Achievable Information Rates for Probabilistic Amplitude Shaping: A Minimum-Randomness Approach via Random Sign-Coding Arguments
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Probabilistic amplitude shaping (PAS) is a coded modulation strategy in which constellation shaping and channel coding are combined. PAS has attracted considerable attention in both wireless and optical communications. Achievable information rates (AIRs) of PAS have been investigated in the literature using Gallager's error exponent approach. In particular, it has been shown that PAS achieves the capacity of a memoryless channel. In this work, we revisit the capacity-achieving property of PAS, and derive AIRs using weak typicality. We provide alternative proofs based on random sign-coding arguments. Our objective is to minimize the randomness in the random coding experiment. Accordingly, in our proofs, only some signs of the channel inputs are drawn from a random code, while the remaining signs and the amplitudes are produced constructively. We consider both symbol-metric and bit-metric decoding.
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