inline compensation can be done by DCF which has a negative dispersion coefficient so you can use it before or after the fiber, just manually calculate the single mode fiber (SMF) dispersion and accordingly connect the required length of the DCF and eliminate dispersion effect. Pre-, post-, and symmetrical-compensation can be done by using DCF.
FBG: The idea is to create a time delay between different spectral components of the signal. Because of this different velocity of propagation of different spectral components, the pulse spreads, so we need to create fiber grating with period linearly reducing along the grating, because the higher frequencies will reflect after longer propagation in the grating a time delay between lower and higher frequency components will appear which is just opposite to this created in the SMF.
OPC: also called as the optical phase conjugationor midspan spectral inversion where the rays retrace the same path as they travelled upto the OPC…in other words the phaseis 180 shifted..
HOLEY FIBER: also called photonic crytal fibers and is emerging technology in terms of dispersion compensation.
GOOD EXPLANATION THAT (y)