Decoding algorithms for binary Raptor codes over nonbinary channels

In this paper, we introduce a class of decoding algorithms for binary Raptor codes used for transmission over q-ary channels, where q = 2
^m
. The algorithms provide a tradeoff between complexity and decoding capability. Whereas the running time of the q-ary belief-propagation algorithms is m2
^m
times that of its binary counterpart, in our case the complexity factor can be chosen between m and 2
^m
, depending on the error-correction capability required. As such, the running time can be much better than the q-ary belief-propagation algorithm. The main idea behind our algorithm is to apply an appropriate set of GF(2)-linear forms of GF(q) to the Raptor code to obtain a set of binary codes which can be decoded independently in parallel. After a prescribed number of iterations, for each of the input symbols of the Raptor code and each of the linear forms an estimate is obtained on the probability that this linear form applied to the input symbol is zero. By gathering these probabilities and performing a maximum-likelihood decoding on a suitable code of very small blocklength, we are able to obtain a good estimate of the value of the input symbol. Simulations results are provided for a families of q-ary symmetric channels and non-symmetric channels which show the performance of our decoding algorithms.