In this letter, a deep neural network (DNN) aided joint source-channel (JSCC) decoding scheme is proposed for polar codes. In the proposed scheme, an integrated factor graph with an unfolded structure is first designed. Then a DNN aided flooding belief propagation decoding (FBP) algorithm is proposed based on the integrated factor, in which both source and channel scaling parameters in the BP decoding are optimized for better performance. Experimental results show that, with the proposed DNN aided FBP decoder, the polar coded JSCC scheme can have about 2-2.5 dB gain over different source statistics p with source message length NSC = 128 and 0.2-1 dB gain over different source statistics p with source message length NSC = 512 over the polar coded JSCC system with existing BP decoder.

This paper proposes two full-digital receive beamforming (BF) methods for low-complexity and high-accuracy uplink signal detection via Gaussian belief propagation (GaBP) at base stations (BSs) adopting massive multi-input multi-output (MIMO) for open radio access network (O-RAN). In addition, beyond fifth generation mobile communication (beyond 5G) systems will increase uplink capacity. In the scenarios such as O-RAN and beyond 5G, it is vital to reduce the cost of the BSs by limiting the bandwidth of fronthaul (FH) links, and the dimensionality reduction of the received signal based on the receive BF at a radio unit is a well-known strategy to reduce the amount of data transported via the FH links. In this paper, we clarify appropriate criteria for designing a BF weight considering the subsequent GaBP signal detection with the proposed methods: singular-value-decomposition-based BF and QR-decomposition-based BF with the aid of discrete-Fourier-transformation-based spreading. Both methods achieve the dimensionality reduction without compromising the desired signal power by taking advantage of a null space of channels. The proposed receive BF methods reduce correlations between the received signals in the BF domain, which improves the robustness of GaBP against spatial correlation among fading coefficients. Simulation results assuming realistic BS and user equipment arrangement show that the proposed methods improve detection capability while significantly reducing the computational cost.

Diffusion least-mean-square (LMS) is a method to estimate and track an unknown parameter at multiple nodes in a network. When the unknown vector has sparsity, the sparse promoting version of diffusion LMS, which utilizes a sparse regularization term in the cost function, is known to show better convergence performance than that of the original diffusion LMS. This paper proposes a novel choice of the coefficients involved in the updates of sparse diffusion LMS using the idea of message propagation. Moreover, we optimize the proposed coefficients with respect to mean-square-deviation at the steady-state. Simulation results demonstrate that the proposed method outperforms conventional methods in terms of the convergence performance.

Positioning information plays a significant role in multi-unmanned aerial vehicles (UAVs) applications. Traditionally, the positioning information is widely provided by Global Navigation Satellite System (GNSS) due to its good performance and global coverage. However, owing to complicated flight environment or signal blockage, jamming and unintentional interference, the UAVs may fail to locate themselves by using GNSS alone. As a new method to resolve these problems, cooperative positioning, by incorporating peer-to-peer range measurements and assisted information, has attracted more and more attentions due to its ability to enhance the accuracy and availability of positioning. However, achieving good performance of cooperative positioning of multi-UAVs is challenging as their mobility, arbitrary nonlinear state-evolution, measurement models and limited computation and communication resources. In this paper, we present a factor graph (FG) representation and message passing methodology to solve cooperative positioning problem among UAVs in 3-dimensional environment where GNSS cannot provide services. Moreover, to deal with the nonlinear state-evolution and measurement models while decreasing the computation complexity and communication cost, we develop a distributed algorithm for dynamic and hybrid UAVs by means of Spherical-Radial Cubature Rules (CR) method with belief propagation (BP) and variational message passing (VMP) methods (CRBP-VMP) on the FG. The proposed CRBP deals with the highly non-linear state-evolution models and non-Gaussian distributions, the VMP method is employed for ranging message, gets the simpler message representation and can reduce communication cost in the joint estimation problem. Simulation results demonstrate that the higher positioning accuracy, the better convergence as well as low computational complexity and communication cost of the proposed CRBP-VMP algorithm, which can be achieved compared with sum-product algorithm over a wireless network (SPAWN) and traditional Cubature Kalman Filters (CKF) method.

This paper proposes a new design criterion of adaptively scaled belief (ASB) in Gaussian belief propagation (GaBP) for large multi-user multi-input multi-output (MU-MIMO) detection. In practical MU detection (MUD) scenarios, the most vital issue for improving the convergence property of GaBP iterative detection is how to deal with belief outliers in each iteration. Such outliers are caused by modeling errors due to the fact that the law of large number does not work well when it is difficult to satisfy the large system limit. One of the simplest ways to mitigate the harmful impact of outliers is belief scaling. A typical approach for determining the scaling parameter for the belief is to create a look-up table (LUT) based on the received signal-to-noise ratio (SNR) through computer simulations. However, the instantaneous SNR differs among beliefs because the MIMO channels in the MUD problem are random; hence, the creation of LUT is infeasible. To stabilize the dynamics of the random MIMO channels, we propose a new transmission block based criterion that adapts belief scaling to the instantaneous channel state. Finally, we verify the validity of ASB in terms of the suppression of the bit error rate (BER) floor.

