i.i.d. That said, we suspect that the MMSE for MMV-1 and MMV-2 could differ by some higher order terms. If the entries of these super symbols are not i.i.d., which is true in some practical MMV applications [@ZinielSchniter2013MMV], then it becomes more difficult to analyze the covariance matrix $\G_{\mu}$ as in Section \[sec:proof\]. Therefore, we do not have an analysis for non-i.i.d. entries within $\s_l$ and $\x_l^{\{\cdot\}}$. However, we speculate that MMV-1 might have lower MMSE than MMV-2 in that case.

[**Link to SMV with block sparse signal:**]{} The signal $\s$ in  is a block sparse signal comprised of $N$ blocks of length $J$. We study a single measurement vector (SMV) problem by replacing the measurement matrix $\F$ in  with an i.i.d. Gaussian matrix ${\mathbf A}\in\mathbb{R}^{MJ\times NJ}$, i.e., $\y={\mathbf A}\s+\z$. The entries of ${\mathbf A}$ follow the distribution, $A_{\mu l}\sim \mathcal{N}(0,\frac{1}{NJ})$. This SMV is similar to the setting in Barbier and Krzakala [@Barbier2015], except for the different priors and different $\ell_2$ norms in each row of ${\mathbf A}$. We consider these differences while following their derivation [@Barbier2015], and obtain the same free energy expression as . We have also shown that MMV-1 and MMV-2 have the same MMSE in the 