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Modulation coding, to limit the number of consecutive zeros in a data stream, is essential in digital magnetic recording/playback systems. Additionally, such systems require error-correction coding to ensure that the decoded output matches the recorder input, even if noise is present. Typically, these two coding steps have been performed independently, although various methods of combining them into one step have recently appeared. Another recent development is two-dimensional modulation codes, which meet runlength constraints using several parallel recording tracks, significantly increasing channel capacity. This correspondence combines these two ideas. Previous techniques (both block and trellis structures) for combining error correction and modulation coding are surveyed, with discussion of their applicability in the two-dimensional case. One approach, based on trellis-coded modulation, is explored in detail, and a class of codes is developed which exploits the increased capacity to achieve good error-correcting ability at the same rate as common non-error-correcting one-dimensional codes. Index Terms - Constrained channels, constrained codes, (d, k) codes, recording codes.

A new construction for n-track (d, k) codes with redundancy r, referred to as (d, k; n, r) codes, is presented. This construction applies single-track (d, k + [Delta]k) codes (with certain extra constraints and appropriate amounts of delay) on each of the n tracks. This construction achieves a large part of the capacity increases possible when using (d, k; n, r) codes, has simple encoders and decoders, and exhibits considerable robustness to faulty tracks. It is shown that under this construction, (d, k; n, r) codes can achieve at least (n - r - 1)/n * 100% of the gap in capacity between conventional (d, k) and (d, [infinity]) codes. Several practical examples of (d, k; n, r) codes under this construction are presented. Index Terms - (d, k) codes, modulation codes, run-length-limited codes, synchronization, capacity.

Multitrack run-length-limited (d, k) modulation codes were recently introduced as a method to increase storage densities in magnetic and optical recording systems. These codes are a generalization of the usual run-length-limited (d, k) codes and provide for increased storage density by relaxing the k-constraint and encoding multiple tracks in parallel. Previously, n-track (d, k) codes used all n tracks to satisfy the k constraint causing synchronization to be completely intolerant of faulty tracks. In this paper, we present multitrack (d, k) codes which allow for r faulty tracks by mandating that all subsets of n - r tracks satisfy the k constraint.

Multitrack run-length-limited (d, k) modulation codes were recently introduced as a method to increase storage densities in magnetic and optical recording systems. These codes are a generalization of the usual run-length-limited (d, k) codes and provide for increased storage density by relaxing the k-constraint and encoding multiple tracks in parallel. This paper introduces a method to construct multitrack (d, k) block codes which are implemented via an enumeration scheme based on the trellis description of the (d, k) constraints. This implementation results in memory requirements which increase only linearly with block length as opposed to the exponential increases arising from look-up table implementations of block codes.