Coding-Shaping Concatenation Scheme for Ultra-Reliable Low-Latency Communications

Designing probabilistic shaping for ultra-reliable low-latency communications (URLLC) is challenging due to significant rate loss in the ultrashort block-length regime. Unlike <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">shaping-coding</i> concatenation schemes as employed by probabilistic amplitude shaping (PAS), this paper proposes a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">coding-shaping</i> concatenation (CSC) such that the rate loss from ultrashort shaping can be reduced by the rate of forward error correction (FEC) coding. Since CSC employs a reversed concatenation of shaping and coding, a soft shaping de-mapper is required before FEC decoding, which could bring high complexity. Thus, this paper proposes to use constant composition distribution matcher (CCDM) as shaper. By exploiting its constant codeword weight property, a low-complexity list de-mapping is proposed by de-mapping CCDM codeword within a small candidate list. Simulations show that, with shaping block-length of 8, the proposed CSC achieves up to 1 dB and 1.2 dB shaping gain compared to uniform signaling with less average iterations over 16QAM and 64QAM, respectively.