Bounds on the Error Probability of Raptor Codes Under Maximum Likelihood Decoding

In this paper upper and lower bounds on the probability of decoding failure under maximum likelihood are derived for different (nonbinary) Raptor code constructions. particular four constructions considered; (i) standard construction, (ii) a multi-edge type (iii) construction where is nonbinary but generator matrix LT has only binary entries, (iv) combination (iii). The latter resembles one employed by RaptorQ codes, which at time writing article represents state art in fountain codes. shown to be tight, provide an important aid design