Statistics of the epoch of reionization 21-cm signal - I. Power spectrum
  error-covariance
  The non-Gaussian nature of the epoch of reionization (EoR) 21-cm signal has a
significant impact on the error variance of its power spectrum $P({\bf
\textit{k}})$. We have used a large ensemble of semi-numerical simulations and
an analytical model to estimate the effect of this non-Gaussianity on the
entire error-covariance matrix ${\mathcal{C}}_{ij}$. Our analytical model shows
that ${\mathcal{C}}_{ij}$ has contributions from two sources. One is the usual
variance for a Gaussian random field which scales inversely of the number of
modes that goes into the estimation of $P({\bf \textit{k}})$. The other is the
trispectrum of the signal. Using the simulated 21-cm signal ensemble, an
ensemble of the randomized signal and ensembles of Gaussian random ensembles we
have quantified the effect of the trispectrum on the error variance
${\mathcal{C}}_{ij}$. We find that its relative contribution is comparable to
or larger than that of the Gaussian term for the $k$ range $0.3 \leq k \leq 1.0
\,{\rm Mpc}^{-1}$, and can be even $\sim 200$ times larger at $k \sim 5\, {\rm
Mpc}^{-1}$. We also establish that the off-diagonal terms of
${\mathcal{C}}_{ij}$ have statistically significant non-zero values which arise
purely from the trispectrum. This further signifies that the error in different
$k$ modes are not independent. We find a strong correlation between the errors
at large $k$ values ($\ge 0.5 \,{\rm Mpc}^{-1}$), and a weak correlation
between the smallest and largest $k$ values. There is also a small
anti-correlation between the errors in the smallest and intermediate $k$
values. These results are relevant for the $k$ range that will be probed by the
current and upcoming EoR 21-cm experiments.
