Nonlinear Turbo Codes for Higher-Order Modulations

Parallel concatenated trellis coded modulation (PC- TCM) has been traditionally designed using parallel concatenated convolutional codes with a bits-to-symbol mapper. However, this paper shows that for higher-order modulations using linear codes is too restrictive. Parallel Concatenated Nonlinear Trellis Coded Modulation (PC-NLTCM) that directly assigns constellation points as output-labels to the branches of the trellis can outperform PC-TCM. Simulation results are shown for a 2 bits/s/Hz 16-state nonlinear turbo code with 8PSK. This code is less than 0.43 dB away from the Shannon limit at a BER = 10 5 with an interleaver length of 10000 bits, and outperforms previous published linear turbo code by around 0.2 dB. This paper also provides an extension of Benedetto's uniform interleaver analysis for nonlinear constituent codes, which accurately predicts the BER of the PC-NLTCM at high SNR.