of information bits, encoding the information bits according to the number of check bits, and transmitting the encoded information bits to a reception-end apparatus.

The disclosed embodiments provide a memory system that provides error detection and correction. Each block of data in the memory system includes an array of bits logically organized into R rows and C columns, including CM1 data-bit columns containing data bits, a row check bit column including row-parity bits for each of the R rows in the block, and M inner check bit columns that collectively include MR inner check bits. These inner check bits are defined to cover bits in the array in accordance with a set of check vectors, wherein each check vector is associated with a different bit in the array and is an element of Res(P), a residue system comprising a set of polynomials with GF(2) coefficients modulo a polynomial P with GF(2) coefficients, wherein each column is associated with a different pin in a memory module interface, and wherein the check bits are generated from the data bits to facilitate block-level detection and correction for errors that arise during the transmission. During operation, the system transmits a block of data from the memory. Next, the system uses an error-detection circuit to examine the block of data, and determine whether an error has occurred during the transmission based on the examination.

The present disclosure relates to multiple-symbol combination based decoding for general polar codes. Multiple-symbol combination based decoding of a received word that is based on a codeword involves determining whether all nodes at an intermediate stage of the multiple-symbol combination based decoding, which provide their outputs as inputs to a subset of nodes at a next stage of the multi-symbol combination based decoding, are associated with trust symbols in the received word that have a higher reliability of being successfully decoded than doubt symbols in the received word. A hard decision is performed in response to a positive determination.

An accelerated erasure coding system includes a processing core for executing computer instructions and accessing data from a main memory, and a non-volatile storage medium for storing the computer instructions. The processing core, storage medium, and computer instructions are configured to implement an erasure coding system, which includes: a data matrix for holding original data in the main memory; a check matrix for holding check data in the main memory; an encoding matrix for holding first factors in the main memory, the first factors being for encoding the original data into the check data; and a thread for executing on the processing core. The thread includes: a parallel multiplier for concurrently multiplying multiple entries of the data matrix by a single entry of the encoding matrix; and a first sequencer for ordering operations through the data matrix and the encoding matrix using the parallel multiplier to generate the check data.

Embodiments of the present disclosure provide a decoding method of a polar code, including: acquiring a receiving sequence and a check matrix, wherein the receiving sequence is output on a channel after an input mapping sequence is encoded; carrying out Trellis path search according to the receiving sequence and the check matrix, and calculating Trellis path likelihood information corresponding to the input mapping sequence; calculating a decision value corresponding to the input mapping sequence according to the Trellis path likelihood information; and de-mapping the calculated decision value corresponding to the input mapping sequence according to a preset mapping relation to obtain a decoding sequence. The input mapping sequence belongs to a finite field GF(q), when decoding the polar code, the Trellis path search is carried out, and the decision value is calculated and de-mapped to simultaneously reduce a maximum list value and greatly reduce an average list value.