Coding Techniques for Multidimensional Constrained Channels A Thesis Proposal

Constrained coding has found widespread use in optical and magnetic data storage devices [9]. Proposals for new storage systems such as holographic storage have caused interest in two-dimensional (2D) and three-dimensional (3D) constrained systems as models of data storage on a surface. One-dimensional constraints were extensively studied and there are several known methodologies for designing codes for such constraints [8], [10], [11]. On the other hand, our knowledge of 2D constraints is much less profound. This might be attributed in part to the fact that the practical interest in those constraints has been risen relatively recently. However, it seems that the main reason for such lack of knowledge is the provable di culty of certain problems that relate to 2D constraints compared to the one-dimensional (1D) case [1], [15].