The previous work developed a language learning system with human-like robots utilizing self-determination theory (SDT) to enhance student’ learning engagement and proficiency. Initial evaluations indicated that typical students encountered stimulated interest and efficacy with the robot. To test the consistency of these findings, we conducted a replication study using the same system, robot, and tasks but with students with dyslexia. Through questionnaires, observations, and proficiency tests, the results confirmed that the interactive robot also improved learning motivation and performance in those with dyslexia, with the same system, robot, and tasks.

As a 5G service category, ultra-reliable low-latency communication (URLLC) raises the challenge of dramatically improving the reliability of short message transmission, for which sparse regression codes (SRCs) and their variations have emerged as promising solutions. In this paper, we propose a generalization of single-section SRCs (SRCl) by designing a sparse vector set that satisfies a certain minimum Euclidean distance constraint. The design problem is first transformed into a constant weight code (CWC) design problem. By extending the binary alphabet to an$M$-ary-phase alphabet, we generalize the CWC to$M$-ary CWC ($M$-CWC) to further increase the achievable minimum Euclidean distance. The increment is theoretically analyzed, and the anticipated performance gain of the resultant$M$-CWC-SRCI over SRCI is verified by simulation. Additionally, our simulation results show that the proposed$M$-CWC-SRCI outperforms the state-of-the-art SRCl-based schemes by about 1 dB gain in EblNo at BLER of Le - 5.

Due to the increasing size of datasets and complexity of models, distributed machine learning is becoming increasingly important. Among the various components of distributed machine learning frameworks, the all-reduce operation holds significant importance, particularly in terms of communication costs among computing nodes. The all-reduce operation distributes to all nodes one or more reductions of data symbols from all nodes. This operation is used in distributed machine learning for aggregating data from computing nodes during the training and synchronizing the results among all computing nodes. This paper considers a distributed system consisting of computing nodes which are connected with each other via one-hop links. The data symbols are encoded and stored in the computing nodes. This paper focuses on the so-called all-linear-reduce operation which distributes to all nodes one or more linear combinations of data symbols from all nodes. This paper aims to determine the optimal bandwidth for the linear all-reduce operation, for an arbitrarily given distributed system. We propose a universal all-linear-reduce operation, which has been proven to achieve the optimal bandwidth in some cases.

Real-world distributed storage systems (DSSs) are heterogeneous because storage nodes may have unequal per-symbol storage costs, and network links may have unequal per-symbol transmission costs. For some general classes of heterogeneous DSSs, the optimal tradeoff between storage and repair costs achievable by functional repair codes is known (at least numerically). However, it is unclear whether exact-repair codes can achieve any point of such an optimal storage-repair tradeoff curve, especially at the point of the minimum storage cost. In this paper, we provide an affirmative answer to the question by constructing the so-called heterogeneous minimum storage repair (HMSR) codes for both the average and worst-case repair costs. To optimize storage and repair costs, a heterogeneous DSS may need to adopt irregular array codes and repair a node by downloading unequal numbers of symbols from helper nodes. However, our results show that for almost all heterogeneous DSSs, exact-repair HMSR codes are regular array codes covering an adequately chosen set of nodes. Specifically, exact-repair HMSR codes are designed by stacking conventional MSR codes and applying different repair schemes to different layers. Still, this does not work for every heterogeneous DSS. It is proven that using regular or linear irregular array codes for constructing exact-repair HMSR codes is insufficient in some cases.

Existing crowdsourced indoor positioning systems (CIPSs) usually require prior knowledge about the site and a tedious calibration process. Moreover, they may require a large number of landmarks while ignoring the topology information that may be contained in the crowdsourced data. In this paper, we present Leto, a system that useslearnedtopology information from combined user traces to construct a radio map. Leto relies on crowdsourced WiFi and accelerometer signals only without requiring any prior knowledge about the site. Our key idea is that learned topology information can reduce the required number of landmarks, while available landmarks can transform the topology into a map. We propose a novel framework that efficiently learns the map topology by a hybrid multidimensional scaling (HMDS) algorithm and accurately rectifies the map using only a few anchors by an adaptive force-directed (AFD) algorithm. We also provide a theoretical convergence analysis of the HMDS algorithm. Experimental results on real-world datasets show that Leto can capture useful topology information and achieve significant improvements in radio map construction compared to existing systems.

Polarization-adjusted convolutional (PAC) codes of short blocklengths over the binary-input additive white Gaussian noise channel have excellent performance. To further improve the performance of the PAC codes, we adopt the asymptotic frame error rate (AFER) optimality criterion, i.e., the primary and secondary criteria are to maximize the minimum Hamming distance and to minimize the error coefficient of the code, respectively.In this paper, we conduct a new optimization search using a graphic processing unit that jointly optimizes the rate profile and the convolutional transform of a PAC code. Our search has discovered many short record-breaking binary linear block codes (representable as PAC codes) which achieve smaller error coefficients at the same best-known minimum distance compared to the best records in the literature. In particular, at a frame error rate of 10−9, an optimized [64, 32] PAC code with a minimum distance of 12 outperforms the best-known counterpart by 0.40 dB and is 1.1 dB away from the Polyanskiy-Poor-Verdú bound.

In an erasure-coded distributed storage system (DSS), requesting a file requires downloading information from multiple storage nodes, called servers, which leads to cross-server network traffic. The cross-server transmission cost can be reduced if these servers are equipped with extra memory to cache some information about the files. This paper considers the so-called cache-aided DSS (CADSS), where each server is connected to several caching proxies through a shared link, and studies the transmission cost incurred by file requests. For simplicity, we focus on a CADSS in which the servers are connected via a one-hop link, and each server is connected to the same number of caching proxies. When the caching proxies receive file requests, a server first downloads some symbols from the other servers, called the helper servers, and then broadcasts some symbols to the caching proxies. For a single server, the maximum number of symbols downloaded from the helper nodes (respectively broadcast to its caching proxies) normalized by the file size is called the cross-server (respectively local) reads. This paper first optimizes the cross-server and local reads separately. Whether from the perspective of optimizing cross-server or local reads, a CADSS can be interpreted as an equivalent single-server caching system but with different system parameters. This paper analyzes the optimal tradeoff between the cross-server and local reads. It is shown that the optimal cross-server and local reads can be achieved simultaneously for some parameters, while a tradeoff exists for some other parameters. We characterize the two extreme points of the optimal tradeoff curve and derive the optimal tradeoff for some specific parameters.

In this paper, we present new constructions for binary linear block codes (BLBCs) that achieve the largest possible minimum Hamming weight and the smallest possible number of minimum-weight codewords (also known as the error coefficient). These [n, k] BLBCs over the additive white Gaussian noise channel, under maximum-likelihood decoding, attain the best possible asymptotic frame error rate (FER) (i.e., at high signal-to-noise ratio) and are said to be asymptotic frame error rate (AFER)-optimal. For l = 0, 1,⋯, k−1 and all positive integers k and m, we give new constructions of [(2k−1)m+l, k] and [12], [5] AFER-optimal codes. Specifically, we have [(2k− 1) + k, k + 1], [15m + 6, 4], and [15m + 4, 4] BLBCs with error coefficient values of 2, 3 and 4, respectively. These values are significantly smaller than the corresponding best-known values in the literature.

In this paper, the problem of efficiently evaluating the error performance of linear block codes over the AWGN channel is considered. Based on the geometric structure of the channel, we define the l2-norm of the noise vector as a random variable and refer to its sample space as the radius domain. A minimum-variance importance sampling (IS) estimator is proposed by deriving the optimal IS distribution on the radius domain. The IS gain of the proposed estimator compared to the Monte Carlo method is analyzed. The asymptotic IS gain for high SNR, which only depends on the minimum distance of the code, is derived. Finally, the effectiveness of the proposed estimator and the accuracy of the asymptotic IS gain are verified through simulation.

In this paper, the problem of designing the maximum-distance-separable (MDS) array codes for repairing a single node failure in a distributed storage system (DSS) is addressed. We consider the class of heterogeneous DSSs which can be represented as a fully connected storage network consisting of links having possibly different per-symbol transmission costs and assume that the repair process only allows a single-hop transmission from any helper node to a failed node. First, we consider the repair cost of a failed node to be the total transmission cost from all helper nodes incurred by the repair process. For a storage network represented by a complete weighted graph with the weights being the persymbol transmission costs, we derive a repair cost lower bound of every node. Somewhat surprisingly, even for a storage network represented by a complete weighted graph with time-varying weights, we can also construct a single optimal-repair-cost MDS array code that can achieve the repair cost lower bounds of all nodes. Next, we consider the repair cost of a failed node to be the worst-case transmission cost over all helper nodes incurred by the repair process. For a storage network represented by a static complete weighted graph, we derive a lower bound on the repair cost of every node and construct a single optimal-repair-cost MDS array code that can achieve the repair cost lower bounds of all nodes.

