Rateless codes from spatially coupled regular-LT codes

Abstract

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