This paper investigates a large unitarily invariant system (LUIS) involving a unitarily invariant sensing matrix, an arbitrarily fixed signal distribution, and forward error control (FEC) coding. A universal Gram-Schmidt orthogonalization is considered for constructing orthogonal approximate message passing (OAMP), enabling its applicability to a wide range of prototypes without the constraint of differentiability. We develop two single-input-single-output variational transfer functions for OAMP with Lipschitz continuous local estimators, facilitating an analysis of achievable rates. Furthermore, when the state evolution of OAMP has a unique fixed point, we reveal that OAMP can achieve the constrained capacity predicted by the replica method of LUIS based on matched FEC coding, regardless of the signal distribution. The replica method is rigorously validated for LUIS with Gaussian signaling and certain sub-classes of LUIS with arbitrary signal distributions. Several area properties are established based on the variational transfer functions of OAMP. Meanwhile, we present a replica constrained capacity-achieving coding principle for LUIS. This principle serves as the basis for optimizing irregular low-density parity-check (LDPC) codes specifically tailored for binary signaling in our simulation results. The performance of OAMP with these optimized codes exhibits a remarkable improvement over the unoptimized codes and even surpasses the well-known Turbo-LMMSE algorithm. For quadrature phase-shift keying (QPSK) modulation, we observe bit error rates (BER) performance near the replica constrained capacity across diverse channel conditions.

Approximate Message Passing (AMP) is an efficient iterative parameter-estimation technique for certain high-dimensional linear systems with non-Gaussian distributions, such as sparse systems. In AMP, a so-called Onsager term is added to keep estimation errors approximately Gaussian. Orthogonal AMP (OAMP) does not require this Onsager term, relying instead on an orthogonalization procedure to keep the current errors uncorrelated with (i.e., orthogonal to) past errors. In this paper, we show the generality and significance of the orthogonality in ensuring that errors are “asymptotically independently and identically distributed Gaussian” (AIIDG). This AIIDG property, which is essential for the attractive performance of OAMP, holds for separable functions. We present a simple and versatile procedure to establish the orthogonality through Gram-Schmidt (GS) orthogonalization, which is applicable to any prototype. We show that different AMP-type algorithms, such as expectation propagation (EP), turbo, AMP and OAMP, can be unified under the orthogonal principle. The simplicity and generality of OAMP provide efficient solutions for estimation problems beyond the classical linear models. As an example, we study the optimization of OAMP via the GS model and GS orthogonalization. More related applications will be discussed in a companion paper where new algorithms are developed for problems with multiple constraints and multiple measurement variables.

This paper investigates a large unitarily invariant system (LUIS) involving a unitarily invariant sensing matrix, an arbitrary fixed signal distribution, and forward error control (FEC) coding. Several area properties are established based on the state evolution of orthogonal approximate message passing (OAMP) in an un-coded LUIS. Under the assumptions that the state evolution for joint OAMP and FEC decoding is correct and the replica method is reliable, we analyze the achievable rate of OAMP. We prove that OAMP reaches the constrained capacity predicted by the replica method of the LUIS with an arbitrary signal distribution based on matched FEC coding. Meanwhile, we elaborate a constrained capacity-achieving coding principle for LUIS, based on which irregular low-density parity-check (LDPC) codes are optimized for binary signaling in the simulation results. We show that OAMP with the optimized codes has significant performance improvement over the un-optimized ones and the well-known Turbo linear MMSE algorithm. For quadrature phase-shift keying (QPSK) modulation, constrained capacity-approaching bit error rate (BER) performances are observed under various channel conditions.

This paper studies a large random matrix system (LRMS) model involving an arbitrary signal distribution and forward error control (FEC) coding. We establish an area property based on the approximate message passing (AMP) algorithm. Under the assumption that the state evolution for AMP is correct for the coded system, the achievable rate of AMP is analyzed. We prove that AMP achieves the constrained capacity of the LRMS with an arbitrary signal distribution provided that a matching condition is satisfied. We provide related numerical results of binary signaling using irregular low-density parity-check (LDPC) codes. We show that the optimized codes demonstrate significantly better performance over unmatched ones under AMP. For quadrature phase shift keying (QPSK) modulation, bit error rate (BER) performance within 1 dB from the constrained capacity limit is observed.

