On Bit-interleaved Coded Modulation with QAM Constellations

Licentiate thesis, 2008

Bit-interleaved coded modulation (BICM) is a flexible modulation/coding scheme which allows the designer to choose a modulation constellation independently of the coding rate. This is because the output of the channel encoder and the input to the modulator are separated by a bit-level interleaver. In order to increase spectral efficiency, BICM can be combined with high-order modulation schemes such as quadrature amplitude modulation (QAM) or phase shift keying. BICM is particularly well suited for fading channels, and it only introduces a small penalty in terms of channel capacity when compared to the coded modulation capacity for both additive white Gaussian noise (AWGN) and fading channels. Additionally, if the so-called BICM with iterative decoding (BICM-ID) is used, the demapper and decoder iteratively exchange information, improving the system performance. At the receiver's side of BICM, the reliability metrics are calculated for the coded bits under the form of logarithmic likelihood ratios, or simply L-values. These metrics are then deinterleaved and further used by the soft-input channel decoder. This thesis deals with the probabilistic characterization of the L-values calculated by the demapper when BICM is used in conjunction with high order QAM schemes. Three contributions are included in this thesis. In Paper A the issue of the probabilistic modelling of the extrinsic L-values for BICM-ID is addressed. Starting with a simple piece-wise linear model of the L-values obtained via the max-log approximation, expressions for the probability density functions (PDFs) for Gray-mapped 16-QAM are found. The developed analytical expressions are then used to efficiently compute the so-called extrinsic information transfer functions of the demapper, and they are also compared with the histograms of the L-values obtained through numerical simulations. In Paper B closed-form expressions for the PDFs of the L-values in BICM with Gray mapped QAM constellations are developed. Based on these expressions, two simple Gaussian mixture approximations that are analytically tractable are also proposed. The developments are used to efficiently calculate the BICM channel capacity and to develop bounds on the coded bit-error rate when a convolutional code is used. The coded performance of an hybrid automatic repeat request based on constellation rearrangement is also evaluated. In Paper C closed-form expressions for the PDFs of the L-values in BICM transmissions with Gray-mapped QAM constellations over fully-interleaved fading channels are derived. The results are particularized for a Rayleigh fading channel, however, developments for the general case of a Nakagami-$m$ case are also included. Using the developed expressions, the performance of BICM transmissions using convolutional and turbo codes is efficiently evaluated. The BICM channel capacity for different fading channels and constellation sizes is also calculated.