Performance Analysis of Short Analog Fountain Codes

Analog fountain codes are a class of rateless codes that have been demonstrated to achieve near-capacity performance for asymptotically long blocks, without any channel state information at the transmitter side. Recently, a new design for these codes has been proposed aimed at improving its performance in the finite block length regime, dubbed short analog fountain codes (S-AFC). S-AFC was shown to score error rates orders of magnitude smaller than AFC for blocks of a few hundred bits long. S-AFC was also shown to achieve average block lengths close to the Polyanskiy-Poor and Verdu bound for high SNR and exhibits no error floors down to 10^-7. In this paper, we derive lower and upper bounds on the block error rate (BLER) of S-AFC. We verify these bounds through Monte Carlo simulations and provide all the proofs in the appendix.