Nested Turbo Codes for the Costa Problem

Driven by the applications in data hiding, multiple-input multiple-output broadcast channel coding, precoding for interference cancellation, and transmitter cooperation in wireless networks, Costa coding has lately become a very active research area. In this paper, we first offer code design guidelines in terms of source channel coding for algebraic binning. We then address a practical code design based on nested lattice codes, and propose nested turbo codes by using turbo-like trellis-coded quantization (TCQ) for source coding and turbo trellis-coded modulation (TTCM) for channel coding. Compared to the TCQ, the turbo-like TCQ offers a structural similarity between the source and channel coding components, leading to a more efficient nesting with TTCM and a better source coding performance. Due to the difference in effective dimensionality between turbo-like TCQ and TTCM, there is a performance tradeoff between these two components when they are nested together, meaning that the performance of the turbo-like TCQ worsens as the TTCM code becomes stronger and vice versa. The optimization of this performance tradeoff leads to our code design that outperforms existing TCQ/TCM and TCQ/TTCM constructions, and exhibits a gap of 0.94, 1.42, and 2.65 dB to the Costa capacity at 2.0, 1.0, and 0.5 b/s, respectively.