A method may be provided to detect and correct data errors in a data system where a data message has been encoded with outer parity bits based on the data message using an outer encoding technique to provide an outer codeword and with inner parity bits based on the outer codeword using an inner encoding technique different than the outer encoding technique to provide an inner codeword. The method may include using the inner parity bits and an inner decoding technique corresponding to the inner encoding technique to perform inner decoding of the inner codeword. Responsive to performing inner decoding of the inner codeword without error, the data message may be extracted from a result of inner decoding the inner codeword without using the outer parity bits to decode the result of inner decoding the inner codeword. Related systems are also discussed.