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.