Two-Dimensional Parity Checking

Two-dimensional arrays of digital information occur frequently in automatic computer systems. Sometimes the two dimensions are physical, as on a magnetic tape or in a magnetic core matrix. Often the two dimensions are conceptual, as in a numerical matrix, or when a two-dimensional structure has been imposed on information by the programmer. For purposes of error detection and correction, redundancy can be incorporated into an array of binary digits, or logical matrix, by the imposition of certain constraints upon specified groups of digits in the array. A common and practical type of constraint is the specification of the pari ty of the sum of the digits in the group. The systematic specification of parity check groups for the purpose of detecting and /or correcting errors with economical circuitry (or programming) has been discussed by Hamming [1], by Sacks [2], and by Bose and Ray-Chaudhuri [3]. Because access to digits within a single row or a single column of the matrix is usually easier than access to scattered digits, it is natural to require tha t each pari ty check group lie wholly within a given row or column. Lower redundancy can be achieved by selection of parity check groups both from rows and from columns than from either alone.