  Due to the short and bursty incoming messages, channel access activities in a
wireless random access system are often fractional. The lack of frequent data
support consequently makes it difficult for the receiver to estimate and track
the time varying channel states with high precision. This paper investigates
random multiple access communication over a compound wireless channel where
channel realization is known neither at the transmitters nor at the receiver.
An achievable rate and error probability tradeoff bound is derived under the
non-asymptotic assumption of a finite codeword length. The results are then
extended to the random multiple access system where the receiver is only
interested in decoding messages from a user subset.
