  This paper studies the second-order asymptotics of coding rates for the
discrete memoryless multiple-access channel with a fixed target error
probability. Using constant-composition random coding, coded time-sharing, and
a variant of Hoeffding's combinatorial central limit theorem, an inner bound on
the set of locally achievable second-order coding rates is given for each point
on the boundary of the capacity region. It is shown that the inner bound for
constant-composition random coding includes that recovered by i.i.d. random
coding, and that the inclusion may be strict. The inner bound is extended to
the Gaussian multiple-access channel via an increasingly fine quantization of
the inputs.
