  We have been investigating the problem of the Anderson localization in a
disordered one dimensional tight-binding model. The disorder is created by the
interaction of mobile particles with other species, immobilized at random
positions. We introduce a novel method of creating correlations in the optical
lattices with such a kind of disorder by using two different lattices with
commensurate lattice lengths to hold two species of the particles. Such a
model, called the generalized random $N$-mer model leads to the appearance of
multiple extended states in contrary to a localization of all states usually
expected in one dimension. We develop a method, based on properties of transfer
matrices which can be used to determine the presence of extended states and
their energies for that class of correlations. Analytical results are compared
with the numerical calculations for several cases which can be realized in
cold-atom experiments.