In this paper, the problem of efficient performance evaluation of linear block codes over the AWGN channel with M-PSK modulation is considered. Based on the geometric structure of the channel, we define the tangent of the half-angle of the circular cone, whose central line passes through the transmitted signal vector and the origin, as a random variable and refer to its sample space as the angular domain. We propose a minimum-variance importance sampling (IS) estimator by deriving the optimal IS distribution in the angular domain. Besides, we derive the asymptotic IS gain of the proposed estimator compared to the Monte Carlo method as SNR tends to infinity. The effectiveness of the proposed estimator and the accuracy of the asymptotic IS gain are verified through simulation.

In recent years, digital copies of paper documents are used widely with the prevalence of various online services. As a result, it is critical to validate the authenticity of the uploaded document images to protect against attacks from malicious users. Out of various types of attacks, the recapture attack (by reprinting and recapturing) is effective in concealing the trace of document forgeries. However, detecting the recaptured document images is challenging. To address this problem, we first study the halftone cell distortion introduced in both the genuine and recaptured document images. Based on our study, a unified model that characterizes the halftone cell distortion (e.g., errors in size and displacement) is then proposed for accurate estimation of the distortion parameters. The statistics of the estimated parameters are then exploited in a hypothesis testing framework to detect the recaptured document images. The questioned document image can be authenticated by testing against the null hypothesis, i.e., the image is a genuine sample. To evaluate the performance of the proposed approach under different application scenarios, extensive experiments are conducted with different prior knowledge of printers (known printer model, known printing technique, and In-The-Wild (unknown printing device and document contents)). The experiment results show that the proposed approach outperforms the data-driven benchmark approaches by a significant margin. Specifically, under the In-The-Wild experiment protocol, the Area Under the Receiver Operating Characteristic (ROC) Curve (AUC) of the proposed approach is above 0.87 while the AUC of the benchmark approaches (even some utilize both genuine and recaptured samples) degrades to less than 0.77.

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.

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 article, 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 explainable 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.

The cooperative relay network is a type of multi-terminal communication system. We present in this paper a Neural Network (NN)-based autoencoder (AE) approach to optimize its design. This approach implements a classical three-node cooperative system as one AE model, and uses a two-stage scheme to train this model and minimize the designed losses. We demonstrate that this approach shows performance close to the best baseline in decode-and-forward (DF), and outperforms the best baseline in amplify-and-forward (AF), over a wide range of signal-to-noise-ratio (SNR) values. It is also shown that training at a list of mixed SNR values can improve the error performance compared to training at a fixed SNR value. Moreover, to verify the robustness of the trained AE model, we test it under the effect of impulse-noise.

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.

In conventional communication systems, quantized source symbols are represented by distinct binary labels, which are then mapped to bandwidth-efficient modulation symbols (such as M-PSK) for transmission. Assigning quantization levels to binary labels is known as the binary index assignment (IA) and has been well studied under the assumption that binary indices are transmitted over the binary symmetric channel. It is well-known that the natural binary code gives the optimal binary IA for uniform quantizers with uniform sources. Alternatively, we can also assign quantization levels to M-ary labels to fit the M-ary transmission. This M-ary IA approach generalizes and could outperform the binary IA, and has potential applications in power-efficient transmission such as wireless sensor networks. Although there exist some significant progresses in the study of finding the optimal M-ary IA, the problem is still open. In this paper, we investigate the M-ary IA problem for equiprobable uniform scalar quantizers and M-PSK transmission. We derive a lower bound on the channel mean-squared distortion (MSD) among all possible M-ary IAs and construct a solution which is optimal for M = 3, 4. For M ≥ 5, the solution becomes near-optimal, and its MSD performance approaches the lower bound to within a small gap. In addition, under some wireless sensor network scenarios with 64-level quantization and 8-PSK, we demonstrate that the percentage energy saving of the proposed nonbinary IA solution could be up to 45% relative to the optimal binary IA approach.

Emerging recently as a novel concept in communication system design, end-to-end learning introduces deep neural networks (NNs) to represent the transmitter and receiver functions. Consequently, the whole system can be interpreted as an autoencoder (AE), which can be optimized from a holistic approach through a data-driven training method. Until now, the AE technique is mainly developed for point-to-point communication scenarios. In this paper, we aim to develop a novel NN-based AE scheme for relay-assisted cooperative communication systems. Specifically, three NN components are constructed to learn the behavior of the transmitter, relay node, and receiver, respectively. As the conventional end-to-end training is inapplicable, a novel two-stage training approach is proposed to indirectly solve the end-to-end training problem. The implicit approximations involved are analytically expressed based on information theory, offering insights on the achievable performance with the proposed training method. The proposed AE model eliminates the need for channel state information and noise variance of any link, and is adaptive to the variation in the input block length. Simulation results verify its advantages over the conventional decode-and-forward (DF) and amplify-and-forward (AF) schemes in various scenarios.

Low density lattice codes (LDLCs) have been shown to approach the AWGN channel capacity and can be decoded by a message passing decoder. The messages passed between check nodes and variable nodes are probability density functions, which are approximated by Gaussian mixtures in existing LDLC decoders. However, in the best-known M-Gaussian decoder, the Gaussian mixtures for approximating variable node messages still contain unnecessary Gaussian components, resulting in exponential decoding complexity in the LDLC degree d. In this paper, an efficient LDLC decoder is proposed from the lattice viewpoint, which only finds out important Gaussian components for approximating the variable node messages. The decoding complexity for the proposed decoder is linear in d. Numerical results show that the proposed decoder can achieve significant complexity saving without degrading the performance compared with the M-Gaussian decoder. In particular, the runtime saving is 75.3% when the code length is 10000 and d is 7.

We re-examine the problem of designing low-complexity detectors and their performance analysis for the 3-node one-way decode-and-forward (DF) relay network, where the destination has the statistical channel state information (CSI) of the source-relay link, and the instantaneous CSI of both the source-destination and relay-destination links. Recently proposed detection schemes, such as the piece-wise linear detector (PLD), achieve near-optimal error performance with linear complexity (with respect to the modulation size). In this paper, we propose two new detectors with near-optimal error performance. One has linear complexity for general modulations and the other has constant complexity for PAM signals. Additionally, an algorithm for computing the upper bound on the symbol error rate (SER) of the new detectors for the static source-destination and relay-destination links is proposed. Simulation results are presented to verify the efficiency of the proposed detectors and the tightness of the proposed SER bound.

In this paper, we propose an Importance Sampling (IS) scheme for fast simulation of linear block codes over binary symmetric channels (BSCs). By re-formulating the IS problem into the one-dimensional Hamming weight space, we propose a novel IS estimator and derive the optimal IS distribution which will minimize the variance of the estimator. Consequently, a corresponding iterative algorithm is proposed. The effectiveness of the proposed IS algorithm compared to the state-of-the-art IS algorithm is demonstrated in the word error rate simulation of both LDPC and Polar codes.

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* ∈ Zn×n. In this paper, we first propose an efficient optimal SMP algorithm with an O(n2) 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 O(n2) flops in each updating, until A* is obtained. Different from existing algorithms which find A* 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 Ω(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.

Due to the rapid advancement in processing power and camera quality of mobile devices, research on the display-to-camera (D2C) communication channel has recently received increasing attention. Unlike the traditional QR Code, the unobtrusive D2C communication scheme normally serves both the human eyes and the mobile camera in commercial advertisements. Thus, attention should be paid to both unobtrusiveness and reliability of the design of a D2C communication scheme. In this paper, 2D barcodes with unobtrusive embedding in the blue channel are proposed in image and video formats to yield the robust and unobtrusive (RU) code and video-based RU (vRU) code, respectively. The proposed RU code is featured with a modulation scheme in blue channel that leverages several important properties of the human visual system; such as insensitivity toward the yellow-blue chrominance component, the proximity principle, and the oblique effect. Both RU code and vRU code employ a low-density-parity-check code for intra-frame channel coding. In addition, vRU code adopts an erasure-correcting Reed-Solomon code for inter-frame channel coding. Under a high perceptual quality constraint (multiscale structural similarity (MS-SSIM) ≈ 0.95), RU code achieves a demodulation bit error probability of 3.84%, which is an order of magnitude smaller than that of the existing picture-embedding 2D barcodes. Meanwhile, under a similar perceptual quality requirement (MS-SSIM ≈ 0.95 for each video frame), the goodput of vRU code is reported to be as high as 34.33 kbps under practical settings, e.g., a display frame rate of 30 fps and a capture frame rate of 42 fps.

With the rapid advancement of sensing capability and computational power in consumer electronic devices, the use of mobile cameras for communications has attracted significant attention from both academia and industry. The design of a reliable communication system over the print-capture channel is a key challenge in some important applications, such as barcoding and document authentication. However, the real-world printcapture channel is spatially non-linear and non-stationary, and lacks a standard parametric model. As a consequence, advanced channel coding techniques developed for common channel models are not applicable in the existing systems without costly and device-dependent pre-training. In this work, an accurate parametric print-capture channel model and an efficient channel estimation scheme requiring low training overhead are proposed. With the estimated parameters, the proposed print-capture channel model can be linearized to the (possibly input-dependent) additive white Gaussian noise (AWGN) channel model. This allows the use of state-of-the-art channel coding schemes, such as low-density parity-check (LDPC) codes with iterative soft decoding, to improve the reliability of the communication system under challenging conditions, e.g., at a low signal-to-noise ratio. As an example application of the proposed print-capture channel model, a demonstrative multilevel 2D barcode using an LDPC code with iterative soft decoding, is designed to enhance the reliability over the conventional QR code which is based on the Reed-Solomon code with hard decoding. At a printing resolution of 600dpi, the 8-level 2D barcode achieves data capacity gains of about 10% and 56% over the QR code in the in-focus and blurlimited scenarios, respectively. It is noteworthy that the enhanced data capacity of the multilevel barcode is made possible by the proposed channel estimation scheme, which incurs an additional training overhead of about 3.3% only.

