Digital fountain codes are an effectiv e kind of rateless codes to avoid “feedback storm” in network broadcast/multic ast with a wide horizon of development in the network transmission of big data. Therefore, the recent research progress of digital fountain codes is summerized and some typical digital fountain codes are intro duced in different c hannels. Since degree distributions are fundamental to design digita l fountain codes, previous work about optimization design of degree distribut i ons is summarized and some linear optimization techniques over different channel s based on density evolution are presented in particular. Meanwhile, the problem s of optimization design are pointed out and some possible improvements are proposed. Finally, the outlook of optimization design in degree distributions and a p plications of digital fountain codes is analyzed.