  We derive various error exponents for communication channels with random
states, which are available non-causally at the encoder only. For both the
finite-alphabet Gel'fand-Pinsker channel and its Gaussian counterpart, the
dirty-paper channel, we derive random coding exponents, error exponents of the
typical random codes (TRCs), and error exponents of expurgated codes. For the
two channel models, we analyze some sub-optimal bin-index decoders, which turn
out to be asymptotically optimal, at least for the random coding error
exponent. For the dirty-paper channel, we show explicitly via a numerical
example, that both the error exponent of the TRC and the expurgated exponent
strictly improve upon the random coding exponent, at relatively low coding
rates, which is a known fact for discrete memoryless channels without random
states. We also show that at rates below capacity, the optimal values of the
dirty-paper design parameter $\alpha$ in the random coding sense and in the TRC
exponent sense are different from one another, and they are both different from
the optimal $\alpha$ that is required for attaining the channel capacity. For
the Gel'fand-Pinsker channel, we allow for a variable-rate random binning code
construction, and prove that the previously proposed maximum penalized mutual
information decoder is asymptotically optimal within a given class of decoders,
at least for the random coding error exponent.