Symbol asynchrony is an important issue in practical implementation of physical-layer network coding (PNC). In this paper, we investigate the asynchronous convolutionally coded PNC over the two-way relay network (TWRN). Symbols from two users arrive at the relay with symbol misalignment. A joint channel-network decoder (JCND) for the relay is proposed. A salient feature for the proposed JCND is that it incorporates the code structure and the symbol misalignment jointly, and the cyclic structure for the channel code is not required to combat the integer symbol misalignment. Furthermore, we derive the bit error rate (BER) bound at the relay utilizing the error state diagram. Simulation results indicate that the performance of the proposed algorithm matches well with the bound.

Recently, some picture-embedding schemes have been proposed to improve the aesthetic appearance of 2D barcodes. However, these aesthetic 2D barcodes are not robust to the distortions incurred by the print/display-and-capture channel under limited rendering space and resolution. In this paper, a picture-embedding 2D barcode named the Robust and Aesthetic (RA) Code is proposed to counter the channel impairments, such as downsampling error and inter-symbol interference. Experimental results demonstrate that the proposed RA Code is more robust than the existing picture-embedding 2D barcodes, especially under limited printing/displaying space. The RA Code of a size as small as 1.5 × 1.5 cm2can be successfully decoded with a demodulated bit error probability of less than 0.1, which corresponds to more than 50% improvement over those of the state-of-the-art picture-embedding 2D barcodes. In addition, the correct decoding probability is improved significantly from as low as 0 to more than 0.8650. The decoding algorithm has been implemented on the Android platform, and the practicality of the RA Code has been successfully demonstrated.

The integer-forcing (IF) linear multiple-input and multiple-output (MIMO) receiver is a recently proposed suboptimal receiver which nearly reaches the performance of the optimal maximum likelihood receiver for the entire signal-to-noise ratio (SNR) range and achieves the optimal diversity multiplexing tradeoff for the standard MIMO channel with no coding across transmit antennas in the high SNR regime. The optimal integer coefficient matrix A* ϵ ZNt×Ntfor IF maximizes the total achievable rate, where Nt is the column dimension of the channel matrix. To obtain A*, a successive minima problem (SMP) on an Nt-dimensional lattice that is suspected to be NP-hard needs to be solved. In this paper, an efficient exact algorithm for the SMP is proposed. For efficiency, our algorithm first uses the LLL reduction to reduce the SMP. Then, different from existing SMP algorithms which form the transformed A*column by column in Ntiterations, it first initializes with a suboptimal matrix which is the Nt× Ntidentity matrix with certain column permutations that guarantee this suboptimal matrix is a good initial solution of the reduced SMP. The suboptimal matrix is then updated, by utilizing the integer vectors obtained by employing an improved Schnorr-Euchner search algorithm to search the candidate integer vectors within a certain hyper-ellipsoid, via a novel and efficient algorithm until the transformed A*is obtained in only one iteration. Finally, the algorithm returns the matrix obtained by left multiplying the solution of the reduced SMP with the unimodular matrix that is generated by the LLL reduction. Simulation results show the optimality of our novel algorithm and indicates that the new one is much more efficient than existing optimal algorithms.

Generalized Levenshtein bound (GLB) is a lower bound on the maximum aperiodic correlation sum of quasi-complementary sequence set (QCSS) which refers to a set of two-dimensional matrices with low non-trivial aperiodic auto- and cross-correlation sums. GLB is an indefinite fractional quadratic function of a “simplex” weight vector w and three additional parameters associated with QCSS. We present a novel approach to analytically conduct fractional quadratic optimization for the tightening of the GLB. Our key idea is to apply the frequency-domain decomposition of the relevant circulant matrix (i.e., the numerator term of GLB) to convert the non-convex problem into a convex one. We derive a new weight vector which asymptotically leads to a tighter GLB (over the Welch bound) for all possible (K, M) cases, where K, M denote the set size, the number of channels, of QCSS, respectively.

Relay-assisted communication has been shown to be an effective technique to improve the reliability and throughput of real-world wireless communication networks. It enables single-antenna users to form a virtual antenna array without installing multiple antennas at the transmitter or the receiver. This paper re-examines the decoding problem in the convolutionally coded relay channel with the classical decode-and-forward protocol. By tackling the challenge of modeling the error propagation effect at the relay, a near BER-optimal decoding (NBOD) algorithm at the destination is derived, assuming the availability of perfect receiver channel state information. Its decoding complexity is linear in the information block length, while the exact BER-optimal decoding algorithm with a sub-exponential complexity is still unknown. The major approximation involved in the derivation of the NBOD algorithm is the pairwise error probability approximation that causes a practically insignificant degradation from the optimal BER performance. Our simulation result confirms that the proposed NBOD algorithm can perform close to the maximum likelihood performance bound on BER in the three-node one-way relay channel scenario. In addition, we have further extended the proposed algorithm for more general single-source single-destination decode-and-forward-based relay networks. Simulation results further verify that the proposed NBOD algorithm can outperform existing decoding algorithms based on maximal-ratio combining and selective decode-and-forward in various relay channel scenarios at the cost of higher complexity.

In this paper, we re-examine the decoding problem of a distributed turbo code (DTC) over the three-node one-way relay channel based on the decode-and-forward protocol. In the traditional DTC scheme, the decoder at the destination assumes the error-free Viterbi decoding at the relay. However, the error propagation effect resulting from unsuccessful decoding at the relay may cause significant performance loss in some practical scenarios. Improved decoders reported in the literature typically assume a certain memoryless error model, which ignores the fact that relay decoding errors are correlated and bursty. In this paper, we propose a novel trellis error model (TEM) to accurately represent the statistics of relay decoding errors and construct two TEM-based iterative decoders (TEM-IDs) with two and three components, respectively. The TEM-ID with three components has a lower complexity than that of the TEM-ID with two components at the cost of minor performance loss. We also derive a new BER bound for the near maximum likelihood decoding of the DTC using a uniform interleaver. In addition, the extrinsic information transfer chart analysis is applied to estimate the threshold performance of the TEM-ID for large code lengths. Extensive simulation results verify that the new decoders can perform close to the derived BER bound and outperform existing decoders. Finally, we show that the TEM-ID can be extended for general distributed concatenated coding systems.

In the scenario of random linear network coding, the channel input and output are matrices over a finite field related by a multiplicative channel matrix. Such channels are called the multiplicative finite-field matrix channels (MFFMC). To communicate over such channels, subspace coding is a promising non-coherent network coding approach which does not require the estimation of the channel matrix. The capacity of subspace coding over the general MFFMC is still unknown (except for some special cases, such as the purely random channel and the uniform full rank channel). In this paper, for a given rank distribution, a class of worst-case channels is characterized and proved to achieve the minimum capacity of subspace coding. Hence the capacity of such a class of channels can serve as the tightest lower bound on the capacity of subspace coding over the MFFMC. Interestingly, for the purely random channel, the uniform full rank channel and the uniform given rank channel, our bound gives the exact value of the capacity of subspace coding. Numerical results show that our bound is tighter than some existing bound at small-to-moderate packet lengths.

The compute-and-forward scheme for wireless relay networks can achieve higher transmission rates than other existing relaying schemes, such as decode-and-forward. The compute-and-forward (CF) design involves finding an integer-valued coefficient vector at each relay so that the set of coefficient vectors form a full rank matrix allowing the destination to perform decoding. The CF design problem is relevant to an instance of the famous shortest lattice vector problem and has attracted much recent research attention. Two representative CF designs, the so-called local optimization scheme and the Wei-Chen scheme, have been introduced in the literature. However, they either achieve relatively low transmission rate, or require a relatively high communication overhead. In this paper, we propose a new compute-and-forward design that can achieve a significantly higher transmission rate than the local optimization scheme and requires a much lower communication overhead than the Wei-Chen scheme. In particular, the new scheme does not require a list of candidate coefficient vectors and their computation rates to be forwarded from each relay to the destination, and hence avoids the heavy communication overhead incurred. Simulation results for a 2-hop wireless relay network with channel vectors consisting of i.i.d. Gaussian entries are presented to demonstrate the transmission rate improvement of the proposed scheme relative to the local optimization scheme. For example, it is shown that the proposed scheme can achieve about 2.5dB gain at moderate SNR in the case of 8 sources/relays.

