In this paper, we analyze the information theoretic lower bound on the
necessary number of samples needed for recovering a sparse signal under
different compressed sensing settings. We focus on the weighted graph model, a
model-based framework proposed by Hegde et al. (2015), for standard compressed
sensing as well as for one-bit compressed sensing. We study both the noisy and
noiseless regimes. Our analysis is general in the sense that it applies to any
algorithm used to recover the signal. We carefully construct restricted
ensembles for different settings and then apply Fano's inequality to establish
the lower bound on the necessary number of samples. Furthermore, we show that
our bound is tight for one-bit compressed sensing, while for standard
compressed sensing, our bound is tight up to a logarithmic factor of the number
of non-zero entries in the signal