Multimode Coding for Generating Conservative Arrays for Holographic Storage

In order to minimize the interference between adjacent data arrays recorded in the same holographic volume, the patterns of 1\´s and 0\´s in each data array should be t- conservative, i.e., for a prescribed integer t, there should be at least t transitions of the form 1 rarr 0 or 0 rarr 1 in each column and row of the data array. In this paper, we present extensions to the algorithm proposed by Vardy et al. for encoding unconstrained binary arrays into t-conservative arrays. We set our work in the context of multimode codes. The multimode encoding process involves adding each input array to a set of control arrays to form a selection set, and selecting one that "best" satisfies the predefined selection criterion. We propose a new approach for construction of the control arrays, and demonstrate how the algorithm proposed by Vardy et al. is a special case of this approach. We also propose a novel approach for embedding the index of the control arrays into the encoded array, and propose alternatives for array selection.