Abstract: A team polar decoder (TPD) includes polar decoders (PPDs) connected to a channel, and a team decision maker (TDM) connected to the PPDs and a destination. Component polar decoders (CPDs) decode a polar code in accordance with a polar code. Each CPD receives a noisy code block (NCB) from the channel, and decodes the NCB in consecutive steps to obtain a decoded transform input block (DTIB). Each CPD is generates, at an end of the decoding step, a candidate decoded data block from the DTIB by a data-demapping operation that is an inverse of a data-mapping operation applied at a polar encoder, then sends the CDDB to the TDM, which receives the CDDBs from the PPDs, generates a decoded data block (DDB), and sends the DDB to the destination.

Abstract: A team polar decoder (TPD) includes polar decoders (PPDs) connected to a channel, and a team decision maker (TDM) connected to the PPDs and a destination. Component polar decoders (CPDs) decode a polar code in accordance with a polar code. Each CPD receives a noisy code block (NCB) from the channel, and decodes the NCB in consecutive steps to obtain a decoded transform input block (DTIB). Each CPD is generates, at an end of the decoding step, a candidate decoded data block from the DTIB by a data-demapping operation that is an inverse of a data-mapping operation applied at a polar encoder, then sends the CDDB to the TDM, which receives the CDDBs from the PPDs, generates a decoded data block (DDB), and sends the DDB to the destination.

Abstract: 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)}i from a concatenated decoder input array y and a cumulative decision feedback ({circumflex over (b)}1, {circumflex over (b)}2, . . . , {circumflex over (b)}i?1).

Abstract: 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=vGout for an outer transform matrix Gout. 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=uGin for an inner transform matrix Gin. 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 Gout 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 Gout and the inner transform matrix Gin are strictly upper- and lower-triangular matrices, respectively.

Abstract: 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)}i from a concatenated decoder input array y and a cumulative decision feedback ({circumflex over (b)}1, {circumflex over (b)}2, . . . , {circumflex over (b)}i?1).

Abstract: A systematic encoder reliably transferring a source data block (SDB) is configured for an outer transform matrix and an inner transform matrix. An inner encoder receives the SDB and generates an output constraint block (OCB) as an SDB image under an inverse of a submatrix of the inner transform matrix. An outer encoder receives a fixed data block (FDB) and the OCB and generates a transform output block (TOB) as a transform input block (TIB) image under the outer transform matrix. The TIB contains the FDB transparently in a sub-block of the TIB, and the TOB contains the OCB transparently in a sub-block of the TOB. The inner encoder receives the TOB and generates a transmitted code block (TCB), transparently containing the SDB in a sub-block therein.

Abstract: A systematic encoder reliably transferring a source data block (SDB) is configured for an outer transform matrix and an inner transform matrix. An inner encoder receives the SDB and generates an output constraint block (OCB) as an SDB image under an inverse of a submatrix of the inner transform matrix. An outer encoder receives a fixed data block (FDB) and the OCB and generates a transform output block (TOB) as a transform input block (TIB) image under the outer transform matrix. The TIB contains the FDB transparently in a sub-block of the TIB, and the TOB contains the OCB transparently in a sub-block of the TOB. The inner encoder receives the TOB and generates a transmitted code block (TCB), transparently containing the SDB in a sub-block therein.

Abstract: A split decoder apparatus in a communication system provides reliable transfer of a transmitted message from a source to a destination. A channel encoder encodes the transmitted message into a transmitted codeword from a channel code and transmits the transmitted codeword over a channel. The channel produces a channel output in response to the transmitted codeword. In the split decoder apparatus, a decode client receives the channel output and generates a compressed error information, and a decode server receives the compressed error information and generates a compressed error estimate. The decode client receives the compressed error estimate and generates a message estimate. Communication complexity between the decode client and the decode server is reduced. The split decoder apparatus optionally generates a no-errors signal from the channel output, where the decode server is not activated if the no-errors signal indicates that the hard decisions correspond to a valid transmitted codeword.

Abstract: 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=vGout for an outer transform matrix Gout. 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=uGin for an inner transform matrix Gin. 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 Gout 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 Gout and the inner transform matrix Gin are strictly upper- and lower-triangular matrices, respectively.

Abstract: A split decoder apparatus in a communication system provides reliable transfer of a transmitted message from a source to a destination. A channel encoder encodes the transmitted message into a transmitted codeword from a channel code and transmits the transmitted codeword over a channel. The channel produces a channel output in response to the transmitted codeword. In the split decoder apparatus, a decode client receives the channel output and generates a compressed error information, and a decode server receives the compressed error information and generates a compressed error estimate. The decode client receives the compressed error estimate and generates a message estimate. Communication complexity between the decode client and the decode server is reduced. The split decoder apparatus optionally generates a no-errors signal from the channel output, where the decode server is not activated if the no-errors signal indicates that the hard decisions correspond to a valid transmitted codeword.

