On performance evaluation of BICM with non-ideal bit interleaving

The paper outlines an efficient approach to evaluating the performance of bit interleaved coded modulation (BICM) systems. Most existing approaches evaluate the probability of individual pairwise error events and obtain a union bound to the bit error probability. This gives very tight bounds on performance for SNRs above the BPSK modulation cutoff rate. However, for higher order modulation systems, the number of bit errors in a symbol slot depends on the two modulated symbols involved in an error event and the linearity of the code cannot be extended to include the modulator. The performance is usually approximated by a few dominant error events which are applicable to AWGN channels. Some approaches consider infinite depth interleaving to obtain a simplified linear model. We study the evaluation and convergence of union bounds for fading channels with finite code block sizes. We develop a general approach which assumes an ideal model for the modulator and enables us to extend the linearity of the considered codes to simplify the computation. This enables us to analyze the performance of concatenated codes with an interleaver of finite length. The approach also gives greater insight into the influence of modulator parameters and the block length of the code on the diversity achieved in BICM systems. The application of our analytical model is demonstrated with examples and simulations.