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 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 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 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.