Method and apparatus for modulation of multi-dimensional data in

Abstract

A modulator apparatus for modulating arrays of input data V.sub.in to be stored in a holographic recording medium is disclosed wherein the final output data array V.sub.out has frequent transitions from light to dark and from dark to light in either dimension across the data page and has the total amount of illuminated regions throughout the entire data page held constant. These two constraints are achieved by a first set of control arrays obtained from two fixed sets of m.times.n binary arrays {A.sub.0, A.sub.1, . . . , A.sub.n } and {B.sub.0, B.sub.1, . . . , B.sub.m } which in turn are obtained from fixed sets of binary control vectors {a.sub.0, a.sub.0, a.sub.1, . . . , a.sub.n }, {b.sub.0, b.sub.1, . . . , b.sub.m }, respectively. The control vectors a.sub.0, a.sub.1, . . . , a.sub.n any n+1 fixed elements of the inverse mapping, .phi. .sup.1 (C.sub.1), of the (t-2) error-correcting code C.sub.1 of length m. The control vectors b.sub.0, b.sub.1, . . . , b.sub.m are any m+1 fixed elements of the inverse mapping, .phi. .sup.1 (C.sub.2), of the (t-s) error-correcting code C.sub.2 of length n. The first constraint is achieved by V'.sub.in =V.sub.in .sym.(A.sym.B). In order to balance the modulated array, a second set of control arrays {W.sub.0, W.sub.1, W.sub.2, . . . , W.sub.1, W.sub.2, . . . , W.sub.mn-1 } is obtained from the set of control vectors {W.sub.0, W.sub.1, W.sub.2, . . . , W.sub.mn-1 }. The second constraint is achieved by complementing the bits of the input binary array V'.sub.in in a horizontal readout order terminating after the first i bits. The final modulated output array V.sub.out =V'.sub.in .sym.W simultaneously satisfies both constraints.