In massive multiple-input multiple-output (MIMO) uplink, linear minimum mean square error (MMSE) detection achieves near-optimal performance but suffers from undesirable computational burden due to the high-dimensional matrix inversion involved. To address this issue, the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) quasi-Newton method is introduced in this paper to realize free-matrix-inversion MMSE detection in an iterative way with significant reduction in computational complexity from $\mathcal {O}(K^{3})$ to $\mathcal {O}(L K^{2})$ , where $K$ and $L$ denote the number of user antennas and iterations, respectively. For the better performance and complexity trade-off, three low-complexity L-BFGS based linear MMSE detection algorithms (namely E-LBFGS, I-LBFGS and S-LBFGS) are proposed successively. Furthermore, an efficient initialization strategy for the L-BFGS method based MMSE detection is devised, which helps to accelerate convergence and improve performance with acceptable complexity overhead added compared to the conventional L-BFGS based detection algorithms. Simulation results finally validate that the proposed detection scheme based on the L-BFGS method can closely approach to the MMSE accuracy with a small number of iterations even in poor propagation environments and provide attractive trade-offs between performance and complexity.

Multiple-input Multiple-output (MIMO) technologies play an important role in modern and future wireless communication systems as they can improve the capacity without increasing the bandwidth. MIMO detection is one of the key technologies for MIMO system designs. MIMO detection schemes based on Message Passing (MP) algorithms have attracted extensive attention in recent years. The MIMO detection scheme based on Expectation Propagation (EP), which is also a kind of MP algorithms, has been proved to achieve the Bayes-optimal performance under the conditions of large system limit and compression rate threshold. However, there is improvement space for the detection performance of the EP algorithm when the conditions are not satisfied, which are the common cases in the practical applications. In this paper, when the conditions of the large system limit and compression rate threshold are not satisfied, we analyze the influences of two factors, the initial parameters selection and the moment matching strategy, on the performance of EP based detection scheme. As a result, we propose an improved EP detection scheme based on optimizing the two factors. Simulation results show that the proposed scheme outperforms the original EP detection scheme in different MIMO scenarios.

Nonorthogonal multiple access technology has been proposed for use in 5G communications systems. In particular, the sparse code multiple access (SCMA) scheme is believed to be one of the most promising techniques among the various nonorthogonal approaches that have been investigated. In this letter, we focus on reducing the complexity of SCMA decoding and we propose a Monte Carlo Markov Chain (MCMC) based SCMA decoder. Benefiting from the linearly increasing complexity of the MCMC method, the proposed SCMA decoder has only 10% of the computational load compared to previous state-of-the-art methods when the codebook size is 64. Consequently, the MCMC SCMA decoder has great potential for use in practical system implementations.

For massive multiple-input multiple-output (MIMO) systems, minimum mean square error (MMSE) detection is near-optimal, but requires high-complexity matrix inversion. To avoid matrix inversion, we formulate MMSE detection as a strictly convex quadratic optimization problem, which can be solved iteratively by the recognized most efficient Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method. According to special properties of massive MIMO systems, we propose a novel limited-memory BFGS (L-BFGS) scheme for MMSE detection with one correction search, unit step length, and simplified initialization, which can greatly reduce the storage and computation cost compared to BFGS method. Simulation results finally verify the effectiveness of the proposed scheme.

We propose and describe new error control algorithms for redundant residue number systems (RRNSs) and residue number system product codes. These algorithms employ search techniques for obtaining error values from within a set of values (that contains all possible error values). For a given RRNS, the error control algorithms have a computational complexity of t·O(log₂ n + log₂ mֿ) comparison operations, where t denotes the error correcting capability, n denotes the number of moduli, and mֿ denotes the geometric average of moduli. These algorithms avoid most modular operations. We describe a refinement to the proposed algorithms that further avoids the modular operation required in their respective first steps, with an increase of ⌈log₂ n⌉ to their computational complexity. The new algorithms provide significant computational advantages over existing methods.

Polar codes have received recent attention due to their potential to be applied in advanced wireless communication protocols such as the fifth generation mobile communication system (5G). Among the existing decoding algorithms, Belief Propagation (BP) exhibits high-throughput, low-latency, and soft output with a high hardware cost. Stochastic computing, as a form of approximate computing, provides a potential low-cost implementation solution for the BP algorithm. However, existing stochastic BP decoders suffer from a relatively long decoding latency resulting in low hardware efficiency. In this paper, a novel bit-wise iterative stochastic decoding architecture for the BP algorithm is proposed to improve the throughput and hardware efficiency. By utilizing the frozen bits of polar codes and stochastic computing, multiple novel optimization methods are presented to further speed up convergence and increase the hardware efficiency.