I have just read a Luby’s paper on the very basic idea of the LT codes, which may be of interest for me. For my application, encoding k information symbols is done in a process that generates a big table T of size k’. Then, for every information symbol s, choose d indices in the table $x_1,\ldots,x_d$ and add s to $T[x_i]$ (And beside $T[x_i]$ store the index of s, but I ignore this for the question).
So basically this is exactly as the encoding of the LT codes except that the degree distribution of the code words is not the same. So I wonder if there is an analysis of this variant. Do you know a paper that treats this variant? Any thoughts on why it should/shouldn’t work?