A Mismatched Joint Source-Channel Coding Perspective of Probabilistic Amplitude Shaping: Achievable Rates and Error Exponents

Probabilistic Amplitude Shaping (PAS) is a novel method of reliable commmunication over channels with non-uniform capacity achieving input distribution. The encoder of PAS is a concatenation of a distribution matcher with systematic encoding of a Forward Error Correction (FEC) code whereas the PAS decoder is a concatenation of a mismatched FEC decoder and dematcher. In recent works PAS has been shown to close the shaping gap to Shannon capacity for discrete input AWGN channel for a wide range of SNR values. In this paper we modify the classical joint source-channel coding setup to include the salient features of PAS and we derive the Gallager style error exponent and consequently achievable rates for this setup.