Absorbing sets of Fountain codes over noisy channels

Abstract

Although error-prone patterns have been extensively studied for low-density parity-check (LDPC) codes, to the best of our knowledge, they have never been fully explored for Fountain codes. It is shown that dominant trapping sets of Fountain codes are the absorbing sets. They happen in the so-called error floor, corresponding to a significant flattening in the error probability curves. In this paper, we introduce the properties of these dominant trapping sets for Fountain codes. This definition of absorbing sets leads to better design of practical finite-length Fountain encoders and decoders.