Abstract: A systematic polar encoder with data checks includes a data mapper receiving input data containing information to be polar coded for transmission and generating modified data, and a nonsystematic polar encoder implementing a transform matrix encoding the modified data to produce a codeword x such that, for some sub-sequence of coordinates S, xS=d. For nonsystematic encoding, a transform input u includes first and second parts for words independent of the data, the second part for an inverse puncture word, a third part carrying the modified data, and a non-null part carrying a check word derived from the modified data. A transform output includes a punctured part for a puncture word, a part carrying the data, and a part serving as redundant symbols, with the codeword x related to the transform output by x=zQ where Q is the complement of the punctured part P.

Abstract: A hybrid automatic repeat request (HARQ) transmitter in a communications system employing a HARQ process, wherein a primary codeword from an arbitrary forward error correction (FEC) code is sent over a communications channel and negatively acknowledged by a HARQ receiver, includes a polar code retransmission apparatus. A primary codeword buffer stores the primary codeword, and a systematic incremental redundancy (IR) encoder receives a first segment of the primary codeword and encodes the first segment into a first IR codeword. The first segment of the primary codeword excludes at least one symbol of the primary codeword, and the systematic IR encoder comprises a systematic polar encoder. Primary codeword segments, received in response to decoding errors, are encoded into IR codewords, with a kth segment xSk of the primary codeword is excluded from retransmission of the kth IR codeword and the IR codewords may be permuted before transmission.

Abstract: A systematic polar encoder with data checks includes a data mapper receiving input data containing information to be polar coded for transmission and generating modified data, and a nonsystematic polar encoder implementing a transform matrix encoding the modified data to produce a codeword x such that, for some sub-sequence of coordinates S, xS=d. For nonsystematic encoding, a transform input u includes first and second parts for words independent of the data, the second part for an inverse puncture word, a third part carrying the modified data, and a non-null part carrying a check word derived from the modified data. A transform output includes a punctured part for a puncture word, a part carrying the data, and a part serving as redundant symbols, with the codeword x related to the transform output by x=zQ where Q is the complement of the punctured part P.

Abstract: A systematic encoder such as a systematic polar encoder for channel encoding to ameliorate the effects of noise in a transmission channel. The codeword carries a data word to be transmitted transparently, and also carries a parity part derived from the data word and a fixed word. Implementations advantageously reduce coding complexity to the order of N log(N), wherein N is the dimension of a matrix of the nth Kronecker power associated with a matrix effectively employed by the encoder.

Abstract: A systematic encoder such as a systematic polar encoder for channel encoding to ameliorate the effects of noise in a transmission channel. The codeword carries a data word to be transmitted transparently, and also carries a parity part derived from the data word and a fixed word. Implementations advantageously reduce coding complexity to the order of Nlog(N), wherein N is the dimension of a matrix of the nth Kronecker power associated with a matrix effectively employed by the encoder.

Abstract: A systematic encoder such as a systematic polar encoder for channel encoding to ameliorate the effects of noise in a transmission channel. The codeword carries a data word to be transmitted transparently, and also carries a parity part derived from the data word and a fixed word. Implementations advantageously reduce coding complexity to the order of N log(N), wherein N is the dimension of a matrix of the nth Kronecker power associated with a matrix effectively employed by the encoder.

Abstract: A systematic encoder such as a systematic polar encoder for channel encoding to ameliorate the effects of noise in a transmission channel. The codeword carries a data word to be transmitted transparently, and also carries a parity part derived from the data word and a fixed word. Implementations advantageously reduce coding complexity to the order of Nlog(N), wherein is the dimension of a matrix of the nth Kronecker power associated with a matrix effectively employed by the encoder.

Abstract: A systematic encoder such as a systematic polar encoder for channel encoding to ameliorate the effects of noise in a transmission channel. The codeword carries a data word to be transmitted transparently, and also carries a parity part derived from the data word and a fixed word. Implementations advantageously reduce coding complexity to the order of N log(N), wherein N is the dimension of a matrix of the n th Kronecker power associated with a matrix effectively employed by the encoder.

Abstract: A systematic encoder such as a systematic polar encoder for channel encoding to ameliorate the effects of noise in a transmission channel. The codeword carries a data word to be transmitted transparently, and also carries a parity part derived from the data word and a fixed word. Implementations advantageously reduce coding complexity to the order of N log(N), wherein N is the dimension of a matrix of the n th Kronecker power associated with a matrix effectively employed by the encoder.

Abstract: A systematic encoder such as a systematic polar encoder for channel encoding to ameliorate the effects of noise in a transmission channel. The codeword carries a data word to be transmitted transparently, and also carries a parity part derived from the data word and a fixed word. Implementations advantageously reduce coding complexity to the order of N log(N), wherein N is the dimension of a matrix of the nth Kronecker power associated with a matrix effectively employed by the encoder.