In this paper

we propose a novel cyclic redundancy check (CRC)-aided method to improve the energy efficiency of distribution matching (DM) algorithms based on fixed empirical distribution codebooks. The core design concept is to map a subset of a DM codebook to the entire codebook. The mapping is identified by a binary vector that is convolved during the CRC encoding; thereby avoiding any additional overhead in a CRC-aided system. At the receiver (RX)

the CRC check not only performs error detection but also identifies the mapping of the transmitted symbol sequences to the original input of the DM. With the information delivered by a quarter-sized codebook

fewer occurrence of high-energy symbols effectively reduces the average symbol energy and the rate-loss. The proposed method can be seamlessly integrated into any DM algorithm that uses fixed empirical distribution codebooks. We demonstrate its implementation in a polar-coded probabilistic amplitude shaping (PAS) system with CRC-aided successive cancellation list decoding. Using this architecture

we show an energy efficiency improvement of up to $26\%$ and a signal-to-noise ratio improvement of up to $0.8$ dB at a fixed target frame error rate of $10^{-3}$.