An encoder receives a concatenated encoder input block d, splits d into an outer code input array a, and encodes a using outer codes to generate an outer code output array b. The encoder generates, from b, a concatenated code output array x using a layered polarization adjusted convolutional (LPAC) code. A decoder counts layers and carries out an inner decoding operation for a layered polarization adjusted convolutional (LPAC) code to generate an inner decoder decision {tilde over (b)}.sub.i from a concatenated decoder input array y and a cumulative decision feedback ({circumflex over (b)}.sub.1, {circumflex over (b)}.sub.2, . . . , {circumflex over (b)}.sub.i−1). The decoder carries out an outer decoding operation to generate from {tilde over (b)}.sub.i an outer decoder decision â.sub.i, and carries out a reencoding operation to generate a decision feedback {circumflex over (b)}.sub.i from â.sub.i, where the number of layers is an integer greater than one, with a concatenated decoder output block {circumflex over (d)} being generated from outer decoder decisions.

Devices, systems and methods for list decoding of polarization-adjusted convolutional (PAC) codes are described. One example method for improving error correction in a decoder for data in a communication channel includes receiving a noisy codeword, the codeword having been generated using a polarization-adjusted convolutional (PAC) code and provided to the communication channel prior to reception by the decoder, and performing PAC list decoding on the noisy codeword, wherein an encoding operation of the PAC code comprises a convolutional precoding operation that generates one or more dynamically frozen bits, and wherein the PAC list decoding comprises extending, based on the one or more dynamically frozen bits, at least two paths of a plurality of paths in the PAC list decoding differently and independently.

The present disclosure relates to a pre-5.sup.th-generation (5G) or 5G communication system to be provided for supporting higher data rates beyond 4.sup.th-generation (4G) communication system such as a long term evolution (LTE). A method for transmitting a signal in a signal transmitting apparatus in a communication system supporting a bit-interleaved coded modulation with iterative decoding (BICM-ID) scheme is provided. The method includes performing an outer encoding operation; performing an interleaving operation on the outer code corresponding to an interleaving scheme which is based on a preset generation matrix to generate an interleaved signal; performing an inner encoding operation; performing a modulating operation; and transmitting the modulated signal, wherein the generation matrix is generated by applying at least one of a preset column permutation rule and a preset row permutation rule to a generation matrix for a quasi-cyclic (QC) interleaver.

Devices, systems and methods for convolutional precoding and decoding of polar codes are disclosed. An example method for error correction in a data processing system includes receiving a noisy codeword, the codeword having been generated based on an outer stream decodable code and an inner polar code and provided to a communication channel or a storage channel prior to reception by the decoder, the stream decodable code characterized by a trellis, and performing, based on the trellis, a list-decoding operation on the noisy codeword vector to generate a plurality of information symbols, the list-decoding operation being configured to traverse through a plurality of states at one or more stages of a plurality of decoding stages.

Methods, apparatus, systems, architectures and interfaces for encoding/decoding a QD-DTS-PrCC are provided. The decoding method includes determining a number k.sub.TS of input bits included in a transmission of a data stream and a first bit of the input bits included in the transmission in the data stream; determining a number of Encoded Bit Blocks (EBBs), each of the EBBs including any number of data blocks that are previously transmitted Transmit Segments (TS) of the data stream, each of the data blocks having a bit length of k.sub.TS bits; selecting that number of EBBs for encoding a QD-DTS-PrCC component codeword (QDCC) of the transmission according to a DTS indexing method for indexing a plurality of EBBs; generating the QDCC including a TS, Virtual Segments (VSs), and r.sub.c parity bits, a dimensionality of the QD-DTS-PrCC being at least 2; and extracting the calculated TS of the QDCC to an output EBB.

Methods, apparatus, systems, architectures and interfaces for encoding/decoding a QD-DTS-PrCC are provided. The decoding method includes determining a number k.sub.TS of input bits included in a transmission of a data stream and a first bit of the input bits included in the transmission in the data stream; determining a number of Encoded Bit Blocks (EBBs), each of the EBBs including any number of data blocks that are previously transmitted Transmit Segments (TS) of the data stream, each of the data blocks having a bit length of k.sub.TS bits; selecting that number of EBBs for encoding a QD-DTS-PrCC component codeword (QDCC) of the transmission according to a DTS indexing method for indexing a plurality of EBBs; generating the QDCC including a TS, Virtual Segments (VSs), and r.sub.c parity bits, a dimensionality of the QD-DTS-PrCC being at least 2; and extracting the calculated TS of the QDCC to an output EBB.

This disclosure describes systems and methods for detecting multiple insertion and deletion errors in the presence of substitution errors in a signal (such as a sequenced DNA string). A convolutional code that includes two or more component convolutional codes is used for encoding. Each of the two or more component convolutional codes generates only a subset of all possible outputs of the convolutional code. The subsets of the two or more component convolutional codes are disjoint from each other. Only one of the two or more convolutional codes is active at any given time. The two or more convolutional codes together define a super code. The two or more convolutional codes are time interlaced within the super code, and the super code defines the convolutional code. A trellis that includes two or more component trellises designed based on the two or more component convolutional codes is used for decoding.

An encoder receives a concatenated encoder input block d, splits d into an outer code input array a, and encodes a using outer codes to generate an outer code output array b. The encoder generates, from b, a concatenated code output array x using a layered polarization adjusted convolutional (LPAC) code. A decoder counts layers and carries out an inner decoding operation for a layered polarization adjusted convolutional (LPAC) code to generate an inner decoder decision {tilde over (b)}.sub.i from a concatenated decoder input array y and a cumulative decision feedback ({circumflex over (b)}.sub.1, {circumflex over (b)}.sub.2, . . . , {circumflex over (b)}.sub.i−1). The decoder carries out an outer decoding operation to generate from {tilde over (b)}.sub.i an outer decoder decision â.sub.i, and carries out a reencoding operation to generate a decision feedback {circumflex over (b)}.sub.i from â.sub.i, where the number of layers is an integer greater than one, with a concatenated decoder output block {circumflex over (d)} being generated from outer decoder decisions.

Devices, systems and methods for convolutional precoding and decoding of polar codes are disclosed. An example method for error correction in a data processing system includes receiving a noisy codeword, the codeword having been generated based on an outer stream decodable code and an inner polar code and provided to a communication channel or a storage channel prior to reception by the decoder, the stream decodable code characterized by a trellis, and performing, based on the trellis, a list-decoding operation on the noisy codeword vector to generate a plurality of information symbols, the list-decoding operation being configured to traverse through a plurality of states at one or more stages of a plurality of decoding stages.

The invention discloses a method and a receiving device of the Viterbi algorithm. The method is applicable for a Viterbi decoder that receives an output signal generated by a convolution code encoder processing an original signal. The convolution code encoder includes M registers and M is a positive integer greater than or equal to 2. The method includes the following steps. First, for the first to the Mth data of the output signal, the Viterbi decoder performs the add-compare-select operation based on the known M initial values of the M registers. Then, for the Mth-last to the last data of the output signal, the Viterbi decoder performs the add-compare-select operation based on the known last M bits values of the original signal, thereby reducing the computational complexity of the add-compare-select unit.