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Text: In this letter, we aim to integrate PAS with HARQ. When applying IR-HARQ, simply performing the sequential puncturing may cause potential distribution distortion in retransmissions. As such, we propose a symbol-wise puncturing scheme to preserve the shaping distribution and realize the promised gain of PAS. First, we consider the standard PAS structure [7] and adopt the constant composition distribution matcher (CCDM) proposed in [17] as a DM to transform the input bits into amplitude symbols. Then, they are represented by their binary labels with a desired probability distribution, while the binary labels are termed as amplitude bits. After FEC encoding, the information bits excluding the amplitude bits and all the parity bits are called sign bits. We apply IR-HARQ in our work, i.e., transmitting **data** packet that is self-decodable for the first transmission and the redundant information for retransmissions. In this case, the traditional sequential puncturing will cause retransmissions with only the sign bits, which brings severe distribution distortion. To address this issue, we pair the amplitude bits and sign bits into a label sequence of shaped modulation symbols. Then, we perform symbol-wise puncturing on the label sequence. In our scheme, a certain proportion of the amplitude bits and sign bits are sent in each transmission to ensure the probability distribution. At the receiver, the a-priori information of the amplitude bits that have not be transmitted is calculated to enhance FEC decoding. Our simulation results indicate that our proposed symbol-wise puncturing can obtain stable shaping gain across the signal-to-noise ratio (SNR) on the throughput over both AWGN and multiple-input multiple-output (MIMO) Rayleigh fading channels and realize the desired probability distribution with only little distortion in each transmission, while the gain of the sequential puncturing drops rapidly with the increase of retransmission times and the distribution of the sequential puncturing in retransmissions tends to be uniform. Note that for type-I and type-III HARQ, since the **data** packets in each transmission are self-decodable, there are enough amplitude bits to preserve the probability distribution. In other words, the conventional PAS would still work when it is integrated with these two types of HARQ. Therefore, we only consider IR-HARQ in our work.<|eot_id|><|start_header_id|>assistant<|end_header_id|>

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