Trapping Sets of Fountain Codes

The remarkable results of Fountain codes over the binary erasure channel (BEC) have motivated research on their practical implementation over noisy channels. Trapping sets are a phenomenon of great practical importance for certain graph codes on noisy channels. Although trapping sets 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. In this letter, we demonstrate that trapping sets are damaging to the realized rate and decoding cost of Fountain codes. Furthermore, we show that through trapping set detection we may combat these negative effects.