Abstract: An error checking method and apparatus for appending a variable number of redundancy coding information at the end of each data message or packet transmitted over a multi-stage network for the purpose of protecting the data by using an error detecting code. The amount of additional redundancy coding information implemented is variable and increases with the size of the data message or packet to provide a consistent level of protection.

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.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 are 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.