A decoder including a decode module, a matrix module, and a marking module. The decode module receives data and performs a first decoding iteration to decode the data. The first decoding iteration includes generating a first matrix having a first byte. The matrix module generates a second matrix based on the first matrix. The second matrix includes the first and second bytes. The second byte is adjacent and sequentially prior or subsequent to the first byte. The marking module: determines whether the first byte has been correctly decoded; based on determining whether the first byte has been correctly decoded, determines a status of the second byte; and based on the status of the second byte, marks the first byte as an erasure. The decode module, based on the second byte being marked as an erasure, corrects the second byte during the second decoding iteration.