Improved decoding for Raptor codes with short block-lengths over BIAWGN channel

Decoding of Raptor codes consists of decoding of both the LT part and the precode part of the codes. When LT decoding is performed, a scenario may arise where the message passing-based decoding process is unable to provide non-zero log-likelihood ratio (LLR) updates to a fraction of input symbols even if it is mathematically possible to do so. The problem is even more critical for codes with short block-lengths and for smaller overheads. We show that this problem degrades the overall decoding performance of Raptor codes over binary input additive white Gaussian noise (BIAWGN) channel. To combat this problem, the Gauss-Jordan elimination (GJE) is used to assist decoding so that the decoder can continuously provide non-zero LLR updates to all the input symbols connected in the decoding graph. Through simulation results we show that the GJE-assisted method provides significantly better bit error rate (BER) performance of Raptor codes than the traditional method across a wide range of signal to noise ratio (SNR) and transmission overheads.