We address the joint device activity detection and channel estimation (JACE) problem in a massive MIMO connectivity scenario in which a large number of mobile devices are connected to a base station (BS), while only a small portion are active at any given time. The main objective is to provide an efficient transmission and detection scheme with both spatial and temporal correlations. We formulate JACE as a multiple measurement vector (MMV) problem with correlated entries in the vectors to be estimated. We propose an MMV form of the orthogonal approximate message passing algorithm (OAMP-MMV). We derive a group Gram-Schmidt orthogonalization (GGSO) procedure for the realization of OAMP-MMV. We outline a state evolution (SE) procedure for OAMP-MMV and examine its accuracy using numerical results. We also compare OAMP-MMV with existing alternatives, including AMP-MMV and GTurbo-MMV. We show that OAMP-MMV outperforms AMP-MMV when pilot sequences are generated using Hadamard pilot matrices. Such a pilot design is attractive due to the low-cost signal processing technique using the fast Hadamard transform (FHT). We also show that OAMP-MMV outperforms GTurbo-MMV in correlated channels.

Approximate message passing (AMP) is an iterative signal recovery algorithm for compressed sensing (CS) applications. In this letter, we present an integral-based orthogonal AMP (IB-OAMP) technique that avoids the requirements of AMP (and also the original form of OAMP) on differentiable and separable denoisers. The orthogonality in IB-OAMP can be established using a Monte Carlo method similar to the training stage in a machine-learning algorithm. These features make IB-OAMP attractive to be used in conjunction with some well-studied denoising algorithms.

This paper studies a large random matrix system (LRMS) model involving an arbitrary signal distribution and forward error control (FEC) coding. We establish an area property based on the approximate message passing (AMP) algorithm. Under the assumption that the state evolution for AMP is correct for the coded system, the achievable rate of AMP is analyzed. We prove that AMP achieves the constrained capacity of the LRMS with an arbitrary signal distribution provided that a matching condition is satisfied. As a byproduct, we provide an alternative derivation for the constraint capacity of an LRMS using a proved property of AMP. We discuss realization techniques for the matching principle of binary signaling using irregular low-density parity-check (LDPC) codes and provide related numerical results. We show that the optimized codes demonstrate significantly better performance over un-matched ones under AMP. For quadrature phase shift keying (QPSK) modulation, bit error rate (BER) performance within 1 dB from the constrained capacity limit is observed.

This paper considers a compressed-coding scheme that combines compressed sensing with forward error control coding. Approximate message passing (AMP) is used to decode the message. Based on the state evolution analysis of AMP, we derive the performance limit of compressed-coding. We show that compressed-coding can approach Gaussian capacity at a very low compression ratio. Further, the results are extended to systems involving non-linear effects such as clipping. We show that the capacity approaching property can still be maintained when generalized AMP is used to decode the message. To approach the capacity, a low-rate underlying code should be designed according to the curve matching principle, which is complicated in practice. Instead, analog spatial-coupling is used to avoid sophisticated low-rate code design.

This paper considers a compressed-coding scheme that combines compressed sensing with forward error control coding. Approximate message passing (AMP) is used to decode the message. Based on the state evolution analysis of AMP, we derive the performance limit of compressed-coding. We show that compressed-coding can approach Gaussian capacity at a very low compression ratio. Further, the results are extended to systems involving non-linear effects such as clipping. We show that the capacity approaching property can still be maintained when generalized AMP is used to decode the message. To approach the capacity, a low-rate underlying code should be designed according to the curve matching principle, which is complicated in practice. Instead, analog spatial-coupling is used to avoid sophisticated low-rate code design. In the end, we study the coupled scheme in a multiuser environment, where analog spatial-coupling can be realized in a distributive way. The overall block length can be shared by many users, which reduces block length per-user.

