Some emerging 5G and beyond use-cases impose stringent latency constraints, which necessitates a paradigm shift towards finite blocklength performance analysis. In contrast to Shannon capacity-achieving codes, the codeword length in the finite blocklength regime (FBR) is a critical design parameter that imposes an intricate tradeoff between delay, reliability, and information coding rate. In this context, this paper presents a novel mathematical analysis to characterize the performance of large-scale downlink networks using short codewords. Theoretical achievable rates, outage probability, and reliability expressions are derived using the finite blocklength coding theory in conjunction with stochastic geometry, and compared to the performance in the asymptotic regime (AR). Achievable rates under practical modulation schemes as well as multilevel polar coded modulation (MLPCM) are investigated. Numerical results provide theoretical performance benchmarks, highlight the potential of MLPCM in achieving close to optimal performance with short codewords, and confirm the discrepancy between the performance in the FBR and that predicted by analysis in the AR. Finally, the meta distribution of the coding rate is derived, providing the percentiles of users that achieve a predefined target rate in a network.

翻译：一些新兴的5G及未来应用场景对时延提出了严格约束，这迫使性能分析范式转向有限块长研究。与香农容量理想编码不同，有限块长机制（FBR）中的码字长度是一个关键设计参数，它在时延、可靠性和信息编码速率之间引入了复杂的权衡关系。在此背景下，本文提出了一种新颖的数学分析方法，用于刻画采用短码字的大规模下行网络性能。通过结合有限块长编码理论与随机几何，推导出理论可达速率、中断概率和可靠性的表达式，并与渐近机制（AR）下的性能进行对比。研究了实际调制方案以及多级极化编码调制（MLPCM）下的可达速率。数值结果提供了理论性能基准，凸显了MLPCM在短码字条件下实现接近最优性能的潜力，并证实了FBR性能与AR分析预测之间的差异。最后，推导了编码速率的元分布，给出了网络中达到预定目标速率的用户百分位数。