  This paper studies the random-coding exponent of joint source-channel coding
for the multiple-access channel with correlated sources. For each user, by
defining a threshold, the messages of each source are partitioned into two
classes. The achievable exponent for correlated sources with two
message-dependent input distributions for each user is determined and shown to
be larger than that achieved using only one input distribution for each user. A
system of equations is presented to determine the optimal thresholds maximizing
the achievable exponent. The obtained exponent is compared with the one derived
for the MAC with independent sources.
