A NEW CLASS OF 2-DIMENSIONAL RLL RECORDING CODES

There exists in multi-channel recording the opportunity to use modulation codes in two dimensions. The benefits of using two dimensions include improved clocking, in terms of more clocking transitions and fewer clock circuits, and improved ratios of user bits to recorded bits. Recent work has described a class of d(x), k(y) codes in two dimensions which satisfy the d(x) constraint in one dimension and the k(y) constraint in the other. In tape systems, for instance, this method is extremely vulnerable to dropouts and might not be useful. We propose a new class of two-dimensional run-length codes that operate using the usual d(x), k(x) constraint along the track and add an additional ky constraint across the tracks. An advantage of this approach is that the horizontal d(x), k(x) code is allowed a much larger k(x) constraint since it is no longer the sole carrier of clocking information. Capacities are calculated for a range of codes and number of channels and an example of the construction one such code by both sliding block and fixed block techniques is given. Finally, an extension of the codes that preserves clocking during channel loss is described.