Constellation Shaping for Bit-Interleaved Coded APSK

This paper considers a technique for shaping a turbo-coded amplitude-phase shift keying (APSK) constellation. After bit-interleaving, a subset of the bits output by a binary turbo encoder are passed through a nonlinear shaping encoder. The bits at the output of the shaping encoder are more likely to be a zero than a one. These "shaping'' bits are interleaved and used to select from among a plurality of subconstellations, while the unshaped bits are used to select the symbol within the subconstellation. Symbols from lower-energy subconstellations are selected more frequently than those from higher-energy subconstellations. Information rates are computed for a variety of APSK and shaping code parameters, in an effort to optimize these parameters. It is found that, in theory, shaping gains of slightly over 0.3 dB may be achieved with 16-APSK and 32-APSK in AWGN, while the gains in ergodic Rayleigh fading are slightly lower. Simulation results show the bit error performance of the constellation-shaping strategy with an actual turbo code. The BER results suggest that gains significantly beyond 0.3 dB may be possible in AWGN when an iterative decoder is used, presumably due to the additional coding gain of the shaping code.