On the performance estimate for Turbo codes

Recently, the scaling law has been extended to approximate the waterfall performance for Turbo codes over the binary erasure channel. However, the waterfall approximation over other channels, such as the AWGN and Rayleigh fading channels, is still unknown for Turbo codes. In this paper, an exponential model was proposed to approximate the waterfall performance for Turbo codes. The relationship between the proposed exponential model and the scaling law will be highlighted at first. Our analysis unveils that the proposed exponential model could be regarded as a generalized scaling law model, which makes it possible to achieve better performance estimate. The results in this paper explicitly shows that, the exponential model offers reasonable waterfall approximation for both word error probability and bit error probability for all packet sizes over a diverse channel, such as the binary erasure channel, the additive white Gaussian noise channel as well as the Rayleigh fading channel. The complete performance model could be derived by combining the exponential model and the known union bound model. Finally, some further discussions are presented to highlight the performance estimate problem for Turbo codes.