An Improved Approximate Formula for Word Error Rate of Turbo-like Codes

For Turbo-like codes, an improved approximate formula of Word Error Rate (WER) is proposed. The formula is simply expressed in the form of the Gaussian Q function, which includes the Signal to Noise Ratio (SNR), the mathematical expectation and the variance of squared radii in decision region, etc. Simulation results show that the error between the proposed formula and Monte Carlo simulation is less than 0.05 dB when the WER is higher than the error floor over Additive White Gaussian Noise (AWGN) channels. Moreover, since the last two parameters connected with the radius of decision region are obtained by simulation, their impacts on the accuracy of the proposed formula are studied. It is shown that the deviation of SNR between the proposed formula and Monte Carlo simulation on the same WER is less than 0.05 dB by using only a few hundreds of radii samples.