  In some applications, the variance of additive measurement noise depends on
the signal that we aim to measure. For instance, additive Gaussian
signal-dependent noise (AGSDN) channel models are used in molecular and optical
communication. Herein we provide lower and upper bounds on the capacity of
additive signal-dependent noise (ASDN) channels. The idea of the first lower
bound is the extension of the majorization inequality, and for the second one,
it uses some calculations based on the fact that $h(Y) > h (Y|Z)$. Both of them
are valid for all additive signal-dependent noise (ASDN) channels defined in
the paper. The upper bound is based on a previous idea of the authors
("symmetric relative entropy") and is used for the additive Gaussian
signal-dependent noise (AGSDN) channels. These bounds indicate that in ASDN
channels (unlike the classical AWGN channels), the capacity does not
necessarily become larger by making the variance function of the noise smaller.
We also provide sufficient conditions under which the capacity becomes
infinity. This is complemented by a number of conditions that imply capacity is
finite and a unique capacity achieving measure exists (in the sense of the
output measure).
