Most multi-dimensional (more than two dimensions) lattice partitions only form additive quotient groups and lack multiplication operations. This prevents us from constructing lattice codes based on multi-dimensional lattice partitions directly from non-binary linear codes over finite fields. In this paper, we design lattice codes from Construction A lattices where the underlying linear codes are non-binary irregular repeat-accumulate (IRA) codes. Most importantly, our codes are based on multi-dimensional lattice partitions with finite constellations. We propose a novel encoding structure that adds randomly generated lattice sequences to the encoder's messages, instead of multiplying lattice sequences to the encoder's messages. We prove that our approach can ensure that the decoder's messages exhibit permutation-invariance and symmetry properties. With these two properties, the densities of the messages in the iterative decoder can be modeled by Gaussian distributions described by a single parameter. With Gaussian approximation, extrinsic information transfer charts for our multi-dimensional IRA lattice codes are developed and used for analyzing the convergence behavior and optimizing the decoding thresholds. Simulation results show that our codes can approach the unrestricted Shannon limit within 0.46 dB and outperform the previously designed lattice codes with 2-D lattice partitions and existing lattice coding schemes for large codeword length.
In this paper we investigate the coded slotted ALOHA (CSA) schemes with repetition codes and maximum distance separable (MDS) codes over erasure channels. We derive the extrinsic information transfer (EXIT) functions of the CSA schemes over erasure channels, which allow an asymptotic analysis of the packet recovering process. Moreover, we define a traffic load threshold provided that the recovered probability is more than a given recovery ratio. The optimal distribution of the codes chosen by users in the CSA schemes is then designed to maximize the peak throughput and traffic load threshold. By performing the asymptotic analysis, we show that our optimal distributions improve the traffic load threshold by 60% for ε = 0.1 and 86% for ε = 0.135 compared to the optimal distribution for collision channels. Using repetition codes as an example, simulation results show that the obtained distributions enhance the peak throughput for erasure channels when both packet erasure channels and slot erasure channels are considered.
In this paper, we propose a frame structure for single carrier transmission to estimate doubly-selective fading channels in high mobility environment. A delay-Doppler (DD) domain channel estimation method with adaptive threshold is introduced, which leverages the DD domain channel characteristics to enhance estimation accuracy. Based on the analysis of missed detection and false alarm probabilities, we derive asymptotically optimum thresholds for determining DD channel taps to minimize the mean square error of estimation. We demonstrate that the proposed method achieves a superior estimation performance gain up to 8–11 dB (dependent on the DD domain channel sparsity) compared to conventional channel interpolation techniques under doubly-selective fading channels.
In this letter, we propose a reliability-based windowed decoding scheme for spatially coupled (SC) low-density parity-check (LDPC) codes. To mitigate the error propagation along the sliding windowed decoder of the SC LDPC codes, a partial message reservation method is proposed where only the reliable messages generated in the previous decoding window are reserved for the next decoding window. We also propose a partial syndrome check stopping rule for each decoding window, in which only the complete variable nodes are checked. Simulation results show that our proposed scheme significantly improves the error-floor performance compared to the sliding windowed decoder with the conventional weighted bit-flipping algorithm.
Orthogonal time frequency space (OTFS) modulation has attracted substantial attention recently due to its great potential of providing reliable communications in high-mobility scenarios. In this article, we propose a novel hybrid signal detection algorithm for OTFS modulation. Based on the system model, we first derive the near-optimal symbol-wise maximum a posteriori (MAP) detection algorithm for OTFS modulation. Then, in order to reduce the detection complexity, we propose a partitioning rule that separates the related received symbols into two subsets for detecting each transmitted symbol, according to the corresponding path gains. According to the partitioning rule, we design the hybrid detection algorithm to exploit the power discrepancy of each subset, where the MAP detection is applied to the subset with larger channel gains, while the parallel interference cancellation (PIC) detection is applied to the subset with smaller channel gains. We also provide the error performance analysis of the proposed hybrid detection algorithm. Simulation results show that the proposed hybrid detection algorithm can not only approach the performance of the near-optimal symbol-wise MAP algorithms, but also offer a substantial performance gain compared with existing algorithms.
A deep learning assisted sum-product detection algorithm (DL-SPA) for faster-than-Nyquist (FTN) signaling is proposed in this paper. The proposed detection algorithm concatenates a neural network to the variable nodes of the conventional factor graph of the FTN system to help the detector converge to the a postenor probabilities based on the received sequence. More specifically, the neural network performs as a function node in the modified factor graph to deal with the residual intersymbol interference (ISI) that is not modeled by the conventional detector with a limited number of ISI taps. We modify the updating rule in the conventional sum-product algorithm so that the neural network assisted detector can be complemented to a Turbo equalization. Furthermore, a simplified convolutional neural network is employed as the neural network function node to enhance the detector's performance and the neural network needs a small number of batches to be trained. Simulation results have shown that the proposed DL-SPA achieves a performance gain up to 2.5 dB with the same bit error rate compared to the conventional sum-product detection algorithm under the same ISI responses.
We propose a new linear physical-layer network coding and information combining scheme for the K-user fading multiple-access relay network (MARN), which consists of K users, one relay and one destination. The relay and the destination are connected via a rate-constraint backhaul link. In the proposed scheme, the K users transmit signals simultaneously. The relay and the destination receive the superimposed signals distorted by fading and noise. The relay reconstructs L linear combinations of the K users' messages, referred to as L network coded (NC) messages, and forwards them to the destination. The destination then attempts to recover all K users' messages by combining its received signals and the NC messages obtained from the relay. We develop an explicit expression on the selection of the coefficients of the NC messages at the relay that minimizes the end-to-end error probability at a high signal to noise ratio. We demonstrate that our proposed scheme outperforms the benchmark scheme significantly in an MARN.
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