In this paper, we focus on the design and analysis of the Analog Fountain Code (AFC) for short packet communications. We first propose a density evolution (DE) based framework, which tracks the evolution of the probability density function of the messages exchanged between variable and check nodes of AFC in the belief propagation decoder. Using the proposed DE framework, we formulate an optimisation problem to find the optimal AFC code parameters, including the weight-set, which minimises the bit error rate at a given signal-to-noise ratio (SNR). Our results show the superiority of our AFC code design compared to existing designs of AFC in the literature and thus the validity of the proposed DE framework in the asymptotically long block length regime. We then focus on selecting the precoder to improve the performance of AFC at short block lengths. Simulation results show that lower precode rates obtain better realised rates over a wide SNR range for short information block lengths. We also discuss the complexity of the AFC decoder and propose a threshold-based decoder to reduce the complexity.
翻译:在本文中,我们侧重于设计和分析用于短包通信的模拟喷泉编码(AFC)的设计和分析。我们首先提出一个基于密度演变的框架,以跟踪AFC在信仰传播解码器中不同变量之间交换的信息的概率密度函数的演变和检查节点。我们利用拟议的DE框架,提出了一个优化问题,以找到最佳的ACFC编码参数,包括重量组,在给定的信号到噪音比率(SNR)中将位误差率最小化。我们的结果显示,我们的AFC编码设计在文献中优于AFC的现有设计,因此,拟议的DE框架在无症状长块长度制度中的有效性。我们然后侧重于选择预编码,在短块长度上改进AFC的性能。模拟结果表明,较低的预编码率在宽的SNR范围内,在短信息区长度上获得更好的实现率。我们还讨论了AFC decoder的复杂程度,并提出了降低复杂性的阈值拆解码器。