Analysis of PCO Raptor codes and Turbo-Fountain codes on noiseless channels

This paper deals with precode-only (PCO) Raptor codes and Turbo fountain codes used on a noiseless channel, as it is the case for the BEC or the AWGN channel with high SNR. The performance measure for such family of codes is the efficiency, i.e., the amount of redundancy needed to decode the information bits. Following a previous paper, we give an exact expression for the average efficiency of maixmum-likelihood (ML) decoded Hamming codes and maximal-length codes. Moreover, we give an expression of the variance of the efficiency. Finally, we improve the bound on the efficiency of Turbo fountain codes, which are iteratively decoded.