Abstract: In application scenarios such as DNA storage, the traditional fountain code algorithm must transmit the number K of source file packets to the decoder through an additional channel. In practical applications, although K can be embedded in each coded data packet to transmit this key parameter, this method will seriously waste the channel's bandwidth. Aiming at the above problems, a large and mini fountain code model is proposed, which optimizes the transmission of critical parameters by adding the out-of-band channel of the mini fountain code. The mini fountain code reduces the granularity of the space occupied by the critical information about the parameter K in each coding group to 1 bit, effectively reducing the consumption of bandwidth resources. In addition, the mini fountain code can also adapt to the restriction of the indefinite length of the coding sequence caused by the inhomogeneity of the DNA storage medium. Under certain conditions, it cannot even occupy additional channel bandwidth at all.

Key words: DNA storage, fountain code, LT code, avoidance sequence