A new fountain decoder escaping almost all absorbing sets

In contrast to the capacity approaching performance of iteratively decoded low-density parity-check (LDPC) codes, many practical finite-length LDPC codes exhibit performance degradation, manifested in a so-called error floor, corresponding to a significant flattening in the error probability curves. Recent works have shown that the dominant trapping sets in the generator-based Tanner Graph (TG) of Fountain codes are the absorbing sets. In this paper, we demonstrate how these absorbing sets are damaging to the realized rate, delay, and decoding cost of Fountain codes. We further introduce the properties of these dominant trapping sets and propose a new encoder and decoder for Fountain codes. Our experimental results show that this new codec leads to improvements in realized rate, decoding cost and error performance.