Evaluating the word error rate of channel codes via the squared radius distribution of decision regions

This letter proposes an efficient approach to evaluate the word error rate (WER) of channel codes with the distribution of squared radius of decision regions. The squared radius can be measured via simulations and then the WER for any signal to noise ratio (SNR) can be evaluated. In addition, by approximating the distribution of squared radius as Gamma distribution, only the mean and variance of squared radius need to be measured. For long codes, the WER can be further simplified to a single term of incomplete gamma function or Gaussian Q function. Moreover, for the code family which has a threshold SNR, the squared radius can be used to estimate the threshold SNR.