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The quality and quantity of data used for training greatly influence the performance and effectiveness of deep learning models. In the context of error correction, it is essential to generate high-quality samples that are neither excessively noisy nor entirely correct but close to the decoding region's decision boundary. To accomplish this objective, this paper utilizes a restricted version of a recent result on Importance Sampling (IS) distribution for fast performance evaluation of linear codes. The IS distribution is used over the segmented observation space and integrated with active learning. This combination allows for the iterative generation of samples from the shells whose acquisition functions, defined as the error probabilities conditioned on each shell, fall within a specific range. By intelligently sampling based on the proposed IS distribution, significant improvements are demonstrated in the performance of BCH(63,36) and BCH(63,45) codes with cycle-reduced parity-check matrices. The proposed IS-based-active Weight Belief Propagation (WBP) decoder shows improvements of up to 0.4dB in the waterfall region and up to 1.9dB in the error-floor region of the BER curve, over the conventional WBP. This approach can be easily adapted to generate efficient samples to train any other deep learning-based decoder.

There are rising scenarios in communication systems, where the noises exhibit impulsive behavior and are not adequate to be modeled as the Gaussian distribution. The generalized Gaussian distribution instead is an effective model to describe real-world systems with impulsive noises. In this paper, the problem of efficiently evaluating the error performance of linear block codes over an additive white generalized Gaussian noise (AWGGN) channel is considered. The Monte Carlo (MC) simulation is a widely used but inefficient performance evaluation method, especially in the low error probability regime. As a variance-reduction technique, importance sampling (IS) can significantly reduce the sample size needed for reliable estimation based on a well-designed IS distribution. By deriving the optimal IS distribution on the one-dimensional space mapped from the observation space, we present a general framework to designing IS estimators for memoryless continuous channels. Specifically, for the AWGGN channel, we propose an $L_p$-norm-based minimum-variance IS estimator. As an efficiency measure, the asymptotic IS gain of the proposed estimator is derived in a multiple integral form as the signal-to-noise ratio tends to infinity. Specifically, for the Laplace and Gaussian noises, the gains can be derived in a one-dimensional integral form, which makes the numerical calculation affordable. In addition, by limiting the use of the union bound to an optimized $L_1$-norm sphere, we derive the sphere bound for the additive white Laplace noise channel. Simulation results verify the accuracy of the derived IS gain in predicting the efficiency of the proposed IS estimator., Comment: 35 pages, 11 figures

This paper investigates the problem of finding an optimal nonbinary index assignment from (M) quantization levels of a maximum entropy scalar quantizer to (M)-PSK symbols transmitted over a symmetric memoryless channel with additive noise following decreasing probability density function (such as the AWGN channel) so as to minimize the channel mean-squared distortion. The so-called zigzag mapping under maximum-likelihood (ML) decoding was known to be asymptotically optimal, but the problem of determining the optimal index assignment for any given signal-to-noise ratio (SNR) is still open. Based on a generalized version of the Hardy-Littlewood convolution-rearrangement inequality, we prove that the zigzag mapping under ML decoding is optimal for all SNRs. It is further proved that the same optimality results also hold under minimum mean-square-error (MMSE) decoding. Numerical results are presented to verify our optimality results and to demonstrate the performance gain of the optimal (M)-ary index assignment over the state-of-the-art binary counterpart for the case of (8)-PSK over the AWGN channel.

In this paper, we analyze the symbol error rate (SER) performance of the simultaneous wireless information and power transfer (SWIPT) enabled three-node differential decode-and-forward (DDF) relay networks, which adopt the power splitting (PS) protocol at the relay. The use of non-coherent differential modulation eliminates the need for sending training symbols to estimate the instantaneous channel state information (CSI) at all network nodes, and therefore improves the power efficiency, as compared with the coherent modulation. However, performance analysis results are not yet available for the state-of-the-art detectors such as the maximum-likelihood detector (MLD) and approximate MLD. Existing works rely on the Monte-Carlo simulation method to show the existence of an optimal PS ratio that minimizes the overall SER. In this work, we propose a near-optimal detector with linear complexity with respect to the modulation size. We derive an approximate SER expression and prove that the proposed detector achieves the full diversity order. Based on our expression, the optimal PS ratio can be accurately estimated without requiring any Monte-Carlo simulation. We also extend the proposed detector and its SER analysis for adopting the time switching (TS) protocol at the relay. Simulation results verify the effectiveness of our proposed detector and the accuracy of our SER results in various network scenarios for both PS and TS protocols., Comment: 30 pages. arXiv admin note: substantial text overlap with arXiv:2005.03096

