| Summary: | Multi-track 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 dissertation focuses on methods of constructing such codes. Two methods are presented. The first uses state-splitting to construct multi-track (d,k) trellis codes. An example is presented in which a (1,3) trellis code is constructed having a code rate of R = 2/3. The second method results in the construction of multi-track (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. Additionally, a new class of multi-track codes referred to as redundant multi-track (d,k) codes, is introduced. These redundant codes, unlike the original multi-track (d,k) codes which are completely intolerant of faulty tracks, allow for r faulty tracks while maintaining synchronization.
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