The invention relates to a soft input decoding method and a decoder for generalized concatenated (GC) codes. The GC codes are constructed from inner nested block codes, such as binary Bose-Chaudhuri-Hocquenghem, BCH, codes and outer codes, such as Reed-Solomon, RS, codes. In order to enable soft input decoding for the inner block codes, a sequential stack decoding algorithm is used. Ordinary stack decoding of binary block codes requires the complete trellis of the code. In one aspect, the present invention applies instead a representation of the block codes based on the trellises of supercodes in order to reduce the memory requirements for the representation of the inner codes. This enables an efficient hardware implementation. In another aspect, the present invention provides a soft input decoding method and device employing a sequential stack decoding algorithm in combination with list-of-two decoding which is particularly well suited for applications that require very low residual error rates.

This application provides a polar encoding and decoding method, a sending device, and a receiving device, to help overcome disadvantages in transmission of medium and small packets, a code rate, reliability, and complexity in the prior art. The method includes: pre-storing, by a computing device, at least one mother code sequence, wherein each mother code sequence comprises at least one subsequence and at least one subset, the at least one subsequence and the at least one subset each comprises one or more sequence numbers corresponding to one or more polarized channels, and wherein the one or more sequence numbers in each subsequence are arranged in an ascending order according to reliability of the corresponding one or more polarized channels; determining, by the computing device, a set of information bit sequence numbers from the at least one mother code sequence based on a code length of a target polar code; and performing, by the computing device, polar encoding on information bits based on the set of information bit sequence numbers.

A framework for error correction coding that takes into account the difference in bit significance in the source symbols by using an appropriate error metric and minimizing it using a Bayes decoder and an optimized codebook. The Bayes decoder performs better than standard soft and hard minimum distance decoding and the optimized codebook performs better than classical linear block codes, e.g., Hamming codes. The error metric is a norm in information symbol space and is based on a loss function appropriately defined according to an approach for assigning significance to the various bits in the source bit stream. The Bayes decoder of this metric is defined and an optimized codebook generated that optimizes this metric under a noisy channel. The framework for error correction coding is implemented for increased reduncancy in a communications system or a data storage system and is optimized to combat noise in such systems.

This application provides a polar encoding and decoding method, a sending device, and a receiving device, to help overcome disadvantages in transmission of medium and small packets, a code rate, reliability, and complexity in the prior art. The method includes: pre-storing, by a computing device, at least one mother code sequence, wherein each mother code sequence comprises at least one subsequence and at least one subset, the at least one subsequence and the at least one subset each comprises one or more sequence numbers corresponding to one or more polarized channels, and wherein the one or more sequence numbers in each subsequence are arranged in an ascending order according to reliability of the corresponding one or more polarized channels; determining, by the computing device, a set of information bit sequence numbers from the at least one mother code sequence based on a code length of a target polar code; and performing, by the computing device, polar encoding on information bits based on the set of information bit sequence numbers.

Methods and apparatus disclosed herein may be used to establish framing more efficiently in communication protocols with block-coded forward error correction. Such protocols generally involve the check of different bit-alignments searching for positions that yield zero syndromes. The search can be undesirably slow, particularly in the presence of received errors. The presently-disclosed bit-alignment testing technique reduces this search time by checking the syndrome at each data word as if that data word was the last of a code. In other words, the word positions are effectively checked without a prior assumption as to which words are the first and last of the code. This reduces the task to the number of different bit-alignments possible within a single data word, rather than the number of bit-alignments possible in a complete FEC code. In one implementation, the lock time is reduced by approximately 50 times when compared to a straightforward solution.

A polar code encoding method and apparatus are provided. The method includes: obtaining a basic sequence, where the basic sequence is a sequence obtained by sorting sequence numbers of polarized channels in descending order or ascending order of reliability, and a length of the basic sequence is L.sub.1; determining, based on a maximum encoding length L.sub.2 supported by a receiving device, a quantity M of segments of an information bit sequence whose length is N after encoding, where a quantity of bits in the information bit sequence before the encoding is K; and performing polar code encoding on the M segments based on the basic sequence. According to the polar code encoding method, during polar code construction, an encoding device needs to know only a reliability order of min(N/M, L.sub.1) polarized channels. In this way, storage overheads of a nested sequence can be effectively reduced, and online computing complexity can be reduced.

A decoding device includes a memory and a processor configured to execute inputting a code word encoded by a polar code from an original message; decoding the original message from the code word based on a conditional probability expressed by a symmetric parameterization and having observation information as a condition; and outputting the decoded original message.

This application provides a polar encoding and decoding method, a sending device, and a receiving device, to help overcome disadvantages in transmission of medium and small packets, a code rate, reliability, and complexity in the prior art. The method includes: pre-storing, by a computing device, at least one mother code sequence, wherein each mother code sequence comprises at least one subsequence and at least one subset, the at least one subsequence and the at least one subset each comprises one or more sequence numbers corresponding to one or more polarized channels, and wherein the one or more sequence numbers in each subsequence are arranged in an ascending order according to reliability of the corresponding one or more polarized channels; determining, by the computing device, a set of information bit sequence numbers from the at least one mother code sequence based on a code length of a target polar code; and performing, by the computing device, polar encoding on information bits based on the set of information bit sequence numbers.

A framework for error correction coding that takes into account the difference in bit significance in the source symbols by using an appropriate error metric and minimizing it using a Bayes decoder and an optimized codebook. The Bayes decoder performs better than standard soft and hard minimum distance decoding and the optimized codebook performs better than classical linear block codes, e.g., Hamming codes. The error metric is a norm in information symbol space and is based on a loss function appropriately defined according to an approach for assigning significance to the various bits in the source bit stream. The Bayes decoder of this metric is defined and an optimized codebook generated that optimizes this metric under a noisy channel. The framework for error correction coding is implemented for increased reduncancy in a communications system or a data storage system and is optimized to combat noise in such systems.

Methods, systems, and devices that support an efficient sequence-based polar code description are described. In some cases, a wireless device (e.g., a user equipment (UE) or a base station) may transmit a codeword including a set of information bits encoded using a polar code or receive a codeword including a set of information bits encoded using a polar code. As described herein, the wireless device may determine the bit locations of the information bits in the polar code based on a partition assignment vector. Specifically, the wireless device may partition bit-channels for one or more stages of polarization and assign information bits to partitions based on the partition assignment vector. Once the bit locations of the information bits are determined, the wireless device may decode a received codeword or transmit an encoded codeword based on the determined bit locations of the information bits.