An Improved Approximate Formula for Word Error Rate of Turbo-like Codes
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摘要: 针对Turbo类编码，该文提出了一种改进的近似码字错误率公式。该近似公式可以简单地表示成高斯Q函数的形式，它包含信噪比、判决域平方半径的数学期望和方差等参数。仿真观察表明，对于AWGN信道，当码字错误率高于平台时，所提近似公式与蒙特卡罗仿真的误差小于0.05 dB。鉴于近似公式中的两个有关判决域半径的参数需要通过仿真测量获得，该文还分析了统计误差的影响。结论认为，用几百个半径样本估计近似公式中的参数，即可使得相同码字错误率下信噪比的相对误差小于0.05 dB。Abstract: 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.
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