Coding-Shaping Concatenation Scheme for Ultrashort Probabilistic Shaping

It's challenging to design probabilistic shaping for ultra-reliable low-latency communications (URLLC), due to significant rate loss in ultrashort block-length regime. Unlike shaping-coding concatenation schemes as employed by probabilistic amplitude shaping (PAS), this paper proposes a coding-shaping concatenation (CSC) such that the rate loss is reduced by the coding rate, promising good performance. Moreover, because de-shaping is performed before decoding, to mitigate error propagation stemming from de-shaping, this paper proposes to use CCDM as shaping codes, and derives an efficient list de-mapping based on their weight constraint. It provides soft information for decoding with limited error propagation. Simulation and analysis results show that, with shaping block-length of 8, the proposed CSC achieves up to 1.1 dB shaping gain compared to uniform signaling with less average iterations.