Rateless Codes from Spatially Coupled regular-LT Codes

In this paper, we study the performance of spatially coupled LT (SC-LT) codes under low-complexity belief-propagation (BP) decoding. We derive tight upper bound and lower bound on the error probability of these rateless codes in terms of overhead and the check degree in the limit of block-length and when the transmission is over binary erasure channels (BEC). We show that for a given encoding overhead, the error probability of SC-LT codes is independent of erasure probability of channel and decays exponentially fast in degree.