Envisioned as a promising component of the future wireless Internet-of-Things (IoT) networks, the non-orthogonal multiple access (NOMA) technique can support massive connectivity with a significantly increased spectral efficiency. Cooperative NOMA is able to further improve the communication reliability of users under poor channel conditions. However, the conventional system design suffers from several inherent limitations and is not optimized from the bit error rate (BER) perspective. In this paper, we develop a novel deep cooperative NOMA scheme, drawing upon the recent advances in deep learning (DL). We develop a novel hybrid-cascaded deep neural network (DNN) architecture such that the entire system can be optimized in a holistic manner. On this basis, we construct multiple loss functions to quantify the BER performance and propose a novel multi-task oriented two-stage training method to solve the end-to-end training problem in a self-supervised manner. The learning mechanism of each DNN module is then analyzed based on information theory, offering insights into the proposed DNN architecture and its corresponding training method. We also adapt the proposed scheme to handle the power allocation (PA) mismatch between training and inference and incorporate it with channel coding to combat signal deterioration. Simulation results verify its advantages over orthogonal multiple access (OMA) and the conventional cooperative NOMA scheme in various scenarios.

This paper studies the detection and performance analysis problems for a relay network with $N$ parallel decode-and-forward (DF) relays. Due to the distributed nature of this network, it is practically very challenging to fulfill the requirement of instantaneous channel state information for coherent detection. To bypass this requirement, we consider the use of non-coherent DF relaying based on a generalized differential modulation (GDM) scheme, in which transmission power allocation over the $M$-ary phase shift keying symbols is exploited when performing differential encoding. In this paper, a novel detector at the destination of such a non-coherent DF relay network is proposed. It is an accurate approximation of the state-of-the-art detector, called the almost maximum likelihood detector (AMLD), but the detection complexity is considerably reduced from $\mathcal{O}(M^2N)$ to $\mathcal{O}(MN)$. By characterizing the dominant error terms, we derive an accurate approximate symbol error rate (SER) expression. An optimized power allocation scheme for GDM is further designed based on this SER expression. Our simulation demonstrates that the proposed non-coherent scheme can perform close to the coherent counterpart as the block length increases. Additionally, we prove that the diversity order of both the proposed detector and the AMLD is exactly $\lceil N/2 \rceil + 1$. Extensive simulation results further verify the accuracy of our results in various scenarios., Comment: 32 pages

In this paper, we analyze the symbol error rate (SER) performance of the simultaneous wireless information and power transfer (SWIPT) enabled three-node differential decode-and-forward (DDF) relay networks, which adopt the power splitting (PS) protocol at the relay. The use of non-coherent differential modulation eliminates the need for sending training symbols to estimate the instantaneous channel state informations (CSIs) at all network nodes, and therefore improves the power efficiency, as compared with the coherent modulation. However, performance analysis results are not yet available for the state-of-the-art detectors such as the approximate maximum-likelihood detector. Existing works rely on Monte-Carlo simulation to show that there exists an optimal PS ratio that minimizes the overall SER. In this work, we propose a near-optimal detector with linear complexity with respect to the modulation size. We derive an accurate approximate SER expression, based on which the optimal PS ratio can be accurately estimated without requiring any Monte-Carlo simulation., Comment: Accepted by IEEE International Conference on Communications (ICC) 2020

IP protocol is the core of TCP/IP network layer. However, since IP address and its Domain Name are allocated and managed by a single agency, there are risks of centralization. The semantic overload of IP address also reduces its scalability and mobility, which further hinders the security. This paper proposes a co-governing Multi-Identifier Network (MIN) architecture that constructs a network layer with parallel coexistence of multiple identifiers, including identity, content, geographic information, and IP address. On the management plane, we develop an efficient management system using consortium blockchain with voting consensus, so the network can simultaneously manage and support by hundreds or thousands of nodes with high throughput. On the data plane, we propose an algorithm merging hash table and prefix tree (HTP) for FIB, which avoids the false-negative error and can inter-translate different identifiers with tens of billions of entries. Further, we propose a scheme to transport IP packets using CCN as a tunnel for supporting progressive deployment. We deployed the prototype of MIN to the largest operators' network in Mainland China, Hongkong and Macao, and demonstrated that the network can register identifier under co-governing consensus algorithm, support VoD service very well., Comment: 13 pages

