i Fàbregas, “Large-SNR error probability analysis of BICM with uniform interleaving in fading channels

This paper studies the average error probability of bit-interleaved coded modulation with uni-form interleaving in fully-interleaved fading channels. At large signal-to-noise ratio, the dominant pairwise error events are mapped into symbols with Hamming weight larger than one, causing a flattening of the error probability. Closed-form expressions for the error probability with general modulations are provided. For interleavers of practical length, the flattening is noticeable only at very low values of the error probability. I. MOTIVATION AND SUMMARY Whilst QPSK is equivalent to two parallel independent BPSK channels in the Gaussian channel, the equivalence fails in fading channels because of the statistical dependence between the quadrature components introduced by the fading coefficients. This dependence ensures that the error probability is dominated by the number of QPSK symbols with Hamming weight two. The asymptotic slope of the error probability is reduced and an error floor results, a phenomenon similar in nature to the floor appearing in turbo codes [1], [2]. More generally, bit-interleaved coded modulation (BICM) [3] is affected by the same phenomenon. For low signal-to-noise ratio (SNR), the error probability is determined by error events with a high diversity, so that the minimum Hamming weight of the code is distributed across the largest possible number of modulation symbols. Although “worse ” error events with smaller diversity are present, they are weighted by a low error probability, and thus remain hidden for most practical purposes. We analyze this behaviour by first studying th