  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).
