Probabilistic Signal Shaping for Bit-Metric Decoding
  A scheme is proposed that combines probabilistic signal shaping with bit-metric decoding. The transmitter generates symbols according to a distribution on the channel input alphabet. The symbols are labeled by bit strings. At the receiver, the channel output is decoded with respect to a bit-metric. An achievable rate is derived using random coding arguments. For the 8-ASK AWGN channel, numerical results show that at a spectral efficiency of 2 bits/s/Hz, the new scheme outperforms bit-interleaved coded modulation (BICM) without shaping and BICM with bit shaping (i Fabregas and Martinez, 2010) by 0.87 dB and 0.15 dB, respectively, and is within 0.0094 dB of the coded modulation capacity. The new scheme is implemented by combining a distribution matcher with a systematic binary low-density parity-check code. The measured finite-length gains are very close to the gains predicted by the asymptotic theory. 
Georg B\"ocherer
cs.IT math.IT