A quasi-complementary sequence set (QCSS) refers to a set of two-dimensional matrices with low non-trivial aperiodic auto- and cross- correlation sums. For multicarrier code-division multiple-access applications, the availability of large QCSSs with low correlation sums is desirable. The generalized Levenshtein bound (GLB) is a lower bound on the maximum aperiodic correlation sum of QCSSs. The bounding expression of GLB is a fractional quadratic function of a weight vector $\mathbf{w}$ and is expressed in terms of three additional parameters associated with QCSS: the set size $K$, the number of channels $M$, and the sequence length $N$. It is known that a tighter GLB (compared to the Welch bound) is possible only if the condition $M\geq2$ and $K\geq \overline{K}+1$, where $\overline{K}$ is a certain function of $M$ and $N$, is satisfied. A challenging research problem is to determine if there exists a weight vector which gives rise to a tighter GLB for \textit{all} (not just \textit{some}) $K\geq \overline{K}+1$ and $M\geq2$, especially for large $N$, i.e., the condition is {asymptotically} both necessary and sufficient. To achieve this, we \textit{analytically} optimize the GLB which is (in general) non-convex as the numerator term is an indefinite quadratic function of the weight vector. Our key idea is to apply the frequency domain decomposition of the circulant matrix (in the numerator term) to convert the non-convex problem into a convex one. Following this optimization approach, we derive a new weight vector meeting the aforementioned objective and prove that it is a local minimizer of the GLB under certain conditions.

In many applications including integer-forcing linear multiple-input and multiple-output (MIMO) receiver design, one needs to solve a successive minima problem (SMP) on an $n$-dimensional lattice to get an optimal integer coefficient matrix $\A^\star\in \mathbb{Z}^{n\times n}$. In this paper, we first propose an efficient optimal SMP algorithm with an $\bigO(n^2)$ memory complexity. The main idea behind the new algorithm is it first initializes with a suitable suboptimal solution, which is then updated, via a novel algorithm with only $\bigO(n^2)$ flops in each updating, until $\A^{\star}$ is obtained. Different from existing algorithms which find $\A^\star$ column by column through using a sphere decoding search strategy $n$ times, the new algorithm uses a search strategy once only. We then rigorously prove the optimality of the proposed algorithm. Furthermore, we theoretically analyze its complexity. In particular, we not only show that the new algorithm is $\Omega(n)$ times faster than the most efficient existing algorithm with polynomial memory complexity, but also assert that it is even more efficient than the most efficient existing algorithm with exponential memory complexity. Finally, numerical simulations are presented to illustrate the optimality and efficiency of our novel SMP algorithm., Comment: To appear in IEEE Transactions on Communications

Using physical layer network coding, compute-and-forward is a promising relaying scheme that effectively exploits the interference between users and thus achieves high rates. In this paper, we consider the problem of finding the optimal integer-valued coefficient vector for a relay in the compute-and-forward scheme to maximize the computation rate at that relay. Although this problem turns out to be a shortest vector problem, which is suspected to be NP-hard, we show that it can be relaxed to a series of equality-constrained quadratic programmings. The solutions of the relaxed problems serve as real-valued approximations of the optimal coefficient vector, and are quantized to a set of integer-valued vectors, from which a coefficient vector is selected. The key to the efficiency of our method is that the closed-form expressions of the real-valued approximations can be derived with the Lagrange multiplier method. Numerical results demonstrate that compared with the existing methods, our method offers comparable rates at an impressively low complexity., Comment: Part of this work has been presented in ISIT'2014

Display-camera communication has become a promising direction in both computer vision and wireless communication communities. However, the consistency of the channel measurement is an open issue since precise calibration of the experimental setting has not been fully studied in the literatures. This paper focuses on establishing a scheme for precise calibration of the display-camera channel performance. To guarantee high consistency of the experiment, we propose an accurate measurement scheme for the geometric parameters, and identify some unstable channel factors, e.g., Moire effect, rolling shutter effect, blocking artifacts, inconsistency in auto-focus, trembling and vibration. In the experiment, we first define the consistency criteria according to the error-prone region in bit error rate (BER) plots of the channel measurements. It is demonstrated that the consistency of the experimental result can be improved by the proposed precise calibration scheme., Comment: 8 pages, preliminary conference version

