Design of short-length message fountain code for erasure channel transmission

The emergence of practical fountain codes (i.e. LT and Raptor codes) may be a presage of Internet evolution. However, the existing fountain codes are only efficient to a long-length message and it will not be useful to current Internet as the majority of which are short-length messages. This manuscript demonstrates the preliminary design of our short-length message fountain code. Our proposed fountain code is simple in design and it is able to achieve a perfect decoding inefficiency ε = 0 in an ideal channel and ε = 1 even in a channel of erasure probability p = 0.5.