  The intra-cluster and inter-galactic media (ICM, IGM) that pervade the large
scale structure of the Universe are known to be magnetised at sub-micro Gauss
to micro Gauss levels and to contain cosmic rays (CRs). The acceleration of CRs
and their evolution along with that of magnetic fields in these media is still
not well understood. Diffuse radio sources of synchrotron origin associated
with the ICM such as radio halos, relics and mini-halos are direct probes of
the underlying mechanisms of CR acceleration. Observations with radiotelescopes
such as the GMRT, the VLA and the WSRT (0.15 - 2 GHz) have revealed scaling
relations between the thermal and non-thermal properties of clusters and favour
the role of shocks in the formation of radio relics and of turbulent
re-acceleration in the formation of radio halos and mini-halos. Due to the
limitations of current radio telescopes, wide-band studies and exploration of
low mass and supercluster-scale systems is difficult. The Square Kilometer
Array (SKA) is a next generation radio telescope that will operate in the
frequency range of 0.05 - 20 GHz with unprecedented sensitivities and
resolutions. The expected detection limits of SKA will reveal a few hundred to
thousand new radio halos, relics and mini-halos providing the first large and
comprehensive samples for their study. The wide frequency coverage along with
sensitivity to extended structures will be able to constrain the CR
acceleration mechanisms. The higher frequency (> 5 GHz) observations will be
able to use the Sunyaev-Zel'dovich effect to probe the ICM pressure in addition
to the tracers such as lobes of head-tail radio sources. The SKA also opens
prospects to detect the "off-state" radio emission from the ICM predicted by
the hadronic models and the turbulent re-acceleration models. [abridged]
