  The DECam Ecliptic Exploration Project (DEEP) is a deep survey of the
trans-Neptunian solar system being carried out on the 4-meter Blanco telescope
at Cerro Tololo Inter-American Observatory in Chile using the Dark Energy
Camera (DECam). By using a shift-and-stack technique to achieve a mean limiting
magnitude of $r \sim 26.2$, DEEP achieves an unprecedented combination of
survey area and depth, enabling quantitative leaps forward in our understanding
of the Kuiper Belt populations. This work reports results from an analysis of
twenty 3 sq.\ deg.\ DECam fields along the invariable plane. We characterize
the efficiency and false-positive rates for our moving-object detection
pipeline, and use this information to construct a Bayesian signal probability
for each detected source. This procedure allows us to treat all of our Kuiper
Belt Object (KBO) detections statistically, simultaneously accounting for
efficiency and false positives. We detect approximately 2300 candidate sources
with KBO-like motion at S/N $>6.5$. We use a subset of these objects to compute
the luminosity function of the Kuiper Belt as a whole, as well as the Cold
Classical (CC) population. We also investigate the absolute magnitude ($H$)
distribution of the CCs, and find consistency with both an exponentially
tapered power-law, which is predicted by streaming instability models of
planetesimal formation, and a rolling power law. Finally, we provide an updated
mass estimate for the Cold Classical Kuiper Belt of $M_{CC}(H_r < 12) =
0.0017^{+0.0010}_{-0.0004} M_{\oplus}$, assuming albedo $p = 0.15$ and density
$\rho = 1$ g cm$^{-3}$.
