Runlength limited codes for single error-detection and single error-correction with mixed type errors

Abstract

Runlength limited (RLL) codes are used in magnetic recording. The error patterns that occur with peak detection magnetic recording systems when using a runlength-limited code consist of both symmetric errors and shift errors. We refer to shift errors and symmetric errors collectively as mixed type errors. A method of providing error control for mixed type errors that occur in a runlength limited code comprised of (d, k) constrained sequences is examined. The coding scheme is to choose parity blocks to insert in the constrained information sequence. The parity blocks are chosen to satisfy the constraints and to provide some error control. The cases of single error-detection and single error-correction are investigated, where the single error is allowed to be a shift error or a symmetric error. Bounds are discussed on the possible lengths for the parity blocks. It is shown that the single error-detection codes are the best possible in terms of the length of the parity blocks.