Iteratively decodable codes for bridging the shaping gap in communication channels

We consider the power-constrained complex memoryless additive white Gaussian noise channel whose channel inputs are drawn from a finite alphabet. It is well known that if the probability mass function over the finite alphabet is uniform, a shaping gap is created that asymptotically approaches 1.53 dB as the constellation cardinality approaches infinity. In a recent paper, we proposed a method to compute the shaping gap for a finite alphabet size and finite SNR. Here, we take advantage of the constellations that can be represented as cross products of the in-phase (real) and quadrature (imaginary) unidimensional constellations. For a 256-QAM constellation, we construct separate simple in-phase and quadrature inner trellis codes whose combined information rate bridges (and nearly closes) the shaping gap. We then demonstrate that a judiciously constructed outer iteratively decodable low-density parity-check code performs inside the shaping gap, which is very near the channel capacity.