Rateless code usually generates a potentially infinite number of coded packets at the encoder and collects enough packets at the decoder to ensure reliable recovery of multiple information packets. The conventional rateless decoder usually works in a parallel manner which needs to initiate a new belief propagation (BP) decoding procedure upon each newly received collection of coded packets

thereby resulting in prohibitive decoding complexity in practice. In this paper

we present a novel serial decoding algorithm

i.e.

the serial storage belief propagation (SS BP) algorithm

for rateless codes over noisy channels. Specifically

upon receiving a new group of coded packets

the decoder initiates a new attempt to decode all the packets received so far

using the results of the previous attempt as initial input. Moreover

in each iteration of the new attempt

the decoder serially propagates the messages group by group from the most recent one to the earliest one. In this way

the newly updated messages can be propagated faster

expediting the recovery of information packets. In addition

the proposed serial decoding algorithm has significantly lower complexity than the existing parallel decoding algorithms. Simulation results validate its effectiveness in AWGN

Rayleigh

and Rician fading channels.