Near-Capacity Adaptive Analog Fountain Codes for Wireless Channels

In this paper, we propose a capacity-approaching analog fountain code (AFC) for wireless channels. In AFC, the number of generated coded symbols is potentially limitless. In contrast to the conventional binary rateless codes, each coded symbol in AFC is a real-valued symbol, generated as a weighted sum of $d$ randomly selected information bits, where $d$ and the weight coefficients are randomly selected from predefined probability mass functions. The coded symbols are then directly transmitted through wireless channels. We analyze the error probability of AFC and design the weight set to minimize the error probability. Simulation results show that AFC achieves the capacity of the Gaussian channel in a wide range of signal to noise ratio (SNR).