# Conservative arrays: Multidimensional modulation codes for holographic recording

## Abstract

In holographic storage, two-dimensional arrays of binary data is optically recorded in a medium via an interference process. To ensure optimum operation of a holographic recording system, it is desirable that the patterns of 1's (light) and 0's (no light) in the recorded array satisfy the following modulation constraint: in each row and column of the array there are at least t transitions of the type 1 → 0 or 0 rarr; 1, for a prescribed integer t. A two-dimensional array with this property is said to be a conservative array of strength t. In general, an n-dimensional conservative array of strength t is a binary array having at least t transitions in each column, extending in any of the n dimensions of the array. We present an algorithm for encoding unconstrained binary data into an n-dimensional conservative array of strength t. The algorithm employs differential coding and error-correcting codes. Using n binary codes - one per dimension - with minimum Hamming distance d ≥ 2t-3, we apply a certain transformation to an arbitrary information array which ensures that the number of transitions in each dimension is determined by the minimum distance of the corresponding code. © 1996 IEEE.