Signal shaping scheme based on the BWT for the transmission of non-binary sources with memory over the AWGN channel

This paper proposes a low-complexity signal shaping scheme for the transmission of non-binary symbols generated by sources with memory over the AWGN channel. It is based on using the Burrows-Wheeler Transform (BWT) [1] and standard two dimensional (QAM) constellations. The constellation points are driven based on the first order probabilities of the BWT output symbols so that shaping gain is maximized. The proposed system is an extension of the one introduced in [2] for binary sources. To evaluate its performance, the corresponding average energy per transmitted symbol is compared with that obtained when using an ideal source encoder followed by a standard uncoded QAM transmission scheme. In addition, it is shown that the power gain ratio between both systems can be assessed based on the Kullback-Leibler divergence between the first order probability distributions of the BWT output symbols and the Maxwell-Boltzmann probability distribution, obtained under the constraint of achieving an entropy equal to the entropy-rate of the original source.