Towards Fully Optimized BICM Transceivers

Bit-interleaved coded modulation (BICM) transceivers often use equally spaced constellations and a random interleaver. In this paper, we propose a new BICM design, which considers hierarchical (nonequally spaced) constellations, a bit-level multiplexer, and multiple interleavers. It is shown that this new scheme increases the degrees of freedom that can be exploited in order to improve its performance. Analytical bounds on the bit error rate (BER) of the system in terms of the constellation parameters and the multiplexing rules are developed for the additive white Gaussian Noise (AWGN) and Nakagami-$m$ fading channels. These bounds are then used to design the BICM transceiver. Numerical results show that, compared to conventional BICM designs, and for a target BER of $10^{-6}$, gains up to 3 dB in the AWGN channel are obtained. For fading channels, the gains depend on the fading parameter, and reach 2 dB for a target BER of $10^{-7}$ and $m=5$.Comment: Submitted to the IEEE Transactions on Communication

On the BICM Capacity

Optimal binary labelings, input distributions, and input alphabets are analyzed for the so-called bit-interleaved coded modulation (BICM) capacity, paying special attention to the low signal-to-noise ratio (SNR) regime. For 8-ary pulse amplitude modulation (PAM) and for 0.75 bit/symbol, the folded binary code results in a higher capacity than the binary reflected gray code (BRGC) and the natural binary code (NBC). The 1 dB gap between the additive white Gaussian noise (AWGN) capacity and the BICM capacity with the BRGC can be almost completely removed if the input symbol distribution is properly selected. First-order asymptotics of the BICM capacity for arbitrary input alphabets and distributions, dimensions, mean, variance, and binary labeling are developed. These asymptotics are used to define first-order optimal (FOO) constellations for BICM, i.e. constellations that make BICM achieve the Shannon limit -1.59 \tr{dB}. It is shown that the \Eb/N_0 required for reliable transmission at asymptotically low rates in BICM can be as high as infinity, that for uniform input distributions and 8-PAM there are only 72 classes of binary labelings with a different first-order asymptotic behavior, and that this number is reduced to only 26 for 8-ary phase shift keying (PSK). A general answer to the question of FOO constellations for BICM is also given: using the Hadamard transform, it is found that for uniform input distributions, a constellation for BICM is FOO if and only if it is a linear projection of a hypercube. A constellation based on PAM or quadrature amplitude modulation input alphabets is FOO if and only if they are labeled by the NBC; if the constellation is based on PSK input alphabets instead, it can never be FOO if the input alphabet has more than four points, regardless of the labeling.Comment: Submitted to the IEEE Transactions on Information Theor

Space-time coding techniques with bit-interleaved coded modulations for MIMO block-fading channels

The space-time bit-interleaved coded modulation (ST-BICM) is an efficient technique to obtain high diversity and coding gain on a block-fading MIMO channel. Its maximum-likelihood (ML) performance is computed under ideal interleaving conditions, which enables a global optimization taking into account channel coding. Thanks to a diversity upperbound derived from the Singleton bound, an appropriate choice of the time dimension of the space-time coding is possible, which maximizes diversity while minimizing complexity. Based on the analysis, an optimized interleaver and a set of linear precoders, called dispersive nucleo algebraic (DNA) precoders are proposed. The proposed precoders have good performance with respect to the state of the art and exist for any number of transmit antennas and any time dimension. With turbo codes, they exhibit a frame error rate which does not increase with frame length.Comment: Submitted to IEEE Trans. on Information Theory, Submission: January 2006 - First review: June 200

On Bit-interleaved Coded Modulation with QAM Constellations

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. <p>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.</p> <p>In <b>Paper A</b> 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.</p> <p>In <b>Paper B</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.</p> <p>In <b>Paper C</b> 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.</p

Error performance analysis of cross QAM and space-time labeling diversity for cross QAM.

Doctoral Degrees. University of KwaZulu-Natal, Durban.Abstract available in the PD