Fountain codes with message passing and maximum likelihood decoding over erasure channels

We investigate the performance of fountain codes on erasure channels with message passing and maximum likelihood decoding algorithms. Fountain codes under message passing decoding are efficient but, for short data length, the decoding overhead may not be optimal. We focus on reducing overhead without losing the code´s efficiency and universality, and propose a hybrid message passing and fast maximum likelihood decoding algorithm for LT codes. We also design Raptor codes with one stage pre-codes which are remarkable LDPC codes in the IEEE 802.16e standard. Simulation results show that small dimension fountain codes can save impressive decoding overhead with the maximum likelihood algorithm and the hybrid scheme.