This paper reexamines the decoding problem for LDPC-coded relay channels applying the decode-and-forward protocol. The error-free decoding process at the relay is typically assumed by the conventional MRC based decoder at the destination. However, in practice, the unsuccessful decoding at the relay is unavoidable and the resultant error propagation may become a performance bottleneck. In this paper, we propose a new Tanner graph error representation to accurately characterize the relay decoding errors. Based on the proposed error representation, we derive a new message passing decoder which is implemented on an extended Tanner graph of the system. It is empirically verified that the new decoder can outperform existing decoders, and achieve promising performance improvement in the scenario of symmetric links. Moreover, the proposed error representation allows us to conduct density evolution to analyze the threshold performance of the new decoder for LDPC-coded relay channels.

Nowadays, 2D barcodes have been widely used as an interface to connect potential customers and advertisement contents. However, the appearance of a conventional 2D barcode pattern is often too obtrusive for integrating into an aesthetically designed advertisement. Besides, no human readable information is provided before the barcode is successfully decoded. This paper proposes a new picture-embedding 2D barcode, called PiCode, which mitigates these two limitations by equipping a scannable 2D barcode with a picturesque appearance. PiCode is designed with careful considerations on both the perceptual quality of the embedded image and the decoding robustness of the encoded message. Comparisons with the existing beautified 2D barcodes show that PiCode achieves one of the best perceptual qualities for the embedded image, and maintains a better tradeoff between image quality and decoding robustness in various application conditions. PiCode has been implemented in the MATLAB on a PC and some key building blocks have also been ported to Android and iOS platforms. Its practicality for real-world applications has been successfully demonstrated.

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 O(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 O(n) flops, under which a unit vector is the optimal coefficient vector. Finally, by considering 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 O(n1.5p0.5) flops for independent identically distributed (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 O(n2.5p0.5+ n1.5p0.5log(L) + nL) flops for i.i.d. Gaussian channel entries.

Motivated by applications such as battery-operated wireless sensor networks (WSN), we propose an easy-to-implement low-complexity 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. As a valuable tool for the BLER analysis, we introduce a new code-theoretic performance metric, named sphere partition function (SPF). 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.

We consider the compute-and-forward protocol design problem with the objective being maximizing the computation rate at a single relay, and propose an efficient method that finds the optimal solution based on sphere decoding. The problem can be transformed into a shortest vector problem (SVP), which can be solved in two steps. First, by fully exploiting the specific structure of the associated Gram matrix using the hyperbolic transformation, the Cholesky factor can be computed with only n2/2 + O(n) flops. Then, taking into account of some useful properties of the optimal solution, we modify the Schnorr-Euchner search algorithm to solve the SVP. Numerical results show that our proposed branch-and-bound method is much more efficient than the existing one that gives the optimal solution. Besides, compared with the suboptimal methods, our method offers the best performance at a cost lower than that of the LLL based method and similar to that of the quadratic programming relaxation method.

This paper reexamines the decoding problem for a distributed Turbo code (DTC) over a 3-node relay network applying the decode-and-forward strategy under the half-duplex constraint. The conventional decoder simply assumes that the relay performs error-free decoding. In practice, unsuccessful decoding at the relay causes error propagation, which may become a performance bottleneck. Improved decoders reported in the literature are all based on memoryless error models, although relay decoding errors are actually correlated. In this paper, we propose a new Markov error modeling approach to accurately characterize the memory effect of relay decoding errors. Based on the proposed error model, we derive a new iterative decoder which includes a component decoder implemented with a product trellis structure. It is empirically verified that the new decoder can outperform existing decoders, and can achieve promising performance improvement in the scenario of symmetric links.

This paper investigates linear precoding over nonsingular linear channels with additive white Gaussian noise, with lattice-type inputs. The aim is to maximize the minimum distance of the received lattice points, where the precoder is subject to an energy constraint. It is shown that the optimal precoder only produces a finite number of different lattices, namely perfect lattices, at the receiver. The well-known densest lattice packings are instances of perfect lattices, but are not always the solution. This is a counter-intuitive result as previous work in the area showed a tight connection between densest lattices and minimum distance. Since there are only finite many different perfect lattices, they can theoretically be enumerated offline. A new upper bound on the optimal minimum distance is derived, which significantly improves upon a previously reported bound, and is useful when actually constructing the precoders.

In wireless networks, the compute-and-forward strategy is a promising physical layer network coding scheme that can achieve high rates by effectively exploiting the interference between users. However, the design of the optimal integer-valued equation coefficient vectors in a compute-and-forward scheme turns out to be a shortest vector problem, which is known to be NP hard. In this work, we consider the problem of designing the equation coefficient vector for each relay with the objective being maximizing the computation rate at that relay. By taking advantage of some useful properties, we show that the problem can be relaxed to a series of equality-constrained quadratic programmings and their closed-form solutions are derived by use of the Lagrange multiplier method, which is the key to the efficiency of our method. A quantization algorithm is then proposed to transform the real-valued approximations to the set of required integer-valued vectors, from which a suboptimal equation coefficient vector is obtained. Numerical results demonstrate that relative to existing methods, our method can offer comparable performance at an impressively low complexity.

Two-dimensional barcodes are widely used in mobile advertisement business, while their decoding performance is not always satisfactory under uncontrolled environments. The corner detection accuracy has been identified as a critical factor affecting the overall system performance. The standard barcode detector performs a candidate search in the binarized barcode image based on the rectangular shape of the barcode. Its performance is not very accurate due to the limited accuracy of the binarized image. In this work, we proposed a coarse-fine corner detection approach for locating the barcode region. It performs far more accurately than the standard barcode detection scheme while keeps the computational complexity affordable. Experimental results for high capacity barcodes show that the proposed detection scheme can extend the range of operation parameters, such as wider angles, and much lower the detection bit error rate, relative to the standard barcode decoder.

Today's large-scale distributed storage systems are commonly built using commodity software and hardware. As a result, crash-stop and Byzantine failures in such systems become more and more prevalent. In the literature, regenerating codes have been shown to be a more efficient way to disperse information across multiple storage nodes and recover from crash-stop failures. In this paper, we propose a novel decoding design of product-matrix constructed regenerating codes in conjunction with integrity check that allows exact regeneration of failed nodes and data reconstruction in the presence of Byzantine failures. A progressive decoding mechanism is incorporated in both procedures to leverage computation performed thus far. Unlike previous works, our new regenerating code decoding has the advantage that its building blocks, such as Reed-Solomon codes and standard cryptographic hash functions, are relatively well-understood because of their widespread applications. The fault tolerance and security properties of the proposed schemes are also analyzed. In addition, the performance of the proposed schemes, in terms of the average number of access nodes and the reconstruction failure probability versus the node failure probability, are also evaluated by Monte Carlo simulations.

Levenshtein improved the famous Welch bound on aperiodic correlation for binary sequences by utilizing some properties of the weighted mean square aperiodic correlation. Following Levenshtein's idea, a new correlation lower bound for quasi-complementary sequence sets (QCSSs) over the complex roots of unity is proposed in this paper. The derived lower bound is shown to be tighter than the Welch bound for QCSSs when the set size is greater than some value. The conditions for meeting the new bound with equality are also investigated.

Favorable characteristics of wireless channels (including the inherent broadcast and superposition nature) provide a fertile ground for the extension of conventional network coding (NC) principles to wireless communication networks. However, the research of emerging wireless (physical layer) network coding (WNC) techniques have already revealed several non-trivial research problems that do not appear in the conventional (wireline) NC systems, including the sensitivity to channel parametrization and challenging multi-source transmission synchronization. In this paper, we uncover another significant research challenge typical for multi-node WNC systems. We show that the performance of contemporary WNC bi-directional relaying strategies is dominated by the availability of a specific hierarchical side information (HSI), required for the successful decoding of desired information from hierarchical (WNC-coded) data streams. We analyze the impact of unreliable transmission of HSI on the performance of a wireless butterfly network (WBN), and we show that all state-of-the-art relaying strategies must be appropriately modified to avoid the deterioration of WBN performance in the limited HSI regime.

The random linear network coding system can be modelled as a linear operator channel (LOC). Among all the LOC models, one of the most interesting models is the sparse LOC model, where the entries of the channel matrix take zero with high probability and any of the nonzero elements in the finite field with equal probabilities. It is well-known that the normalized capacity of LOC is characterized by the rank distribution of the channel matrix. Furthermore, Yang et al. derived upper and lower capacity bounds for LOC in terms of the expected rank of the channel matrix, and the two bounds coincide with the expected rank of the channel matrix as the packet size increases. Therefore, in this paper, we investigate the expected rank of the sparse LOC matrix. By calculating the number of vectors in the null space of the sparse LOC matrix, a lower bound on the expected rank of the sparse matrix is obtained. The linear rank distribution of the sparse LOC matrix is also calculated, which is then used to derive an upper bound on the expected rank of such matrices. Besides, the upper bound can be shown to be exact as the matrix size tends to infinity. Numerical results show that the bounds are rather tight for various matrix sizes and sparsity.

