Fettweis, “Turbo codes with non-uniform constellation

Absrract-This paper presents parallel concatenated turbo codes that employ a non-uniform constellation to achieve shaping gain. The output signal approximates the Gaussian distribution by using equally likely signals with unequal spacing (a non-uniform constel-lation). The small distance of points near the center of the constella-tion may lead to a small overall free distance and thus a high error floor for turbo codes. We avoid this situation by a two-step design procedure, that first creates an interleaver according to the criteria in 113, and then identifies the constituent encoders that maximize the turbo code free distance. Simulation results for 4 bitshedHz show that this use of shaping can offer an improvement of approximately 0.2 dB for turbo codes. I