Simple Capacity-Achieving Ensembles of Rateless Erasure-Correcting Codes

Abstract—This paper is concerned with a simple binary erasure-recovery coding scheme that falls into the family of so-called semi-random low-density-parity-check (SR-LDPC) codes. Based on a constrained random-scrambling technique, the proposed coding scheme is systematic, rateless, and capacity-achieving. We provide simulation examples comparing the new scheme with the well-known Luby Transform (LT) and raptor codes. It is shown that the new scheme has advantages in complexity and performance over its counterparts especially in channels with a relatively low erasure rate. Index Terms—LT codes, raptor codes, tornado codes, SR-LDPC codes, rateless codes