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.

翻译：针对基于不规则重复时隙ALOHA（IRSA）协议、在高斯多址信道上运行的同步免授权海量多址接入方案，提出了一种分析框架。本文将基于IRSA的方案视为无源时隙随机接入码类的一个实例，其运行于按时间时隙划分的帧结构上，并通过在整帧上链接媒体接入控制层码字与每个时隙的物理层码字实现。在该框架下，针对信道噪声导致的碰撞及时隙解码错误，进行了渐近分析，由此推导出密度进化方程、最小丢包概率与平均负载阈值的渐近极限，以及阈值值的逆向界。该分析作为工具用于评估在满足给定丢包概率所需的最小信噪比方面的性能极限，并给出了适用于任何给定物理层编码方案的IRSA方案的收敛边界。通过对比若干已知编码选项（包括在时隙级别达到随机编码界的方案），对能量效率与频谱效率之间的权衡进行了数值评估。结果表明，当活跃发射机数量足够大时，基于IRSA的方案收敛边界与随机编码界相差在数分贝以内。