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.