  It was recently shown that spatial coupling of individual low-density
parity-check codes improves the belief-propagation threshold of the coupled
ensemble essentially to the maximum a posteriori threshold of the underlying
ensemble. We study the performance of spatially coupled low-density
generator-matrix ensembles when used for transmission over binary-input
memoryless output-symmetric channels. We show by means of density evolution
that the threshold saturation phenomenon also takes place in this setting. Our
motivation for studying low-density generator-matrix codes is that they can
easily be converted into rateless codes. Although there are already several
classes of excellent rateless codes known to date, rateless codes constructed
via spatial coupling might offer some additional advantages. In particular, by
the very nature of the threshold phenomenon one expects that codes constructed
on this principle can be made to be universal, i.e., a single construction can
uniformly approach capacity over the class of binary-input memoryless
output-symmetric channels. We discuss some necessary conditions on the degree
distribution which universal rateless codes based on the threshold phenomenon
have to fulfill. We then show by means of density evolution and some simulation
results that indeed codes constructed in this way perform very well over a
whole range of channel types and channel conditions.
