Analysis and Design of Analog Fountain Codes for Short Packet Communications in IoT

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 minimizes the bit error rate at a given signal-to-noise ratio (SNR). Our results show the superiority of our code design in comparison to existing code designs and thus the validity of the proposed DE framework in the asymptotic block length regime. We then focus on the selection of the precoder to improve the performance of AFC at short block lengths. Simulation results show that lower precoder rates obtain better realised rates over a wide SNR range for short information block length.