Abstract: A Binary Exponential Random Degree Distribution (BERDD) is proposed, the generated fountain codes using BERDD function improve the probability of generating degree 1 in encoding, decreases the probability of degree 1 chasm in decoding, so the decoding complexity is lowed and iteration efficiency is improved. Further, in order to solve the problem of wide transmission bandwidth, a new transmission scheme of compressing fountain coding is proposed based on codebook. It increases bandwidth utilization. Simulation results show that the proposed BERDD function improves decoding efficiency compared with robust soliton degree distribution and binary exponential degree distribution, and the compressing fountain codes reduce transmitting bandwidth effectively in the condition of Rayleigh fading channel.