Exploring the spectral \textit{information content} in the LAMOST
  medium-resolution survey (MRS)
  Low-resolution spectra are proved competitive to high-resolution spectra in
determining many stellar labels at comparable precision. It is useful to
consider the spectral information content when assessing the capability of a
stellar spectrum in deriving precise stellar labels. In this work, we quantify
the information content brought by the LAMOST-II medium-resolution
spectroscopic survey (MRS) using the gradient spectra and the
coefficients-of-dependence (CODs). In general, the wavelength coverage of the
MRS well constrains the stellar labels but the sensitivities of different
stellar labels vary with spectral types and metallicity of the stars of
interest and, therefore, affect the performance of the stellar label
determination from the MRS spectra. Applying the SLAM to the synthetic spectra
which mimic the MRS data, we find the precision of the fundamental stellar
parameters Teff, logg and [M/H] are better when combining both the blue and red
bands of the MRS. This is especially important for warm stars since the
H$\alpha$ line located in the red part plays a more important role in
determining the effective temperature for warm stars. With blue and red parts
together, we are able to reach similar performance to the low-resolution
spectra except for warm stars. However, at [M/H]$\sim-2.0$ dex, the
uncertainties of fundamental stellar labels estimated from MRS are
substantially larger than those from low-resolution spectra. We also tested the
uncertainties of Teff, logg and [M/H] of from MRS data induced from the radial
velocity mismatch and find that a mismatch of about 1 km s$^{-1}$, which is
typical for LAMOST MRS data, would not significantly affect the stellar label
estimates. At last, reference precision limits are calculated using synthetic
gradient spectra, according to which we expect abundances of at least 17
elements to be measured precisely from MRS spectra.
