Abstract-In this work, we present a novel construction for solving the linear multiuser detection problem using the Gaussian Belief Propagation algorithm. Our algorithm yields an efficient, iterative and distributed implementation of the MMSE detector. Compared to our previous formulation, the new algorithm offers a reduction in memory requirements, the number of computational steps, and the number of messages passed. We prove that a detection method recently proposed by Montanari et al. is an instance of ours, and we provide new convergence results applicable to both.

The canonical problem of solving a system of linear equations arises in numerous contexts in information theory, communication theory, and related fields. In this contribution, we develop a solution based upon Gaussian belief propagation (GaBP) that does not involve direct matrix inversion. The iterative nature of our approach allows for a distributed message-passing implementation of the solution algorithm. We also address some properties of the GaBP solver, including convergence, exactness, its max-product version and relation to classical solution methods. The application example of decorrelation in CDMA is used to demonstrate the faster convergence rate of the proposed solver in comparison to conventional linear-algebraic iterative solution methods.

-We propose a generalized belief propagation (GBP) receiver for two-dimensional (2-D) channels with memory, which is applicative to 2-D intersymbol interference (ISI) equalization and multi-user detection (MUD). Our experimental study demonstrates that under non-trivial interference conditions, the performance of this fully tractable GBP receiver is almost identical to the performance of the optimal maximum a-posteriori (MAP) receiver.

Understanding fundamental limits of the various technologies suggested for future 5G and beyond cellular systems is crucial for developing efficient state-of-the-art designs. A leading technology of major interest is non-orthogonal multiple-access (NOMA). In this paper, we derive an explicit rigorous closed-form analytical expression for the optimum spectral efficiency in the large-system limit of regular sparse NOMA, where only a fixed and finite number of orthogonal resources are allocated to any designated user, and vice versa. The basic Verdú-Shamai formula for (dense) randomly-spread code-division multiple-access (RS-CDMA) turns out to coincide with the limit of the derived expression, when the number of orthogonal resources per user grows large. Furthermore, regular sparse NOMA is rigorously shown to be spectrally more efficient than RS-CDMA across the entire system load range. It may therefore serve as an efficient means for reducing the throughput gap to orthogonal transmission in the underloaded regime, and to the ultimate Cover-Wyner bound in overloaded systems. The results analytically reinforce preliminary conclusions in [1], which mostly relied on heuristics and numerical observations. The spectral efficiency is also derived in closed form for the suboptimal linear minimum-mean-square-error (LMMSE) receiver, which again extends the corresponding Verdú-Shamai LMMSE formula to regular sparse NOMA. arXiv:1801.04427v1 [cs.IT] 13 Jan 2018 R 1 x−z dµ(x), z ∈ C + . The measure µ can be recovered from m(z) via the Stieltjes inversion formula dµ(λ) = 1 π lim →0 + Im(m(z))| z=λ+j dλ, where the limit is in the sense of weak convergence of measures (e.g., [11]).

A closed-form analytical expression is derived for the limiting empirical squared singular value density of a spreading (signature) matrix corresponding to sparse low-density code-domain (LDCD) non-orthogonal multiple-access (NOMA) with regular random user-resource allocation. The derivation relies on associating the spreading matrix with the adjacency matrix of a large semiregular bipartite graph. For a simple repetition-based sparse spreading scheme, the result directly follows from a rigorous analysis of spectral measures of infinite graphs. Turning to random (sparse) binary spreading, we harness the cavity method from statistical physics, and show that the limiting spectral density coincides in both cases. Next, we use this density to compute the normalized input-output mutual information of the underlying vector channel in the large-system limit. The latter may be interpreted as the achievable total throughput per dimension with optimum processing in a corresponding multiple-access channel setting or, alternatively, in a fully-symmetric broadcast channel setting with full decoding capabilities at each receiver. Surprisingly, the total throughput of regular LDCD-NOMA is found to be not only superior to that achieved with irregular user-resource allocation, but also to the total throughput of dense randomly-spread NOMA, for which optimum processing is computationally intractable. In contrast, the superior performance of regular LDCD-NOMA can be potentially achieved with a feasible message-passing algorithm. This observation may advocate employing regular, rather than irregular, LDCD-NOMA in 5G cellular physical layer design.