As 2D barcodes become more and more popular, their new applications, like mobile marketing, give a strong motivation for embedding visual information in them. Information stored on a 2D barcode, being printed on paper or shown on a display device, can be delivered to people via a camera phone with suitable decoding software. The barcoding system can be viewed as a communication system with key functional modules, including channel coding, modulation, channel estimation, demodulation and channel decoding. By applying advanced communications principles, a way to integrate a picture into a 2D barcode (called PiCode) is developed. By extending the idea, a way to integrate a video into a series of 2D barcodes, called ViCode, is also developed. To realize PiCode and ViCode, new modulation and demodulation schemes are designed. Based on our channel estimation technique, a new decoding scheme for low-density parity-check (LDPC) codes is devised to provide more robust error rate performance than traditional 2D barcodes. A US patent and a Chinese patent have already been filed based on the innovative methods developed for PiCode.

The Lenstra-Lenstra-Lovász (LLL) algorithm is a popular lattice reduction algorithm in communications. In this paper, variants of the LLL algorithm with either reduced or fixed complexity are proposed and analyzed. Specifically, 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 (measured by the number of floating-point operations and averaged over i.i.d. standard normal lattice bases) is shown to be O(n3log n), where n is the lattice dimension. This average complexity is an order lower than previously thought. To address the issue of variable complexity of the LLL algorithm, two fixed-complexity approximations are proposed. One is fixed-complexity effective LLL, for which the first vector of the basis is proven to be bounded in length; the other is fixed-complexity LLL with deep insertion, which is shown to be 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.

It is well known that communication systems are susceptible to strong impulsive noises. To combat this, convolutional coding has long served as a cost-efficient tool against moderately frequent memoryless impulses with given statistics. Nevertheless, impulsive noise statistics are difficult to model accurately and are typically not time-invariant, making the system design challenging. In this paper, because of the lack of knowledge regarding the probability density function of impulsive noises, an efficient decoding scheme was devised for single-carrier narrowband communication systems; a design parameter was incorporated into recently introduced joint erasure marking and Viterbi decoding algorithm, dubbed the metric erasure Viterbi algorithm (MEVA). The proposed scheme involves incorporating a well-designed clipping operation into a Viterbi algorithm, in which the clipping threshold must be appropriately set. In contrast to previous publications that have resorted to extensive simulations, in the proposed scheme, the bit error probability performance associated with the clipping threshold was characterized by deriving its Chernoff bound. The results indicated that when the clipping threshold was judiciously selected, the MEVA can be on par with its optimal maximum-likelihood decoding counterpart under fairly general circumstances.

Consider the communication system model y = HFx + n, where H and F are the channel and precoder matrices, x is a vector of data symbols drawn from some lattice-type constellation, such as M-QAM, n is an additive white Gaussian noise vector and y is the received vector. It is assumed that both the transmitter and the receiver have perfect knowledge of the channel matrix H and that the transmitted signal Fx is subject to an average energy constraint. The columns of the matrix HF can be viewed as the basis vectors that span a lattice, and we are interested in the precoder F that maximizes the minimum distance of this lattice. This particular problem remains open within the theory of lattices and the communication theory. This paper provides the complete solution for any nonsingular M × 2 channel matrix H. For real-valued matrices and vectors, the solution is that HF spans the hexagonal lattice. For complex-valued matrices and vectors, the solution is that HF, when viewed in four-dimensional real-valued space, spans the Schlafli lattice D4.

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 the 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.

We perform a minimum distance analysis of a class of two-dimensional intersymbol interference (ISI) channels applicable to multitrack magnetic recording and orthogonal frequency division multiplex transmission systems. Exact minimum distance for a wide class of ISI responses is derived. The fundamental analytical technique is to transform the channel into an equivalent minimum phase channel. The results improve upon the prior work of Soljanin and Georghiades.

Motivated by the noncoherent subspace coding approach and the low-complexity sparse coding approach to realize random linear network coding, we consider the problem of characterizing the probability of having a full rank (or nonsingular) square transfer matrix over a finite field, for which the probability of choosing the zero element is different from that of choosing a nonzero element. We found that for a sufficiently large field size, whether the transfer matrix is singular or not is determined with probability one by the zero pattern of the matrix, i.e., where the zeroes are located in the matrix. This result provides insight for optimizing sparse random linear network coding schemes and allows the problem of determining the probability of having a nonsingular transfer matrix over a large field size to be transformed into a combinatorial problem. By using some combinatorial arguments, useful upper and lower bounds on the singularity probability of the random transfer matrix are derived.

Consider the communication model ȳ = HF x̄ + n̄, where H; F are real-valued matrices, x̄ is a data vector drawn from some real-valued lattice (e.g. M-PAM), n̄ is additive white Gaussian noise and ȳ is the received vector. It is assumed that the transmitter and the receiver have perfect knowledge of the channel matrix H (perfect CSI) and that the transmitted signal F x̄ is subject to an average energy constraint. The columns of the matrix HF can be viewed as basis vectors that span a lattice, and we are interested in the minimum distance of this lattice. More precisely, for a given H, which F under an average energy constraint will maximize the minimum distance of the lattice HF? This particular question remains open within the theory of lattices. This work provides the solution for 2×2 matrices H; F. The answer is an F such that HF is a hexagonal lattice.

The Welch bound for aperiodic correlation for binary sequence set was improved by Levenshtein by weighting the cyclic shifts of the sequence vectors. Taking Levenshtein's idea, a new lower bound for quasi-complementary sequence set (QCSS) over the complex roots-of-unity is derived in this paper. It is shown to be tighter than the Welch bound for QCSS in one of the following cases: 1) K = 4M − 1, M ≥ 2 and equation; 2) K ≥ 4M, M ≥ 2 and N ≥ 2. where K,M,N respectively denotes the set size, number of channels, elementary sequence length of QCSS.

In this paper, the problem of index assignments for quantizers with uniform encoders and channel-optimized decoders for M-PSK schemes is studied. The analytical expressions of MSD (Mean-Squared Distortion) for such quantizers with the natural, zigzag and NBC-Gray mappings, respectively, have been derived. An interesting result is that at a wide range of MSD levels, the zigzag mapping can offer a significant gain in SNR over the other two mappings when used in such quantizers, especially when the alphabet size M gets larger, which is agreed by simulation results.

In this paper, we consider the construction of efficient rate-compatible (RC) low-density parity-check (LDPC) codes. Specifically, we introduce a novel criterion to rank puncturing patterns and splitting patterns for RC LDPC codes. Based on the Gaussian approximation density evolution (GADE), cost functions are devised to characterize the degree distribution of the punctured or split code matrices, which are derived from a given code's parity check matrix by some matrix row transformations. These cost functions allow us to effectively compare the estimated performance of the candidate patterns and to sort out good ones. Based on the proposed ranking criterion, we provide a good RC LDPC code structure, which can support a wide range of code rates and outperform most of the existing RC LDPC codes in literatures. Moreover, the proposed scheme has the important advantage of reduced decoding latency and complexity without sacrificing performance. Numerical results demonstrate that the proposed RC LDPC codes can lead to nearly 25% decoding complexity saving and latency reduction at comparable or even better performance.

In this paper, we introduce a novel criterion to rank puncturing patterns for rate-compatible LDPC codes. Specifically, based on Gaussian approximation density evolution, a cost function is devised to characterize the degree distribution of the punctured code matrices, which are derived from a mother code matrix by matrix transformation. This cost function allows us to effectively compare the expected performance of candidate puncturing patterns and to sort out good ones. Combined with well-designed search algorithms, the proposed criterion can be applied on both standardized block-LDPC codes and generic binary LDPC codes to get good puncturing patterns with manageable complexity. Numerical simulation results verify the effectiveness of the proposed ranking criterion, and demonstrate that a series of good rate-compatible LDPC codes can be obtained by the proposed ranking criterion.

Assuming perfect channel state information (CSI), linear precoding/decoding for multiple-input multiple-output (MIMO) systems has been considered in the literature under various performance criteria, such as minimum total mean-square error (MSE), maximum mutual information, and minimum average bit error rate (BER). It has been shown that these criteria belong to a set of reasonable Schur-concave or Schur-convex objective functions of the diagonal entries of the system mean-square error (MSE) matrix. In this paper, assuming only the knowledge of channel mean and transmit correlation at both ends, a general theoretical framework is presented to derive the optimum precoder and decoder for MIMO systems using these objective functions. It is shown that for all these objective functions the optimum transceivers share a similar structure. Compared to the case with perfect CSI, a linear filter is added to both ends to balance the suppression of channel noise and the additional noise induced from channel estimation error. Simulation results are provided.

To improve the efficiency and simplify the complexity of the relay in cooperative communication systems, an one-bit soft forwarding (SF) scheme is proposed to exploit the erroneously decoded packets that are normally abandoned by the selection decode-and-forward (DF) scheme at the relay, as side information to assist decoding of the direct-link packet at the base station. As this side information from relay is encoded and transmitted in the same format as the usual data packet, the proposed SF scheme can be implemented with the same coding scheme and same encoder/decoder as the DF scheme. It only requires the additional transmission of a packet reliability value from the relay to the basestation, unlike the previous soft relaying schemes which require more complicated soft output decoding and signaling format. The new scheme not only allows low complexity implementation, but also offers considerable error performance gain. Simulation results demonstrate that our SF scheme outperforms the selection DF by up to 2 dB, especially when the inter-link channel is poor.

