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.