Analysis and Design of Short Analog Fountain Codes for the Multiple Access Channel

In this letter, we design and analyse analog fountain codes (AFC) for the multiple access channel (MAC). First, we present several encoding schemes, including the superposition coding and joint encoding, and decoding schemes, including successive interference cancellation and joint decoding, for multiple access AFC (MA-AFC). We propose different combinations of encoding and decoding schemes for MA-AFC and evaluate their performance in terms of block error rate (BLER) to determine which combination has the best performance. We propose a density evolution (DE) based framework to track the evolution of messages exchanged between check nodes and variable nodes in the iterative joint belief propagation (BP) decoder of MA-AFC. With the proposed DE framework, we formulate optimisation problems to find the optimal AFC code parameters, specifically the weight set, which minimises the bit error rate at a given signal-to-noise ratio (SNR). Simulation results show that the AFC code with the optimised parameters outperforms existing AFC code designs in the multiple access scenario.