Detecting matrices are a class of combinatorial objects originated from the coin weighing problem of Soderberg and Shapiro in the early 1960s. In this paper, various known recursive construction techniques for binary, bipolar, and ternary detecting matrices are reexamined in a unifying framework. New, general recursive constructions of detecting matrices, which include previous recursive constructions as special cases, are derived. Such matrices find applications in multiuser coding since they are equivalent to a certain class of uniquely decodable multiuser codes for the binary adder channel. Interestingly, it is found that among the three kinds of detecting matrices, ternary detecting matrices are of fundamental significance from the combinatorial theoretic, as well as from the multiuser coding application, point of view.

In this paper we perform a minimum distance analysis of a class of two dimensional intersymbol interference channels. In particular, some important cases of multitrack multihead magnetic recording systems fall into the studied class. Previously, Soljanin and Georghiades have studied the same problem as we do. The results derived in this paper are more conclusive and they improve upon theirs. The fundamental proof technique that we will use is to transform the channel into an equivalent minimum phase channel.

In this letter, we introduce a novel technique to speed up the famous LLL lattice reduction algorithm by use of sorting. Simulation results reveal that when applied to LLL-reduction-aided MIMO detectors, our proposed joint sorting and reduction technique can find an LLL-reduced basis with the average number of basis vector swappings reduced by about 47.5% for a 2 times 2 system and more for higher dimensional systems, without degrading the detection performance. Moreover, when the maximum number of vector swapping is limited, our proposed algorithm significantly outperform the conventional one at low-to-moderate bit error rates. This suggests that it can be applied advantageously to those MIMO systems with a strict delay constraint.

In the literature, many constructions of zero correlation zone (ZCZ) sequences have been reported. While most of them are suboptimal with respect to the known upper bound, some constructed by Matsufuji et al. and Torii et al. respectively, are almost optimal (or even optimal). In this paper, we propose a systematic construction of almost optimal ZCZ sequence sets which generalizes the aforementioned constructions so that more flexible relationships between the set size and the sequence length are allowed. In particular, the obtained almost optimal ZCZ sequence sets of size m and length mn are new for 1 < gcd(m, n) < min(m, n). In addition, their alphabets can be binary or nonbinary since our construction is only based on interleaving perfect sequences according to a certain orthogonal matrix.

This paper analyzes bit error rate (BER) and outage probability of singular value decomposition-based multiple-input multiple-output systems with channel estimation error and feedback delay over uncorrelated Ricean fading channels. By utilizing marginal unordered and ordered eigenvalue distributions of complex noncentral Wishart matrices, we derive exact closed-form expressions on the average system performance and high signal- to-interference-plus-noise ratio (SINR) approximations on the individual eigen-subchannels, respectively, under the assumption of equal power allocation. Our expressions apply for various modulation formats and arbitrary numbers of transmit and receive antennas. Our results show that in low-to-moderate SINR regimes, both the BER and the outage probability increase with channel estimation error, feedback delay and the Ricean K-factor at a polynomial rate that is inversely proportional to the difference between the numbers of transmit and receive antennas. We also show that, with channel estimation error and feedback delay, the diversity orders of the BER and outage probability are zero and an irreducible error floor exists at high SINR.

The input-output weight enumerator of a convolutional code characterizes the distance spectrum and allows error probability bounds to be conveniently evaluated. To efficiently compute the weight enumerator, Pimentel recently introduced the so-called state reduction algorithm which has a convenient implementation using existing symbolic mathematical software. In this paper, we propose a dynamic state elimination ordering heuristic to further accelerate the algorithm. As demonstrated by our empirical results, the accelerated state reduction algorithm can achieve impressive complexity savings relative to the original algorithm when applied to compute the weight enumerators and its various truncated versions of convolutional codes with moderate-to-large constraint lengths.

In many real-world communication systems, the channel noise is non-Gaussian due to the presence of impulsive noise as well as the background Gaussian noise. In such situations, the conventional Euclidean distance based decoder may suffer from the problem of severe metric mismatch. To overcome the problem, we recently proposed the joint erasure marking and Viterbi algorithm (JEVA) as a robust trellis decoder that does not require an estimate of the impulsive noise distribution. In this work, two ways to further improve JEVA are presented for systems with an error detecting code. Specifically, the JEVA is integrated with the list Viterbi algorithm (LVA) to form the two-dimensional joint erasure marking and list Viterbi algorithm (JELVA) and the switched JELVA, respectively. By combining the respective strengths of the JEVA and the LVA, the integrated decoding schemes are able to achieve significant performance gains over the original JEVA and achieve a wide range of performance-complexity-delay tradeoffs.

In many real-world communication systems, the extent of non-Gaussian impulsive noise (IN) rather than Gaussian noise poses practical limits on the achievable system performance. The decoding of IN-corrupted signals is complicated by the fact that accurate IN statistics are typically unavailable at the receiver. Without exploiting the IN statistics, the conventional method is to try to mark the IN-corrupted symbols as erasures preceding a Euclidean metric based decoder. In this work, a novel joint erasure marking and Viterbi algorithm (JEVA) is proposed to decode the convolutionally coded data transmitted over an unknown impulsive noise channel. Based on the Bernoulli-Gaussian IN model, it is empirically demonstrated that JEVA not only can offer significant performance improvement over the conventional separate erasure marking and Viterbi decoding method, but also can almost achieve the optimal performance of the maximum likelihood decoder that fully exploits the perfect knowledge of the IN probability density function. Various implementations of JEVA are proposed to provide different performance-complexity trade-offs.

This paper analyzes the average bit error rate (BER) performance of singular value decomposition-based multiple-input multiple-output systems with channel estimation error and feedback delay over uncorrelated Ricean fading channels. By utilizing marginal unordered eigenvalue distributions of complex noncentral Wishart matrices, we derive exact closed- form BER expression under the assumption of equal power allocation. Our results apply for various modulation formats and arbitrary numbers of transmit and receive antennas. Our results show the average BER increases with channel estimation error, feedback delay and Ricean A'-factor at a polynomial rate that is inversely proportional to the difference between the numbers of transmit and receive antennas. We also show that the achievable BER performance is limited by the presence of an irreducible error floor as the signal-to-interference-plus-noise ratio increases.

Non-linear amplitude distortion may be the key impairment in some practical multiple-input multiple-output (MIMO) communications systems. However, there are only a few past investigations addressing its impact on the system performance. In this paper, we derive an approximate upper bound on the bit error rate for MIMO zero-forcing receivers with M-ary quadrature amplitude modulation (MQAM) in the presence of channel estimation error, which is valid for any order of non-linearity and arbitrary numbers of transmit and receive antennas. In the absence of channel estimation error, the results derived herein give a true BER upper bound. Comparison with Monte Carlo simulations suggest that the theoretical bound is accurate and useful for practical system design.

Cognitive radio technology facilitates spectrum reuse and alleviates spectrum crunch. One fundamental problem in cognitive radio is to avoid the interference caused by other communication systems sharing the same frequency band. However, spectrum sensing cannot guarantee accurate detection of the interference in many practical situations. Hence, it is crucial to design robust receivers to combat the in-band interference. In this paper, we first present a simple pilot aided interference detection method. To combat the residual interference that cannot be detected by the interference detector, we further propose a robust joint interference detection and decoding scheme. By exploiting the code structure in interference detection, the proposed scheme can successfully detect most of the interfered symbols without requiring the knowledge of the interference distribution. Our simulation results show that, even without any prior knowledge of the interference distribution, the proposed joint interference detection and decoding scheme is able to achieve a performance close to that of the maximum likelihood decoder with the full knowledge of the interference distribution

Link adaptation allows the transmitter to adapt to changing channel conditions. Critical to the design of link adaptation is the accuracy of channel state information at the transmitter. In this paper, we investigate the effect of imperfect channel state information and feedback delay on the performance of a multiple-input multiple-output zero-forcing receiver with adaptive power allocation. A closed-form approximate upper bound on bit error rate is derived for M-ary phase shift keying and M-ary quadrature amplitude modulation and it is valid for arbitrary numbers of transmit and. receive antennas. Comparison with Monte Carlo simulations is also provided, showing that the results derived from this analytical bound are useful for system design.

Orthogonal frequency division multiple access (OFDMA) and multicarrier code division multiple access (MC-CDMA) have recently drawn much attention for being potential candidates of future generation cellular systems. In single-cell scenario, while MC-CDMA is good at achieving frequency diversity when there is no channel state information available at the transmit side (CSIT), OFDMA achieves higher capacity than MC-CDMA due to its finer resolution in exploiting multiuser diversity with CSIT. Whether multiple-input-multiple-output (MIMO) MC-CDMA or OFDMA is a better option in multi-cell system remains unjustified in the literature. In this paper, we study the ergodic capacity and the goodput of MIMO-MC-CDMA and MIMO-OFDMA downlink systems with CSIT in multi-cell scenario assuming that the base station has the knowledge of the average inter-cell interference level only. Several types of users modeling different interference patterns are considered: (I) high data rate delay-insensitive users, (II) high data rate delay-sensitive .users, and (III) voice users (low data rate and bursty). Optimal resource allocation algorithms are used to compute the capacities of the systems, while a simple heuristic is used to obtain the achievable goodputs for both systems. The effects of path loss, number of antennas and different user types are studied and insightful results are obtained. We find that OFDMA has a higher system goodput for both Type I and Type II high data rate users, while MC-CDMA has a higher goodput for Type III users. Compared to MC-CDMA, the goodput of an OFDMA system is more sensitive to the activity factor of the voice users and suffers from noticeable loss. This demonstrates the superiority of the two systems in different practical situations.

