IRSA-based Random Access over the Gaussian Channel

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.