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，该方案以帧为单位划分时隙，通过将整个帧上的介质访问控制层码与每个时隙上的物理层码进行级联而获得。在该框架下，结合信道噪声引起的时隙解码错误与数据包碰撞场景，进行了渐近分析，推导出密度演进方程、最小丢包概率与平均负载阈值的渐近极限，以及阈值值的逆界。该分析被用作评估性能极限的工具，具体表现为达到给定丢包概率所需的最小信噪比，同时为具有特定物理层编码方案的任意IRSA方案提供了收敛边界极限。通过比较若干已知编码选项（包括在时隙级实现随机编码界的选项），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方案的收敛边界极限距离随机编码界在数分贝以内。