  For several communication models, the dispersive part of a communication
channel is described by a bilinear operation $T$ between the possible sets of
input signals and channel parameters. The received channel output has then to
be identified from the image $T(X,Y)$ of the input signal difference sets $X$
and the channel state sets $Y$. The main goal in this contribution is to
characterize the compressibility of $T(X,Y)$ with respect to an ambient
dimension $N$. In this paper we show that a restricted norm multiplicativity of
$T$ on all canonical subspaces $X$ and $Y$ with dimension $S$ resp. $F$ is
sufficient for the reconstruction of output signals with an overwhelming
probability from $\mathcal{O}((S+F)\log N)$ random sub-Gaussian measurements.
