A method in a node (110, 115) comprises generating (604) a plurality of constituent polar codes, each of the plurality of constituent polar codes having an associated block length and an associated set of information bits. The method comprises coupling (608) at least a portion of the sets of information bits associated with each of the plurality of constituent polar codes to generate a spatially coupled polar code. The method comprises encoding (612) a wireless transmission using the spatially coupled polar code.

Disclosed are devices, systems and methods for precoding and decoding polar codes using local feedback are described. One example method for improving an error correction capability of a decoder includes receiving a noisy codeword vector of length n, the codeword having been generated based on a concatenation of a convolutional encoding operation and a polar encoding operation and provided to a communication channel prior to reception by the decoder, performing a successive-cancellation decoding operation on the noisy codeword vector to generate a plurality of polar decoded symbols (n), generating a plurality of information symbols (k) by performing a convolutional decoding operation on the plurality of polar decoded symbols, wherein k/n is a rate of the concatenation of the convolutional encoding operation and the polar encoding operation, and performing a bidirectional communication between the successive-cancellation decoding operation and the convolutional decoding operation.

Techniques are presented for mapping a digital data sequence into a signal point sequence for transmission. The signal point sequence belongs to a set of possible signal point sequences. In one example, a digital data sequence is received. Forbidden branch flags that forbid certain signal points in the possible signal points sequences are applied. The signal point sequence is selected from a subset of all the possible signal point sequences based on the digital data sequence. The subset is defined by the forbidden branch flags.

An encoder apparatus for reliable transfer of a source data block d in a communication system includes an outer transform configured to receive a data container block v and compute an outer transform block u, whereby u=vG.sub.out for an outer transform matrix G.sub.out. The encoder apparatus also includes an inner transform configured to receive the outer transform block u and compute a transmitted code block x, whereby x=uG.sub.in for an inner transform matrix G.sub.in. The data container block v is obtained from the source data block d and a frozen data block a. The frozen data block a is a predetermined block of symbols. The outer transform matrix G.sub.out and the inner transform matrix form a triangular factorization of a transform matrix G, which optionally is a non-triangular matrix, while the outer transform matrix G.sub.out and the inner transform matrix G.sub.in are strictly upper- and lower-triangular matrices, respectively.

A codeword is generated based on a segmentation transform and a Polarization-Assisted Convolutional (PAC) code that includes an outer convolutional code and a polar code, and based on separate encoding of respective different segments of convolutionally encoded input bits according to the polar code. Each segment of the respective segments includes multiple bits of the convolutionally encoded input bits for which the separate encoding of the segment is independent of the separate encoding of other segments. Separate decoding may be applied to segments of such a codeword to decode convolutionally encoded input bits corresponding to the separately encoded segments of the convolutionally encoded input bits.

A codeword is generated based on a segmentation transform and a Polarization-Assisted Convolutional (PAC) code that includes an outer convolutional code and a polar code, and based on separate encoding of respective different segments of convolutionally encoded input bits according to the polar code. Each segment of the respective segments includes multiple bits of the convolutionally encoded input bits for which the separate encoding of the segment is independent of the separate encoding of other segments. Separate decoding may be applied to segments of such a codeword to decode convolutionally encoded input bits corresponding to the separately encoded segments of the convolutionally encoded input bits.

Disclosed are devices, systems and methods for precoding and decoding polar codes using local feedback are described. One example method for improving an error correction capability of a decoder includes receiving a noisy codeword vector of length n, the codeword having been generated based on a concatenation of a convolutional encoding operation and a polar encoding operation and provided to a communication channel prior to reception by the decoder, performing a successive-cancellation decoding operation on the noisy codeword vector to generate a plurality of polar decoded symbols (n), generating a plurality of information symbols (k) by performing a convolutional decoding operation on the plurality of polar decoded symbols, wherein k/n is a rate of the concatenation of the convolutional encoding operation and the polar encoding operation, and performing a bidirectional communication between the successive-cancellation decoding operation and the convolutional decoding operation.

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.

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.

An encoding method includes: processing a plurality of data blocks to generate a plurality of partial parity blocks, wherein the partial parity blocks includes a first portion and a second portion; using a first computing circuit to generate a first calculating result according to the second portion of the partial parity blocks; using the first calculating result to adjust the first portion of the partial parity blocks; performing circulant convolution operations upon the adjusted first portion to generate a first portion of parity blocks; and using a second computing circuit to generate a second portion of the parity blocks according to at least the first portion of parity blocks; wherein the first portion of the parity blocks and the second portion of the parity blocks serve as a plurality of parity blocks generated in response to encoding the data blocks.