From f9feb4cb5a39609ffdf39b086e8d796592a71da5 Mon Sep 17 00:00:00 2001 From: cguyeux Date: Mon, 4 Feb 2013 10:29:00 +0100 Subject: [PATCH 1/1] Relecture --- stc.tex | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/stc.tex b/stc.tex index 1ed8b44..e98589f 100644 --- a/stc.tex +++ b/stc.tex @@ -11,14 +11,14 @@ this is for instance the LSBs of the image edge bits. The objective is thus to find $y$ that minimizes $D_X(x,y)$. Hamming embedding proposes a solution to this problem. -Some steganographic +This is why some steganographic schemes~\cite{DBLP:conf/ih/Westfeld01,DBLP:conf/ih/KimDR06,DBLP:conf/mmsec/FridrichPK07} are based on this binary embedding. Furthermore this code provides a vector $y$ s.t. $Hy$ is equal to $m$ for a given binary matrix $H$. Let us explain this embedding on a small illustrative example where $\rho_X(i,x,y)$ is identically equal to 1, -$m$ and $x$ are respectively a 3 bits column +whereas $m$ and $x$ are respectively a 3 bits column vector and a 7 bits column vector. Let then $H$ be the binary Hamming matrix $$ @@ -53,13 +53,13 @@ It is not hard to see that if $y$ is $\overline{x}^j$, then $m = Hy$. It is then possible to embed 3 bits in only 7 LSBs of pixels by modifying at most 1 bit. -In the general case, when communicating $n$ message bits in -$2^n-1$ pixels needs $1-1/2^n$ average changes. \CG{Phrase pas claire}. +In the general case, communicating $n$ message bits in +$2^n-1$ pixels needs $1-1/2^n$ average changes. Unfortunately, for any given $H$, finding $y$ that solves $Hy=m$ and -that minimizes $D_X(x,y)$ has an exponential complexity with respect to $n$. +that minimizes $D_X(x,y)$, has an exponential complexity with respect to $n$. The Syndrome-Trellis Codes (STC) presented by Filler \emph{et al.} in~\cite{DBLP:conf/mediaforensics/FillerJF10} is a practical solution to this complexity. Thanks to this contribution, @@ -73,7 +73,7 @@ every solution of $m=Hy$ as a path through a trellis. Next, the process of finding $y$ consists of two stages: a forward and a backward part. \begin{enumerate} -\item Forward construction of the trellis that depends on $\hat{H}$, on $x$, on $m$, and on $\rho$; +\item Forward construction of the trellis that depends on $\hat{H}$, on $x$, on $m$, and on $\rho$. \item Backward determination of $y$ that minimizes $D$, starting with the complete path having the minimal weight. \end{enumerate} -- 2.39.5