CONSERVATIVE ARRAYS - MULTIDIMENSIONAL MODULATION CODES FOR HOLOGRAPHIC RECORDING

In holographic storage, two-dimensional arrays of binary data is optic ally recorded in a medium via an interference process. To ensure optim um operation of a holographic recording system, it is desirable that t he patterns of 1's (light) and 0's (no light) in the recorded array sa tisfy the following modulation constraint: in each row and column of t he array there are at least t transitions of the type 1 --> 0 or 0 --> 1, for a prescribed integer t. A two-dimensional array with this prop erty is said to be a conservative array of strength t. In general, an n-dimensional conservative array of strength t is a binary array havin g at least t transitions in each column, extending in any of the n dim ensions of the array. We present an algorithm for encoding unconstrain ed 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 greater than or equal to 2t-3, we apply a certain transformation to an arbitrary information array which ensures that the number of transi tions in each dimension is determined by the minimum distance of the c orresponding code.