It was recently shown that spatial coupling of individual low-densityparity-check codes improves the belief-propagation threshold of the coupledensemble essentially to the maximum a posteriori threshold of the underlyingensemble. We study the performance of spatially coupled low-densitygenerator-matrix ensembles when used for transmission over binary-inputmemoryless output-symmetric channels. We show by means of density evolutionthat the threshold saturation phenomenon also takes place in this setting. Ourmotivation for studying low-density generator-matrix codes is that they caneasily be converted into rateless codes. Although there are already severalclasses of excellent rateless codes known to date, rateless codes constructedvia spatial coupling might offer some additional advantages. In particular, bythe very nature of the threshold phenomenon one expects that codes constructedon this principle can be made to be universal, i.e., a single construction canuniformly approach capacity over the class of binary-input memorylessoutput-symmetric channels. We discuss some necessary conditions on the degreedistribution which universal rateless codes based on the threshold phenomenonhave to fulfill. We then show by means of density evolution and some simulationresults that indeed codes constructed in this way perform very well over awhole range of channel types and channel conditions.
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