Performance Analysis of Finite Length Non-Binary Raptor Codes under Ordered Statistics Decoder

Raptor code is the current standard of 4G long term evolution (LTE) evolved multimedia broadcast and multi-cast services (eMBMS), which is viewed as a potential approach in the design of ultra-reliable low latency communications (uRLLC) for 5G. This paper analyzes the performance of finite length non-binary (over finite field of order q, GF(q)) Raptor codes under ordered statistics decoder (OSD) towards uRLLC, where the non-binary Raptor code ensembles by a non-binary low density parity-check (LDPC) code as pre-code and a non-binary inner Luby transform (LT) code. Moreover, by investigating the property of code structure and decoding algorithm, an upper bound of decoding failure probability (DFP) of finite length non-binary Raptor code under OSD is derived. Simulation results validate the accuracy of our derived upper bound, and demonstrate that our non-binary Raptor codes can achieve 10â'5 DFP with block length 128 bits at SNR 3.6 dB.