  Compressed sensing is a new scheme which shows the ability to recover sparse
signal from fewer measurements, using $l_1$ minimization. Recently, Chartrand
and Staneva shown in \cite{CS1} that the $l_p$ minimization with $0<p<1$
recovers sparse signals from fewer linear measurements than does the $l_1$
minimization. They proved that $l_p$ minimization with $0<p<1$ recovers
$S$-sparse signals $x\in\RN$ from fewer Gaussian random measurements for some
smaller $p$ with probability exceeding $$1 - 1 / {N\choose S}.$$ The first aim
of this paper is to show that above result is right for the case of
random,Gaussian measurements with probability exceeding $1-2e^{-c(p)M},$ where
$M$ is the numbers of rows of random, Gaussian measurements and $c(p)$ is a
positive constant that guarantees $1-2e^{-c(p)M}>1 - 1 / {N\choose S}$ for $p$
smaller. The second purpose of the paper is to show that under certain weaker
conditions, decoders $\triangle_p$ are stable in the sense that they are
$(2,p)$ instance optimal for a large class of encoder for $0<p<1.$
