RUNLENGTH-LIMITED CODES FOR SINGLE ERROR-DETECTION AND SINGLE ERROR-CORRECTION WITH MIXED-TYPE ERRORS

Runlength-limited (RLL) codes are used in magnetic recording. The erro r patterns that occur with peak detection magnetic recording systems w hen using a runlength-limited code consist of both symmetric errors an d shift errors, We will refer to shift errors and symmetric errors col lectively as mixed-type errors. In this correspondence, a method of pr oviding 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 con straints and to provide some error control. The cases of single error detection and single error correction are investigated, where the sing le error is allowed to be a shift error or a symmetric error. Bounds a re discussed on the possible lengths for the parity blocks. It is show n that the single error-detection codes are the best possible in terms of the length of the parity blocks.