A New Decoding Method for Double Error Correcting Cross Parity Codes

Abstract

In this paper a new and simple method for 2-bit error correction for cross parity codes is proposed. All single and double bit errors, concerning data bits, are corrected. For checkbit errors up to a weight of 2, this method ensures that the data bits are free of errors. In a cross parity code the data bits are conceptually arranged in a rectangular array. The check sums are formed over bits along columns, rows and diagonals. In addition, the parity of all data bits is determined. If a 1-bit error occurs in the data bits, the erroneous bit is located at the intersection of three straight lines: a row, a column and a diagonal. For 2-bit data errors on distinct lines, the erroneous bits are located in the same way. For 2-bit data errors, that share a line, two straight lines per erroneous bit can be identified by the check bits. In a first step the bits at the four intersection points are inverted. Thereby the two errors are corrected and two new errors are generated. In case of odd side length, the two generated errors are located at three different straight lines each and can be easily corrected in a second step.