A transmitter generates an encoded vector by encoding a data vector, the encoded vector representing payload information and parity information. The encoding is mathematically equivalent to calculating three or more forward error correction (FEC) codewords from the data vector and then calculating the encoded vector from the codewords, at least one codeword being calculated from at least one recursion of a mathematical operation, and at least one codeword comprising more than 6 terms. The transmitter transmits a signal representing the encoded vector over a communication channel. A receiver determines a vector estimate from the signal and recovers the data vector from the vector estimate by sequentially decoding the codewords, wherein at least one codeword that is decoded earlier in the decoding enhances an estimate of at least one codeword that is decoded later in the decoding.