On lowering the error floor of bit-interleaved turbo-coded modulation

In this paper we introduce an algorithm to optimize the performance in the error floor region of bit-interleaved turbo-coded modulation (BITCM) on the additive white Gaussian noise (AWGN) channel. The key ingredient is an exact turbo code weight distribution algorithm producing a list of all codewords in the underlying turbo code of weight less than a given threshold. In BITCM, the information sequence is turbo-encoded, bit- interleaved, and mapped to signal points in a signal constellation. Using the union bounding technique, we show that a well-designed bit-interleaver is crucial to have a low error floor. Furthermore, the error rate performance in the waterfall region depends on the bit-interleaver, since the level of protection from channel noise on the bit-level depends on the bit-position and the neighboring bit values within the same symbol in the transmitted sequence. We observe a trade-off between error rate performance in the waterfall and error floor regions as illustrated by an extensive case study of a high-rate BITCM scheme. The reported case study shows that it is possible to design bit-interleavers with our proposed algorithm with equal or better performance in the waterfall region and superior performance in the error floor region compared to randomly generated bit-interleavers. In particular, we were able to design BITCM schemes with maximum-likelihood decoding frame error rates of 10^-12 and 10^-17 at 2.6 dB and 3.8 dB away from unconstrained channel capacity at spectral efficiencies of 3.10 and 6.20 b/s/Hz using square 16 and 256-QAM signal constellations, respectively.