Optimal Signaling and Labelling For Constellation-Constrained Communication Systems

[摘要] Most communication systems use a finite signal set as their alphabet set to form a codebookto transmit data over a communication channel in a reliable fashion. The problem withConventional methods which implement Coded Modulation (CM) schemes such as TrellisCoded Modulation or Multi-level Coding Multi-Stage Decoding is their complexity of dealingwith codes with different rates in each level which makes the design and implementation adifficult task.One simple way to implement Coded Modulation is Bit-Interleaved CodedModulation (BICM) which uses only a single binary encoder to transmit data. Although BICM isa suboptimal scheme compared to CM, its simplicity, from a practical point of view, is a greatmotivation to design BICM scheme achieving rates close to those obtained by CM.Lots of efforts have been taken place in the past twenty years to design optimal constellation fordifferent snr regimes in CM under various constraints. Some of them are revisited in this study.A novel approach, called Adjustable Weights Model (AWM), will be presented to designconstellations which work very well in both CM and BICM schemes. The model also induces aparticular labelling on the constellation.In this work, some properties of AWM are studied. AWM is used to facilitate design of nearoptimal signalling for CM and BICM schemes. An optimization problem is formed to find theoptimal parameters of the proposed model. Global optimization methods are used to solvethe optimization problems. It is shown that the optimal points are always on the boundary ofthe domain by using data processing inequality . Some suboptimal solutions are provided bymoment and cumulants matching techniques. The model has the ability to produce differentconstellations by adjusting its weights. It is well established that the optimal constellation forhigh snr region is equillattice. This model also converges to an equillattice constellation in highsnr region. Number of nonzero weight parameters in the model can vary according to snr, help usto circumvent the saturation problem with conventional CM scheme.BICM capacity is presented and its relation with CM capacity is discussed. BICM capacity, asa function of snr, is expanded around zero snr. Different constellations and their labeling canbe characterized based on the coefficients in the Taylor expansion. The most importantdifference between CM and BICM is the effect of labelling in the former scheme. Labelling isirrelevant in CM, but greatly influences the system performance in BICM. Effect of labellingand how to search for optimal labeling is part of this study. It is shown that AWM is optimal atmedium and low snr regimes. The model coupled with its underlying labelling isfirst order optimal. Although Gray labelling is optimal at high snr, it is not optimal in the lowsnr regime. Higher order optimal constellations are defined to be the constellations that havemore than one coefficient in their Taylor expansion matched with CM capacity coefficients. Itgives us a powerful tool to study constellation in medium snr regime which has not been alreadydiscovered. In addition, optimality criterion is provided.

[发布机构] University of Waterloo

[关键词] Electrical and Computer Engineering