  As an extension of the discrete Sommerfeld problems on lattices, the
scattering of a time harmonic wave is considered on an infinite square lattice
when there exists a pair of semi-infinite cracks or rigid constraints. Due to
the presence of stagger, also called offset, in the alignment of the defect
edges the asymmetry in the problem leads to a matrix Wiener-Hopf kernel that
cannot be reduced to scalar Wiener-Hopf in any known way. In the corresponding
continuum model the same problem is a well known formidable one which possesses
certain special structure with exponentially growing elements on the diagonal
of kernel. From this viewpoint the present paper tackles a discrete analogue of
the same by reformulating the Wiener-Hopf problem and reducing it to a finite
set of linear algebraic equations; the coefficients of which can be found by an
application of the scalar Wiener-Hopf factorization. The considered discrete
paradigm involving lattice waves is relevant for modern applications of
mechanics and physics at small length scales.
