  This paper studies multiuser random coding techniques for channel coding with
a given (possibly suboptimal) decoding rule. For the mismatched discrete
memoryless multiple-access channel, an error exponent is obtained that is tight
with respect to the ensemble average, and positive within the interior of
Lapidoth's achievable rate region. This exponent proves the ensemble tightness
of the exponent of Liu and Hughes in the case of maximum-likelihood decoding.
An equivalent dual form of Lapidoth's achievable rate region is given, and the
latter is shown to extend immediately to channels with infinite and continuous
alphabets. In the setting of single-user mismatched decoding, similar analysis
techniques are applied to a refined version of superposition coding, which is
shown to achieve rates at least as high as standard superposition coding for
any set of random-coding parameters.
