Error probability of bit-interleaved coded modulation using the Gaussian approximation

This paper presents a very accurate and simple to compute approximation to the performance of bit-interleaved coded modulation (BICM) systems. The proposed method is based on approximating the binary-input continuous-output equivalent BICM channel by a binary-input AWGN (BI-AWGN) channel with scaled SNR. The scaling factor can be easily computed numerically and depends on the actual channel SNR and on the modulation signal set and binary labeling. The key is that very good approximation results when the Bhattacharyya parameter is used to estimate the variance of the underlying Gaussian channel. Under such approximation, we can use all bounding techniques known for binary codes in Gaussian channels. In particular, we use the union and the tangential-sphere bounds and we apply such results to both convolutional and turbo-like codes. The proposed method represents a simple yet powerful tool for estimating the error probability of finite-length turbo-like codes with BICM.