A quantum error correcting code with dynamically generated logical qubits is provided. When viewed as a subsystem code, the code has no logical qubits. Nevertheless, the measurement patterns generate logical qubits, allowing the code to act as a fault-tolerant quantum memory. Each measurement can be a two-qubit Pauli measurement.

The present disclosure discloses a new coding scheme, which is constructed by superimposing together a pair of basic codes in a twisted manner. A SCL decoding algorithm is proposed for the TPST codes, which may be early terminated by a preset threshold on the empirical divergence functions (EDF) to trade off performance with decoding complexity. The SCL decoding of TPST is based on the efficient list decoding of the basic codes, where the correct candidate codeword in the decoding list is distinguished by employing a typicality-based statistical learning aided decoding algorithm. Lower bounds for the two layers of TPST are derived, which may be used to predict the decoding performance and to show the near-ML performance of the proposed SCL decoding algorithm. The construction of TPST codes may be generalised by allowing different basic codes for the two layers.

The present disclosure discloses a new coding scheme, which is constructed by superimposing together a pair of basic codes in a twisted manner. A SCL decoding algorithm is proposed for the TPST codes, which may be early terminated by a preset threshold on the empirical divergence functions (EDF) to trade off performance with decoding complexity. The SCL decoding of TPST is based on the efficient list decoding of the basic codes, where the correct candidate codeword in the decoding list is distinguished by employing a typicality-based statistical learning aided decoding algorithm. Lower bounds for the two layers of TPST are derived, which may be used to predict the decoding performance and to show the near-ML performance of the proposed SCL decoding algorithm. The construction of TPST codes may be generalised by allowing different basic codes for the two layers.

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, there is provided 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.

The invention relates to a method for decoding at least M.sub.0 symbols X.sup.0.sub.1, . . . , X.sup.0.sub.M0 received from a transmitter through a wireless communication medium, said received symbols representing symbols encoded by an encoder E of the transmitter, said method comprising: inputting in a decoder the M.sub.0 symbols X.sup.0.sub.1, . . . , X.sup.0.sub.M0, said decoder comprising an artificial neural network system, wherein at least an activation function of the artificial neural network system is a multiple level activation function.

An apparatus for decoding a TPC codeword is disclosed. The apparatus includes a memory and a processor coupled to the memory. The processor is configured to receive a first set of soft information corresponding to the TPC codeword. The TPC codeword includes at least one codeword corresponding to each of first, second, and third dimensions. The processor is further configured to iteratively perform a first soft decoding procedure on the at least one codeword corresponding to the first dimension to generate a first candidate codeword and upon determining that the first candidate codeword is not a correct codeword, and perform a second decoding procedure on the at least one codeword corresponding to the third dimension to generate a second candidate codeword. The second decoding procedure generates a second set of soft information to be used at a later iteration of the first decoding procedure.

An apparatus and method for optimizing the performance of satellite communication system receivers by using the Soft-Input Soft-Output (SISO) BCJR (Bahl, Cocke, Jelinek and Raviv) algorithm to detect a transmitted information sequence is disclosed. A Sliding Window technique is used with a plurality of reduced state sequence estimation (RSSE) equalizers to execute the BCJR algorithm in parallel. A serial data stream is converted into a plurality of data blocks using a serial-to-parallel converter. After processing in parallel by the equalizers, the output blocks are converted back to a serial data stream by a parallel-to-serial converter. A path history is determined using maximum likelihood (ML) path history calculation.

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.

Techniques for achieving reductions in cost of encoding and decoding operations used in DNA data storage systems to facilitate reducing errors in those encoding and decoding operations while accounting for a code structure used during the encoding and decoding by constructing and using insertion-deletion-substitution (IDS) trellises for multiple traces are disclosed. A DNA sequencing channel is used to randomly sample and sequence DNA strands to generate noisy traces. Multiple trellises are independently constructed for each respective noisy trace. A forward-backward algorithm is run on each trellis to compute posterior marginal probabilities for vertices included in each trellises. An estimate of the data message sequence is then computed.

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.