Luby Transform Codes with Priority Encoding

Rateless codes over a binary erasure channel (BEC) provide successful transmission independent of the erasure probability. Luby Transform (LT) codes and raptor codes are examples of rateless codes over a BEC. For successful decoding, LT codes require either a large overhead at linear complexity, or capacity-approaching overheads with nonlinear complexity. When overhead is low at linear complexity, LT decoding results in a large number of residual errors. In raptor codes, an erasurecorrecting low-density parity-check (LDPC) code is used as a precode to recover message symbols that cannot be recovered by the LT decoder at low overhead. Hence, raptor codes function closer to capacity than LT codes at almost linear complexity. In this paper, we propose a novel modification of the encoding method for LT codes that significantly decreases the fraction of undecoded message symbols without increasing complexity at low overheads. The effects of this modification, which we call priority encoding, have been studied through simulations. The simulations suggest that use of LT codes with priority encoding could facilitate the use of a weaker, less-complex pre-code in the construction of raptor codes.