Achieving Short-Blocklength RCU Bound via CRC List Decoding of TCM with Probabilistic Shaping

This paper applies probabilistic amplitude shaping (PAS) to a cyclic redundancy check (CRC) aided trellis coded modulation (TCM) to achieve the short-blocklength random coding union (RCU) bound. In the transmitter, the equally likely message bits are first encoded by a distribution matcher to generate amplitude symbols with the desired distribution. The binary representations of the distribution matcher outputs are then encoded by a CRC code. Finally, the CRC-encoded bits are encoded and modulated by Ungerboeck’s TCM scheme, which consists of a systematic $\frac{{{k_0}}}{{{k_0} + 1}}$ tail-biting convolutional code and a mapping function that maps coded bits to channel signals with capacity-achieving distribution. This paper proves that, for the proposed transmitter, the CRC bits have uniform distribution and that the channel inputs have symmetric distribution. In the receiver, the serial list Viterbi decoding (S-LVD) is used to estimate the information bits. Simulation results show that, for the proposed CRC-TCM-PAS system with 87 input bits and 65-67 8-AM coded output symbols, the decoding performance under additive white Gaussian noise channel achieves the RCU bound with properly designed CRC and convolutional codes.