  A framework for the analysis of synchronous grant-free massive multiple
access schemes based on the irregular repetition slotted ALOHA (IRSA) protocol
and operating over the Gaussian multiple access channel is presented.
IRSA-based schemes are considered here as an instance of the class of unsourced
slotted random access codes, operating over a frame partitioned in time slots,
and are obtained by concatenation of a medium access control layer code over
the entire frame and a physical layer code over each slot. In this framework,
an asymptotic analysis is carried out in presence of both collisions and slot
decoding errors due to channel noise, which allows the derivation of
density-evolution equations, asymptotic limits for minimum packet loss
probability and average load threshold, and a converse bound for threshold
values. This analysis is exploited as a tool for the evaluation of performance
limits in terms of minimum signal-to-noise ratio required to achieve a given
packet loss probability, and also provides convergence boundary limits that
hold for any IRSA scheme with given physical layer coding scheme. The tradeoff
between energy efficiency and spectrum efficiency is numerically evaluated
comparing some known coding options, including those achieving random coding
bounds at slot level. It is shown that IRSA-based schemes have a convergence
boundary limit within few dB from the random coding bound when the number of
active transmitters is sufficiently large.