In this paper, we examine and compare the potential maximum sum capacity of downlink multiple-input-multiple-output orthogonal frequency division multiple access (MIMO-OFDMA) and multiple-input-multiple-output multicarrier code division multiple access (MIMO-MC-CDMA) in a single-cell multiuser environment with channel side information at the transmitter, with and without a fairness constraint. The resource allocation is formulated as a cross-layer optimization framework and optimal power allocation and user selection algorithms are proposed for both scenarios. We find that for delay-sensitive applications, where fairness is imposed, the performance gain of OFDMA over MC-CDMA is quite large at moderate path loss exponents and number of antennas. However, for delay-insensitive applications, the benefits of OFDMA over MC-CDMA are significantly reduced when the path loss exponent or the number of antennas is large

By employing spatial multiplexing, multiple-input multiple-output (MIMO) wireless antenna systems provide increases in capacity without the need for additional spectrum or power. Zero-forcing (ZF) detection is a simple and effective technique for retrieving multiple transmitted data streams at the receiver. However the detection requires knowledge of the channel state information (CSI) and in practice accurate CSI may not be available. In this letter, we investigate the effect of channel estimation error on the performance of MIMO ZF receivers in uncorrelated Rayleigh flat fading channels. By modeling the estimation error as independent complex Gaussian random variables, tight approximations for both the post-processing SNR distribution and bit error rate (BER) for MIMO ZF receivers with M-QAM and M-PSK modulated signals are derived in closed-form. Numerical results demonstrate the tightness of our analysis

Few works have addressed the effect of CFO (carrier frequency offset) on channel estimation performance. In this paper, compact analytical expressions on the mean square error of channel estimation in the presence of CFO are derived for OFDM (orthogonal frequency division multiplexing) systems employing single and multiple antennas. Concise upper bounds are also derived for SISO-OFDM systems. It is revealed that channel estimation MSE (mean square error) increases at the rate of approximately the square of the CFO and increasing the number of pilots does not contribute to better suppression of the MSE caused by CFO. In addition, it is observed that LMMSE (linear minimum mean square error) channel estimation is more resistant to CFO compared to LS (least square) in terms of channel estimation MSE. Furthermore, from the results derived herein, a clue for the pilot design of OFDM systems with CFO can be obtained

Bit-interleaved coded modulation (BICM) is a bandwidth efficient coding scheme and has been extensively studied for Gaussian distributed additive channel noise. In many real-world communication systems, the additive noise is non-Gaussian impulsive. In such situations, the conventional squared Euclidean distance based decoding metric suffers from severe metric mismatch. The optimal metric in maximum likelihood sense may not be applicable because the exact noise probability density function is unavailable at the receiver due to the dynamically changing nature of the impulsive noise (IN). It is therefore important to design decoding algorithms that are robust to the IN distributions. In this work, we propose two novel decoding schemes for BICM in the presence of unknown IN. The proposed decoding schemes alleviate metric mismatch by automatically ignoring the impulse-corrupted symbols in decoding. It is demonstrated that the proposed decoding schemes offer great performance improvement over the conventional decoder counterparts.

We derive exact closed-form expressions on the bit error rate (BER) for the singular value decomposition (SVD)-based multiple-input multiple-output (MIMO) systems using Mary phase-shift keying (MPSK) and M-ary quadrature amplitude modulation (MQAM), respectively, with optimal detection under the assumptions of equal power allocation and Gaussian distributed cochannel interference. From the expressions derived herein, we investigated the effect of imperfect channel state information (CSI) on the average BER. It can be concluded from our theoretical analysis that the channel estimation error always induces an irreducible error floor and may severely deteriorate the BER performance.

The recently proposed loosely synchronized (LS) spreading code can in principle realize an intracell-interference-free quasi-synchronous code-division multiple-access (QS-CDMA) system by creating a wide enough interference-free window (IFW). However, the problem of minimizing intercell interference (ICI) in a cellular QS-CDMA system remains an open issue. Addressing the problem from a sequence design viewpoint, the key challenge is how to generalize the known construction of a single LS code to the design of many families of generalized LS (GLS) codes so that a desirable code family can be selected for the realization of a low-ICI cellular QS-CDMA system. Our main contribution is a systematic construction of new families of GLS codes with favorable intercode cross-correlation properties within a certain window, while maintaining the desirable IFW property. Many such code families can be obtained from our construction by choosing different Hadamard matrices and different uncorrelated complementary pairs. Their effectiveness with respect to some meaningful evaluation criteria are compared. In particular, by a simplified system bit-error rate analysis, it is demonstrated that a new GLS code family significantly outperforms the conventional scrambled LS codes.

Bit-interleaved coded modulation with iterative decoding (ID) is an effective scheme for both AWGN and fading channels because it simultaneously realizes large Euclidean distance and high diversity. In the literature, ID schemes with hard-decision feedback (HDF), as well as soft-decision feedback (SDF), have been investigated. While HDF/ID exhibits a performance inferior to SDF/ID, it is much simpler to implement. To enhance the performance of HDF/ID with moderate additional complexity, we propose a uniform soft-decision feedback ID (USF/ID) scheme. The proposed scheme is applicable in both single antenna and multiple antenna communication systems. The simulation results verify that it achieves impressive performance gain over HDF/ID and has a practically more attractive implementation than SDF/ID, especially for complexity-constrained wireless applications

In this paper, we first investigate the performance of optimum multi-head multi-track detection systems for the two-dimensional recording channels and compare their performance for various intertrack interference levels in terms of minimum-distance parameters. Then we propose a low-complexity multi-head data detection algorithm for multi-track partial response and two-dimensional recording channels based on the ordered successive interference algorithm but it is different in the way that the detection order is pre-defined according to channel conditions and the data at successive time instants are simultaneously estimated by using group receivers. Compared with the optimal MLSD approach based on the multi-dimensional Viterbi algorithm, the complexity of the proposed algorithm is only linearly proportional to the number of tracks at an expense of small performance degradation

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 yet with complexity similar to linear receiver. However, these lattice-reduction-aided detectors are based on the traditional LLL reduction algorithm that was originally introduced for reducing real lattice basis, even though the channel matrices are inherently complex-valued. In this paper, we introduce the complex LLL algorithm for direct application to the channel matrix which naturally defines the basis of a complex lattice. Simulation results reveal that the new complex LLL algorithm can achieve a saving in complexity of nearly 50% over the traditional LLL algorithm, when applied to MIMO detection. We also show that the algorithm can further be accelerated by pre-ordering the basis vectors prior to the lattice reduction. It is noteworthy that the complex LLL algorithms aforementioned incur negligible bit-error-rate performance loss relative to the traditional LLL algorithm.

We present improved differential lattice decoding (DLD) for multi-antenna differential modulation by exploiting both basis reduction and sphere decoding. The extra complexity of DLD is shown to be worthwhile in terms of the obtained performance gain over Clarkson et al.'s decoding scheme. With roughly another fold of complexity of basis reduction, DLD augmented by a local search practically attains the maximum-likelihood decoding performance.

The weight enumerator of a convolutional code is an important function that characterizes the codeword distance distribution and allows the error probability bounds of the code to be conveniently computed. An efficient state reduction algorithm to compute weight enumerators by iteratively modifying the symbolic adjacency matrix associated with the code was recently introduced. In this paper, we propose a dynamic elimination ordering technique that exploits the state diagram structure of the convolutional encoder for improving the efficiency of the state reduction algorithm.

This paper studies the problem of non-binary index assignment for scalar quantizer with M-ary phase shift keying (M-PSK). An interesting observation enables us to well approximate this problem to the well-known traveling salesman problem (TSP). A unique optimum solution to the approximation is resulted. Optimality of the solution is agreed by simulation results

From a lattice viewpoint, Clarkson, Sweldens and Zheng significantly reduced the complexity of multiantenna differential decoding. Their approximate decoding algorithm, however, has not unleashed the full potential of lattice decoding. In this paper, we present several improved algorithms, generally referred to as differential lattice decoding (DLD), for multiantenna communication. We first analyze two distinct approximate DLD algorithms, and then develop an algorithm that exactly finds the closest lattice point in the Euclidean space. This exact DLD is subsequently augmented by local search to compensate for the remaining approximation. The small amount of extra complexity of the exact or augmented DLD is rewarded by a clear performance gain. We find that employing basis reduction is very effective to reduce the overall decoding complexity for high lattice dimensions. Moreover, the dimension of the lattice defined in this paper is independent of the number of receive antennas, which results in not only lower complexity, but also better performance for a multiantenna receiver.

