  One dimensional lattice with an on-site cubic-quintic nonlinear response
described by a cubic-quintic discrete nonlinear Schr\"odinger equation is
tested for asymmetric wave propagation. The lattice is connected to linear side
chains. Asymmetry is introduced by breaking the mirror symmetry of the lattice
with respect to the center of the nonlinear region. Three cases corresponding
to dimer, trimer and quadrimer are discussed with focus on the corresponding
diode-like effect. Transmission coefficients are analytically calculated for
left and right moving waves via backward transfer map. The different
transmission coefficients for the left and right moving waves impinging the
lattice give rise to a diode-like effect which is tested for different
variations in asymmetry and site dependent coefficients. We show that there is
a higher transmission for incoming waves with lower wavenumbers as compared to
the waves with comparatively larger wavenumbers and a diode-like effect
improves by increasing the nonlinear layers. We also show that in the context
of transport through such lattices, the cooperation between cubic and quintic
nonlinear response is not "additive". Finally, we numerically analyse Gaussian
wave packet dynamics impinging on the CQDNLS lattice for all three cases.
