  Motivated by the analogy between successive interference cancellation and
iterative belief-propagation on erasure channels, irregular repetition slotted
ALOHA (IRSA) strategies have received a lot of attention in the design of
medium access control protocols. The IRSA schemes have been mostly analyzed for
theoretical scenarios for homogenous sources, where they are shown to
substantially improve the system performance compared to classical slotted
ALOHA protocols. In this work, we consider generic systems where sources in
different importance classes compete for a common channel. We propose a new
prioritized IRSA algorithm and derive the probability to correctly resolve
collisions for data from each source class. We then make use of our theoretical
analysis to formulate a new optimization problem for selecting the transmission
strategies of heterogenous sources. We optimize both the replication
probability per class and the source rate per class, in such a way that the
overall system utility is maximized. We then propose a heuristic-based
algorithm for the selection of the transmission strategy, which is built on
intrinsic characteristics of the iterative decoding methods adopted for
recovering from collisions. Experimental results validate the accuracy of the
theoretical study and show the gain of well-chosen prioritized transmission
strategies for transmission of data from heterogenous classes over shared
wireless channels.