We propose three effective approximate belief propagation decoders for polar codes using Maclaurin's series, piecewise linear function, and stepwise linear function. The proposed decoders have the better performance than that of existing approximate belief propagation polar decoders, min-sum decoder and normalized min-sum decoder, and almost the same performance with that of original belief propagation decoder. Moreover, the proposed decoders achieve such performance without any optimization process according to the code parameters and channel condition unlike normalized min-sum decoder, offset min-sum decoder, and their variants.

Detecting signals in a very large multiple-input multiple-output (MIMO) system requires high complexy of implementation. Thus, belief propagation based detection has been studied recently because of its low complexity. When the transmitted signal sequence is encoded using a channel code decodable by a factor-graph-based algorithm, MIMO signal detection and channel decoding can be combined in a single factor graph. In this paper, a low density parity check (LDPC) coded MIMO system is considered, and two types of factor graphs: bipartite and tripartite graphs are compared. The former updates the log-likelihood-ratio (LLR) values at MIMO detection and parity checking simultaneously. On the other hand, the latter performs the updates alternatively. Simulation results show that the tripartite graph achieves faster convergence and slightly better bit error rate performance. In addition, it is confirmed that the LLR damping in LDPC decoding is important for a stable convergence.

Recently, much progress has been made in the study of belief propagation (BP) based signal detection with large-scale factor graphs. When we apply the BP algorithm to equalization in a SISO multipath channel, the corresponding factor graph has many short loops and patterns in an edge connection/strength. Thus, proper convergence may not be achieved. In general, the log-likelihood ratio (LLR) oscillates in ill-converged cases. Therefore, LLR oscillation avoidance is important for BP-based equalization. In this paper, we propose applying node selection (NS) to prevent the LLR from oscillating. The NS extends the loop length virtually by a serial LLR update. Thus, some performance improvement is expected. Simulation results show that the error floor is significantly reduced by NS in the uncoded case and that the NS works very well in the coded case.

It is well known that spatially coupled (SC) codes with erasure-BP decoding have powerful error correcting capability over memoryless erasure channels. However, the decoding performance of SC-codes significantly degrades when they are used over burst erasure channels. In this paper, we propose band splitting permutations (BSP) suitable for (l,r,L) SC-codes. The BSP splits a diagonal band in a base matrix into multiple bands in order to enhance the span of the stopping sets in the base matrix. As theoretical performance guarantees, lower and upper bounds on the maximal burst correctable length of the permuted (l,r,L) SC-codes are presented. Those bounds indicate that the maximal correctable burst ratio of the permuted SC-codes is given by λmax≃1/k where k=r/l. This implies the asymptotic optimality of the permuted SC-codes in terms of burst erasure correction.

In this paper, we propose a message passing decoding algorithm which lowers decoding error rates in the error floor regions for non-binary low-density parity-check (LDPC) codes transmitted over the binary erasure channel (BEC) and the memoryless binary-input output-symmetric (MBIOS) channels. In the case for the BEC, this decoding algorithm is a combination with belief propagation (BP) decoding and maximum a posteriori (MAP) decoding on zigzag cycles, which cause decoding errors in the error floor region. We show that MAP decoding on the zigzag cycles is realized by means of a message passing algorithm. Moreover, we extend this decoding algorithm to the MBIOS channels. Simulation results demonstrate that the decoding error rates in the error floor regions by the proposed decoding algorithm are lower than those by the BP decoder.

Recently, non-binary low-density parity-check (NB-LDPC) codes starts to show their superiority in achieving significant coding gains when moderate codeword lengths are adopted. However, the overwhelming decoding complexity keeps NB-LDPC codes from being widely employed in modern communication devices. This paper proposes a hybrid message-passing decoding algorithm which consumes very low computational complexity. It achieves competitive error performance compared with conventional Min-max algorithm. Simulation result on a (255,174) cyclic code shows that this algorithm obtains at least 0.5dB coding gain over other state-of-the-art low-complexity NB-LDPC decoding algorithms. A partial-parallel NB-LDPC decoder architecture for cyclic NB-LDPC codes is also developed based on this algorithm. Optimization schemes are employed to cut off hard decision symbols in RAMs and also to store only part of the reliability messages. In addition, the variable node units are redesigned especially for the proposed algorithm. Synthesis results demonstrate that about 24.3% gates and 12% memories can be saved over previous works.

