New stopping criteria for Fountain decoders

For rateless codes, such as Fountain codes, the fundamental tradeoff is among realized rate, error performance, and complexity. Stopping criteria for the decoder play an important role in these tradeoffs. In this paper we propose two decoders for Fountain codes which use new stopping criteria based on trapping set detection. We compare our proposed decoders to previous decoders in terms of realized rate, error performance, and decoding complexity. In particular, we show that through the use of appropriate stopping criteria it is possible to both reduce average decoding complexity and greatly increase average realized rate at negligible expense in error performance.