Abstract
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 the additive white Gaussian noise channel (Böcherer, 2018). In this work, we revisit the capacity-achieving property of PAS and derive AIRs using weak typicality. Our objective is to provide alternative proofs based on random sign-coding arguments that are as constructive as possible. Accordingly, in our proofs, only some signs of the channel inputs are drawn from a random code, while the remaining signs and amplitudes are produced constructively. We consider both symbol-metric and bit-metric decoding.
Highlights
Coded modulation (CM) refers to the design of forward error correction (FEC) codes and high-order modulation formats, which are combined to reliably transmit more than one bit per channel use
Examples of CM strategies include multilevel coding (MLC) [1,2] in which each address bit of the signal point is protected by an individual binary FEC code, and trellis CM [3], which combines the functions of a trellis-based channel code and a modulator
We studied achievable information rates (AIRs) of probabilistic amplitude shaping (PAS) for discrete-input memoryless channels
Summary
Coded modulation (CM) refers to the design of forward error correction (FEC) codes and high-order modulation formats, which are combined to reliably transmit more than one bit per channel use. CM (BICM) [4,5], which combines a high-order modulation format with a binary FEC code using a binary labeling strategy and uses bit-metric decoding (BMD) at the receiver, is the de-facto standard for CM. We provide a random sign-coding framework based on weak-typicality that contains the achievability proofs relevant for the PAS architecture. The first main contribution of this paper is to provide a framework that combines the constructive approach to amplitude shaping with randomly-chosen error-correcting codes, where the randomness is concentrated only in the choice of the signs. The second contribution is to provide a unifying framework of achievability proofs to bring together PAS results that are somewhat scattered in the literature, using a single proof technique, which we call the random sign-coding arguments.
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