Coding Principle and Information-Theoretic Limit of OAMP Receiver in Unitary-Transform Generalized Linear Systems

In wireless communications, the unitary-transform generalized linear system (GLS) has been widely used to evaluate the impact of nonlinear preprocessing on transceivers. Generalized approximate message passing (GAMP) is a state-of-the-art low-complexity signal recovery algorithm, but it is only applicable to independent and identically distributed (IID) Gaussian matrices. To overcome this limitation, generalized orthogonal AMP (GOAMP) has been developed for unitarily invariant matrices, however, its information-theoretic limit analysis is numerical and limited by the high-complexity linear minimum mean-squared error (LMMSE), which is difficult to be analyzed analytically. Meanwhile, it is unable to effectively utilize the properties of unitary matrices, rendering the information-theoretic analysis still complex. To address these issues, in this paper, we provide the achievable rate analysis and optimal coding principle for GOAMP in unitary-transform GLS with arbitrary input distributions, establishing its information-theoretic limit (i.e., maximum achievable rate). Specifically, the simplified variational state evaluation (VSE) of GOAMP are developed using the unitary matrix properties to analyze the achievable rate, and the optimal code principle is derived with goal of maximizing the achievable rate. In addition, it is rigorously proved that GOAMP outperforms GAMP in terms of asymptotic MSE with lower complexity. Furthermore, quantization is used as an example to demonstrate the maximum achievable rate and practical low-density parity-check (LDPC) code design for GOAMP. The optimized LDPC code can approach the threshold limit within 0.8 dB and overcome the decoding deterioration and even divergence of the existing state-of-the-art methods.