Capacity approaching analog fountain codes

In this paper, we propose an analog fountain code (AFC) to approach the capacity of the Gaussian channel in a wide range of signal to noise ratios (SNRs). The proposed code is rateless as the number of the generated coded symbols is potentially limitless; thus, enabling the transmitter to automatically adapt to the channel condition and sending as many coded symbols as required by the destination. Each coded symbol in AFC is directly generated from information symbols, by linearly combining them with real weighting coefficients. Weight coefficients and the degree of each coded symbol are chosen from predetermined weight set and degree distribution function, respectively. We further formulate an optimization problem to find the optimum weight set in order to maximize the efficiency of the proposed code. Simulation results show that the proposed code can approach the capacity of the Gaussian channel across a wide range of SNR values.