Optimal Rectangular Code for High Density Magnetic Tapes

Abstract

IBM's 6250 bpi 3420 series tape units require a powerful error-correcting code for the standard 9-track format. The optimal rectangular code (0 RC), presented here, is designed to correct any single-track error or, given erasure pointers, any double-track error in the tape. The code achieves this by conforming to a rectangular codeword of which two orthogonal sides are check bits. The code is specially tailored from a general class of b-adjacent codes. The ORC can be implemented without a buffer for encoding and offers a simple error-correction mechanism. The code can be generalized to multiple-channel applications.

MDS array codes for correcting a single criss-cross error

“…If there was an error E in, say, column t, and all the other columns are correct, (10) and (11) give…”

“…First, assume that two erasures have occurred in columns s and t, 0 s < t p 0 2. In order to compute the column syndromes according to (10) and (11), we assume that r s () = r t () = 0. Then, we have to find the missing elements Es and Et.…”

“…Find S1() according to (10) and S l () according to (11). Then, let E s be the solution of the recursion given by (20) The last case we need to consider in order to complete the decoding of two erasures, is the case in which a row and a column have been erased.…”

On the construction of irreducible self-reciprocal polynomials over finite fields

“…Self-reciprocal polynomials over finite fields are used to generate reversible codes with a read-backward property (J. L. Massey [13], S. J. Hong and D. C. Bossen [10], A. M. Patel and S. J. Hong [15]). The fact that self-reciprocal polynomials are given by specifying only half of their coefficients is of importance (E. R. Berlekamp [2]).…”

Error Recovery Scheme for the IBM 3850 Mass Storage System

“…The bit shift usually results in a two-bit error, where 01 is read in place of 10 or vice versa. The nine-track 6250-bpi tape machines feature an error-correction code [4] which corrects various combinations of one or two full tracks and multiple numbers of one-bit and two-bit errors.…”