We consider the problem of finding the optimal coefficient vector that maximizes the computation rate at a relay in the compute-and-forward scheme. Based on the idea of sphere decoding, we propose a highly efficient algorithm that finds the optimal coefficient vector. First, we derive a novel algorithm to transform the original quadratic form optimization problem into a shortest vector problem (SVP) using the Cholesky factorization. Instead of computing the Cholesky factor explicitly, the proposed algorithm realizes the Cholesky factorization with only $\bigO(n)$ flops by taking advantage of the structure of the Gram matrix in the quadratic form. Then, we propose some conditions that can be checked with $\bigO(n)$ flops, under which a unit vector is the optimal coefficient vector. Finally, by taking into account some useful properties of the optimal coefficient vector, we modify the Schnorr-Euchner search algorithm to solve the SVP. We show that the estimated average complexity of our new algorithm is $\bigO(n^{1.5}P^{0.5})$ flops for i.i.d. Gaussian channel entries with SNR $P$ based on the Gaussian heuristic. Simulations show that our algorithm is not only much more efficient than the existing ones that give the optimal solution, but also faster than some best known suboptimal methods. Besides, we show that our algorithm can be readily adapted to output a list of $L$ best candidate vectors for use in the compute-and-forward design. The estimated average complexity of the resultant list-output algorithm is $\bigO\left(n^{1.5}P^{0.5}\log L + nL\right)$ flops for i.i.d. Gaussian channel entries., Comment: This work will appear in IEEE Transactions on Wireless Communications

Motivated by applications such as battery-operated wireless sensor networks (WSN), we propose an easy-to-implement energy-efficient two-way relaying scheme. In particular, we address the challenge of improving the standard two-way selective decode-and-forward protocol (TW-SDF) in terms of block-error-rate (BLER) with minor additional complexity and energy consumption. By following the principle of soft relaying, our solution is the two-way one-bit soft forwarding (TW-1bSF) protocol in which the relay forwards the one-bit quantization of a posterior information metric about the transmitted bits, associated with an appropriately designed reliability parameter. In WSN-related standards (such as IEEE802.15.6 and Bluetooth), block codes are adopted instead of convolutional and other sophisticated codes, due to their efficient decoder hardware implementation. As the second main contribution, we derive tight upper bounds on the BLER performance for both TW-SDF and TW-1bSF, when the two-way relaying network employs block codes and hard decoding. The error probability analysis confirms the superiority of TW-1bSF. Moreover, we derive the asymptotic performance gain of TW-1bSF over TW-SDF, which further suggests that the proposed protocol is a good choice, especially when long block codes are used., Comment: 32 pages, 9 figures, 1 table. submitted to IEEE Trans. Wireless Commun

Due to the use of commodity software and hardware, crash-stop and Byzantine failures are likely to be more prevalent in today's large-scale distributed storage systems. Regenerating codes have been shown to be a more efficient way to disperse information across multiple nodes and recover crash-stop failures in the literature. In this paper, we present the design of regeneration codes in conjunction with integrity check that allows exact regeneration of failed nodes and data reconstruction in presence of Byzantine failures. A progressive decoding mechanism is incorporated in both procedures to leverage computation performed thus far. The fault-tolerance and security properties of the schemes are also analyzed., Comment: Submitted to INFOCOM 2012 on 28 July 2011

The Lenstra-Lenstra-Lov\'asz (LLL) algorithm is the most practical lattice reduction algorithm in digital communications. In this paper, several variants of the LLL algorithm with either lower theoretic complexity or fixed-complexity implementation are proposed and/or analyzed. Firstly, the $O(n^4\log n)$ theoretic average complexity of the standard LLL algorithm under the model of i.i.d. complex normal distribution is derived. Then, the use of effective LLL reduction for lattice decoding is presented, where size reduction is only performed for pairs of consecutive basis vectors. Its average complexity is shown to be $O(n^3\log n)$, which is an order lower than previously thought. To address the issue of variable complexity of standard LLL, two fixed-complexity approximations of LLL are proposed. One is fixed-complexity effective LLL, while the other is fixed-complexity LLL with deep insertion, which is closely related to the well known V-BLAST algorithm. Such fixed-complexity structures are much desirable in hardware implementation since they allow straightforward constant-throughput implementation., Comment: remove redundant figures

Recently, lattice-reduction-aided detectors have been proposed for multiple-input multiple-output (MIMO) systems to give performance with full diversity like maximum likelihood receiver, and yet with complexity similar to linear receivers. However, these lattice-reduction-aided detectors are based on the traditional LLL reduction algorithm that was originally introduced for reducing real lattice bases, in spite of the fact that the channel matrices are inherently complex-valued. In this paper, we introduce the complex LLL algorithm for direct application to reduce the basis of a complex lattice which is naturally defined by a complex-valued channel matrix. We prove that complex LLL reduction-aided detection can also achieve full diversity. Our analysis reveals that the new complex LLL algorithm can achieve a reduction in complexity of nearly 50% over the traditional LLL algorithm, and this is confirmed by simulation. It is noteworthy that the complex LLL algorithm aforementioned has nearly the same bit-error-rate performance as the traditional LLL algorithm., Comment: Submitted to IEEE Transactions on Wireless Communication in March 2006. Part of this work was presented at the 2005 Global Telecommunications Conference, United States, November 2005