Coded Slotted ALOHA Random Access over the Gaussian Channel

Energy efficiency maximization for given traffic and target packet loss probability is a main design goal for grant-free protocols supporting massive connectivity. This paper investigates the performance limits of a class of coded slotted ALOHA (CSA)based protocols over the Gaussian channel. Assuming a multipacket reception decoder with perfect estimation of the number of packets in a slot and ideal error detection, we present a novel asymptotic analytical framework that allows deriving the minimum packet loss probability limits, the conditions for an <on-off” behavior of packet loss probability versus average load with a well-defined threshold, a converse bound for threshold values, and the achievable <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$E_{b} / N_{0}$</tex> limits. Numerical results show that CSA schemes have energy efficiency limits within few dB from the random coding bounds, with 1-2 dB improvement to irregular repetition slotted ALOHA (IRSA) ones.