In this paper, we compare the decoding error rates in the error floors for non-binary low-density parity-check (LDPC) codes over general linear groups with those for non-binary LDPC codes over finite fields transmitted through the q-ary memoryless symmetric channels under belief propagation decoding. To analyze non-binary LDPC codes defined over both the general linear group GL(m, F2) and the finite field F2m, we investigate non-binary LDPC codes defined over GL(m3, F2m4). We propose a method to lower the error floors for non-binary LDPC codes. In this analysis, we see that the non-binary LDPC codes constructed by our proposed method defined over general linear group have the same decoding performance in the error floors as those defined over finite field. The non-binary LDPC codes defined over general linear group have more choices of the labels on the edges which satisfy the condition for the optimization.

This letter addresses antenna ordering to improve the performance of the MIMO detectors in [4], where two low complexity MIMO detectors have been proposed based on either fully-connected or ring type pair-wise Markov random field (MRF). The former was shown to be better than the latter, while being more complex. The objective of this letter is to make the performance of the detector based on ring-type MRF (with complexity of O(2M 22m)) close to or better than that of fully-connected MRF (with complexity of O(M (M-1)22m)), by applying appropriate antenna ordering. The simulation results validate the proposed antenna ordering methods.

Kudekar et al. proved an interesting result in low-density parity-check (LDPC) convolutional codes: The belief-propagation (BP) threshold is boosted to the maximum-a-posteriori (MAP) threshold by spatial coupling. Furthermore, the authors showed that the BP threshold for code-division multiple-access (CDMA) systems is improved up to the optimal one via spatial coupling. In this letter, a phenomenological model for elucidating the essence of these phenomenon, called threshold improvement, is proposed. The main result implies that threshold improvement occurs for spatially-coupled general graphical models.

In this paper, we investigate the error floors of the non-binary low-density parity-check codes transmitted over the binary erasure channels under belief propagation decoding. We propose a method to improve the decoding erasure rates in the error floors by optimizing labels in zigzag cycles in the Tanner graphs of codes. Furthermore, we give lower bounds on the bit and the symbol erasure rates in the error floors. The simulation results show that the presented lower bounds are tight for the codes designed by the proposed method.

A novel signaling scheme is proposed for iterative channel estimation and data decoding in fast fading channels. The basic idea is to bias the occurrence probability of transmitted symbols. A priori information about the bias is utilized for channel estimation. The bias-based scheme is constructed as a serially concatenated code, in which a convolutional code and a biased nonlinear block code are used as the outer and inner codes, respectively. This construction allows the receiver to estimate channel state information (CSI) efficiently. The proposed scheme is numerically shown to outperform conventional pilot-based schemes in terms of spectral efficiency for moderately fast fading channels.

We propose a novel and efficient approach for tracking 2D articulated human body parts. In our approach, the human body is modeled by a graphical model where each part is represented by a node and the relationship between a pair of adjacent parts is indicated by an edge in the graph. Various approaches have been proposed to solve such problems, but efficiency is still a vital problem. We present a new Quick Shift Belief Propagation (QSBP) based approach which benefits from Quick Shift, a simple and efficient mode seeking method, in a part based belief propagation model. The unique aspect of this model is its ability to efficiently discover modes of the underlying marginal probability distribution while preserving the accuracy. This gives QSBP a significant advantage over approaches like Belief Propagation (BP) and Mean Shift Belief Propagation (MSBP). Moreover, we demonstrate the use of QSBP with an action based model; this provides additional advantages of handling self-occlusion and further reducing the search space. We present qualitative and quantitative analysis of the proposed approach with encouraging results.

For decoding non-binary low-density parity-check (LDPC) codes, logarithm-domain sum-product (Log-SP) algorithms were proposed for reducing quantization effects of SP algorithm in conjunction with FFT. Since FFT is not applicable in the logarithm domain, the computations required at check nodes in the Log-SP algorithms are computationally intensive. What is worth, check nodes usually have higher degree than variable nodes. As a result, most of the time for decoding is used for check node computations, which leads to a bottleneck effect. In this paper, we propose a Log-SP algorithm in the Fourier domain. With this algorithm, the role of variable nodes and check nodes are switched. The intensive computations are spread over lower-degree variable nodes, which can be efficiently calculated in parallel. Furthermore, we develop a fast calculation method for the estimated bits and syndromes in the Fourier domain.

This letter proposes extended single parity check product codes and presents their empirical performances on a Gaussian channel by belief propagation (BP) decoding algorithm. The simulation results show that the codes can achieve close-to-capacity performance in high coding rate. The code of length 9603 and of rate 0.96 is only 0.77 dB away from the Shannon limit for a BER of 10-5.

A continuous belief propagation (BP) decoding algorithm for a hybrid automatic repeat request (ARQ) system is proposed in this paper. The proposed continuous BP decoding algorithm utilizes the extrinsic information generated in the last iteration of the previous transmission for a continuous progression of the decoding through retransmissions. This allows the continuous BP decoding algorithm to accelerate the decoding convergence for codeword determination, especially when the number of retransmissions is large or a currently combined packet has punctured nodes. Simulation results verify the effectiveness of the proposed continuous BP decoding algorithm.