A system for providing data encoding includes: an encoder configured to encode message data with an encoding parity-check matrix having a parity part that is in lower-triangular form to generate an encoded message data, the encoded message data being for decoded by a decoder; wherein the encoding parity-check matrix is based on a decoding parity-check matrix that does not comprise any degree-1 node in a parity part of the decoding parity-check matrix; and wherein the system further comprises a non-transitory medium for storing the encoding parity-check matrix, wherein the non-transitory medium is a part of the encoder or is communicatively coupled to the encoder.