Two simple but effective methods for reducing the average complexity (and power consumption) of the conventional turbo-cyclic-redundancy-check decoding scheme with negligible performance degradation in a wideband direct-sequence code-division multiple-access (W-CDMA) environment are introduced. When applied to a W-CDMA turbo code with frame length 640 b at a bit-error rate (BER) of 10/sup -6/, the resultant modified schemes can save up to 73% of the average decoding complexity, relative to the conventional scheme. In general, the proposed schemes are more attractive for short-frame and low-BER applications.

A current-mode binary-search sensing scheme for a 4-state one-transistor one-magnetic tunnel junction (1T1MTJ) magneto-resistive random access memory (MRAM) is proposed. By using the switched-current technique, it is able to read data non-destructively with a magneto-resistive (MR) ratio of as low as 5%. The circuit is designed using a 0.18mm CMOS process and the performance is verified by HSPICE. Compared to the parallel sensing approach, the proposed sensing scheme consumes less power and chip area and requires fewer comparison steps. Compared to the serial sensing approach, it allows a shorter read access time while requiring the same number of comparisons.

The idea of formulating the detection of a lattice-type modulation transmitted over a linear channel as the so-called universal lattice decoding problem dates back to at least the early 1990s. The principle of universal lattice decoding can trace its roots back to the theory developed for solving the shortest/closest lattice vector problem. In this paper, such a principle and its applications in communications are reviewed. In addition, it will be shown that with some lattice preprocessing steps, impressive performance improvement and/or complexity reduction of some well-known detectors (e.g. ZF, DFE, and VBLAST) can be achieved.

In this letter, we propose two near maximum-likelihood detection (MLD) schemes for multiple input-multiple output antenna systems over flat fading channels. The schemes are based on utilizing an initial estimate of the received symbol and improving it by selectively updating various bits within the symbol. Simulation results show that the performance of the proposed schemes can approach that of MLD but with a significant reduction in complexity.

A simple but effective method for reducing the average complexity (and power consumption) of turbo decoding with negligible performance degradation in a W-CDMA environment is introduced. It modifies the conventional turbo-CRC decoding scheme by performing two CRC tests per iteration to detect at the earliest a correctly converged decoding process. When applied to a W-CDMA turbo code with frame length 640 bits at a BER of 10/sup -6/, it can save about 50% of the average decoding complexity, relative to the conventional scheme. Further complexity reduction can be achieved by integrating the CRC test as an intermediate step in the component SlSO decoder. In general, the proposed scheme is more attractive for short-frame and low-BER applications.

Abstract The idea of formulating the detection of a lattice‐type modulation, such as M‐PAM and M‐QAM, transmitted over a linear channel as the so‐called universal lattice decoding problem dates back to at least the early 1990s. The applications of such lattice decoders have proliferated in the last few years because of the growing importance of some linear channel models such as multiple‐antenna fading channels and multi‐user CDMA channels. The principle of universal lattice decoding can trace its roots back to the theory and algorithms developed for solving the shortest/closest lattice vector problem for integer programming and cryptoanalysis applications. In this semi‐tutorial paper, such a principle as well as some related recent advances will be reviewed and extended. It will be shown that the lattice basis reduction algorithm of Lenstra, Lenstra and Lovász (LLL) can significantly improve the performance of suboptimal lattice decoders such as the zero‐forcing and VBLAST detectors. In addition, new implementation of the optimal lattice decoder that is particularly efficient at moderate signal‐to‐noise ratios will also be presented. Copyright © 2003 John Wiley & Sons, Ltd.

We argue that due to the existence of the even-odd transforms, the smallest possible maximum periodic and odd correlation magnitudes are identical for complex-valued sequence sets under the equi-energy (or constant-envelope) constraint. This trivializes most of the conventional formulations of odd correlation lower bounds for BPSK/CDMA sequences. By generalizing the even-odd transforms, we also extend this insightful result for complex-valued sequence sets applied to asynchronous M-PSK/CDMA schemes with M /spl ges/ 2, whose multiple access interferences are characterized by the M-phase correlation magnitudes. Next, a general transform that translates known inner-product lower bounds into M-phase correlation bounds is introduced. Finally, we conclude that in order to formulate nontrivial M-phase correlation lower bounds for equi-energy (or constant-envelope) sequences, additional phase alphabet constraints must be incorporated into the formulation.

Space-time coding has been proposed as a coding scheme for multiple-input multiple output (MIMO) antenna systems. However, when the delay spread of the MIMO channel is too large there is significant performance degradation and there is a need for equalization. In this paper we use MLSE structures that decode the space-time codes and equalize the channel in one structure. The resulting complexity of MLSE is therefore increased and it is necessary to took at ways to minimize this. Here we compare the Forney and Ungerboeck forms and we find that the Ungerboeck form is more attractive. In particular its complexity does not depend on the number of receive antennas.

In this paper, we study the performance of the OFDM receiver using FFT based on the log number system (Log-FFT) in a wireless environment. By using the log number system (LNS), complex multiplications of the FFT are reduced to simple additions. The effect of finite bit precision on the receiver performance is analyzed theoretically under the AWGN channel. Simulation results for both AWGN and fading channels are presented. It is shown that the bit width requirement of the receiver is quite small. In a coded OFDM system, there is no degradation in bit error rate performance when only two fractional bits are used for the LNS under a slow fading channel. The size of the look-up tables are small and the complexity of the log-FFT implementation is simple. Thus log-FFT is an attractive implementation method for the OFDM receiver design in wireless environment.

An iterative decoding approach to joint equalization and decoding for convolutional codes over intersymbol-interference (ISI) channels was previously proposed as the so-called turbo equalization scheme. To increase the coding gain, the use of turbo codes in place of convolutional codes in such a scheme was also investigated. Motivated by the recent result that serially concatenated convolutional codes (SCCC) exhibit a lower error floor than turbo codes in AWGN channels, we investigate here the performance of iterative decoding of SCCC over multipath ISI channels. Using the presented iterative decoding method, our simulation results demonstrate that even in the presence of ISI, the SCCC is superior to the turbo code for low bit error rate (BER) applications.

The standard upper bound on discrete entropy was derived based on the differential entropy bound for continuous random variables. A tighter discrete entropy bound is derived using the transformation formula of Jacobi theta function. The new bound is applicable only when the probability mass function of the discrete random variable satisfies certain conditions. Its application to the class of binomial random variables is presented as an example.

A detailed analysis of the maximum aperiodic autocorrelation of the original Chu sequences (equivalently, P3/P4 pulse compression codes) is presented. The result implies the best known upper bound on the minimax aperiodic autocorrelation for polyphase sequences except when the length is very small or a perfect square. It is well known that determining the minimax aperiodic correlation for polyphase sequence sets is an intractable task. The simplest nontrivial cases for Barker and general polyphase sequences are solved for the first time.

Sets of decimated Frank (1962) sequences with optimal correlation properties were first considered by Alltop (1984). By regarding decimated Frank sequences as special cases of the generalized Frank sequences proposed by Suehiro and Hatori (1988), the set size of decimated Frank sequences can be doubled without sacrificing the optimality of the correlation properties. Besides, the proposed sequences form representatives of generalized Frank sequences of different classes. They thus provide an efficient way to generate signature sequences for spread spectrum multiple access systems with dynamic signature assignments.>

A construction, similar to that of Sidelnikov (1971) and Welch (1974), is proposed to transform bounds on inner products into bounds on odd correlations of a set of sequences with equal energy. Contrary to Sarwate's (1979) result, the present authors show that bounds on odd cross-correlation and autocorrelation can easily be derived from Welch's more general bounds. Generally speaking, since all known lower bounds on periodic correlation have been derived from bounds on inner products, the construction implies that the periodic and odd correlation can share all of these lower bounds.>

Considers the problem of data detection in multilevel lattice-type modulation systems in the presence of intersymbol interference and additive white Gaussian noise. The conventional maximum likelihood sequence estimator using the Viterbi algorithm has a time complexity of O(m/sup /spl nu/+1/) operations per symbol and a space complexity of O(/spl delta/m/sup /spl nu//) storage elements, where m is the size of input alphabet, /spl nu/ is the length of channel memory, and /spl delta/ is the truncation depth. By revising the truncation scheme and viewing the channel as a linear transform, the authors identify the problem of maximum likelihood sequence estimation with that of finding the nearest lattice point. From this lattice viewpoint, the lattice sequence estimator for PAM systems is developed, which has the following desired properties: 1) its expected time-complexity grows as /spl delta//sup 2/ as SNR/spl rarr//spl infin/; 2) its space complexity grow as /spl delta/; and 3) its error performance is effectively optimal for sufficiently large m. A tight upper bound on the symbol error probability of the new estimator is derived, and is confirmed by the simulation results of an example channel. It turns out that the estimator is effectively optimal for m/spl ges/4 and the loss in signal-to-noise ratio is less than 0.5 dB even for m=2. Finally, limitations of the proposed estimator are also discussed.>