Fountain Codes Over GF(q)

Binary fountain codes such as Luby transform codes are a class of erasure codes which have demonstrated an asymptotic performance close to the Shannon limit when decoded with the belief propagation algorithm. When these codes are generalized to GF(q) for q > 2, their performance approaches the Shannon limit much faster than the usual binary fountain codes. In this paper, we extend binary fountain codes to GF(q). In particular, we generalize binary Luby transform codes to GF(q) to develop a low complexity maximum likelihood decoder. The proposed codes have numerous advantages, including low coding overhead, low encoding and decoding complexity, and good performance over various message block lengths, making them practical for real-time applications. Copyright (c) 2011 John Wiley & Sons, Ltd.