Let us explain this embedding on a small illustrative example where
$m$ and $x$ are respectively a 3 bits column
-vector and a 7 bits column vector and where
+vector and a 7 bits column vector, and where
$\rho_X(i,x,y)$ is equal to 1 for any $i$, $x$, $y$
-(\textit{i.e.}, $\rho_X(i,x,y) = 0$ if $x = y$ and $0$ otherwise).
+(\textit{i.e.}, $\rho_X(i,x,y) = 0$ if $x = y$ and $1$ otherwise).
Let $H$ be the binary Hamming matrix
$$
In the general case, communicating a message of $p$ bits in a cover of
$n=2^p-1$ pixels needs $1-1/2^p$ average changes.
-This Hamming embeding is really efficient to very small payload and is
-not well suited when the size of the message is larger, as in real situation.
+This Hamming embedding is really efficient to very small payload and is
+not well suited when the size of the message is larger, as in real situations.
The matrix $H$ should be changed to deal with higher payload.
Moreover, for any given $H$, finding $y$ that solves $Hy=m$ and
that minimizes $D_X(x,y)$, has an exponential complexity with respect to $n$.
