Abstract
The asymptotic performance and optimisation of systematic fountain codes are investigated on Rayleigh fading and Nakagami fading channels. Firstly, the closed-form bit error rates (BER) of systematic LT (SLT) codes and systematic Raptor (SR) codes are derived based on Gaussian approximation method, the results of which are close to that obtained by discretised density evolution. Secondly, a novel optimisation model combining linear programming and theoretical error probability is proposed to design the degree distributions of SLT/SR codes on fading channels. The simulation results show that the optimised codes provide better BER performance than the codes originally designed for binary erasure channel and additive white Gaussian noise channel. Moreover, the proposed method is easily extended to Rician fading channel and unfading channel.
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