We establish a multiuser extrinsic information transfer (EXIT) chart area theorem for the interleave-division multiple access (IDMA) scheme, a special form of superposition coding, in multiple access channels (MACs). A low-cost multi-user detection (MUD) based on the Gaussian approximation (GA) is assumed. The evolution of mean-square errors (MSE) of the GA-based MUD during iterative processing is studied. We show that the K-dimensional tuples formed by the MSEs of K users constitute a conservative vector field. The achievable rate is a potential function of this conservative field, so it is the integral along any path in the field with value of the achievable rate solely determined by the two path terminals. Optimized error correcting codes can be found given the integration paths in the MSE fields by matching EXIT type functions. The above findings imply that i) low-cost GA detection can provide MAC capacity-approaching performance, ii) the sum-rate capacity can be achieved independently of the integration path in the MSE fields; and iii) the integration path determining achievable rate tuples of all users can be an extra degree of freedom for code design.

We establish a multi-user extrinsic information transfer (EXIT) chart area theorem for the interleave-division multiple-access (IDMA) scheme, a special form of superposition coding, in multiple access channels (MACs). A low-cost multi-user detection (MUD) based on the Gaussian approximation (GA) is assumed. The evolution of mean-square errors (MSE) of the GA-based MUD during iterative processing is studied. We show that the K-dimensional tuples formed by the MSEs of K users constitute a conservative vector field. The achievable rate is a potential function of this conservative field, so it is the integral along any path in the field with value of the integral solely determined by the two path terminals. Optimized codes can be found given the integration paths in the MSE fields by matching EXIT type functions. The above findings imply that i) low-cost GA-based MUD can provide near capacity performance; ii) the sum-rate capacity (region) can be achieved independently of the integration path in the MSE fields; and iii) the integration path can be an extra degree of freedom for code design.

In massive multiple-input multiple-output (MIMO) systems with hybrid analog/digital architectures, large training overhead is required for conventional pilot-only methods to estimate channel accurately before detecting data. To reduce the training overhead, a semi-blind detection method is proposed for data detection without knowing channel in an uplink multi-user system. The main idea is to exploit the received signal corresponding to both the pilot and data payload for channel estimation or data detection via a low-rank matrix completion formulation. The leveraged low-rank property stems from the fact that the number of active users K is typically much smaller than the number of antennas Naat a base station and the number of time slots Tcin a coherence interval. Compared with the pilot-only method, the number of pilots required is reduced from an order of Nato K. Two iterative algorithms are introduced to solve the low-rank matrix completion problem: regularized alternating least squares and bilinear generalized approximate message passing. We further extend the semi-blind detection method to systems with low-resolution analog-to-digital converters. Simulation results show that the proposed methods achieve significant performance gain over the pilot-only method with reduced training overhead for hybrid massive MIMO systems in various settings.

Linear minimum mean square error (LMMSE) estimation based turbo detection has been extensively studied for coded linear systems since the seminal work of Wang and Poor (WP). The WP algorithm operates iteratively between a linear detector (LD) and a nonlinear detector (NLD): the LD suppresses the interference based on LMMSE filtering, and the NLD decodes the data by treating the output of the LD as an observation from an additive white Gaussian noise (AWGN) channel. In WP, the messages exchanged between LD and NLD are required to beextrinsic. For the NLD, the extrinsic message comes from the constraint imposed on feedforward error correction (FEC) codes. Therefore, WP does not work in an un-coded linear system. Recently, we proposed an orthogonal approximate message passing (OAMP) algorithm, which only requires the input/output error terms of LD and NLD to beorthogonal. We conjectured that for un-coded linear systems that involve certain large random matrices, the dynamics of OAMP can be accurately characterized by state evolution (SE). In this paper, we consider a coded linear system and develop an extrinsic message aided OAMP (EMA-OAMP) algorithm. Similar to the un-coded case, EMA-OAMP relaxes the requirements on output messages to be orthogonal instead of extrinsic. We derive an SE procedure to characterize the performance of OAMP in coded systems. We conjecture that this SE procedure is accurate, which is verified by simulation results. Under this conjecture, we show that EMA-OAMP can outperform WP under certain standard assumptions for iterative decoding. Extensive simulations results are provided to verify the advantages of OAMP in coded MIMO systems.

We show that non-orthogonal multiple access (NOMA) and orthogonal multiple access (OMA) have similar performance in systems with centralized control and perfect channel state information (CSI). Otherwise, NOMA has distinct advantages over OMA. We outline a randomized power control (RPC) strategy for NOMA. RPC can provide significantly enhanced throughput in random access systems with successive interference cancelation (SIC) or iterative detection. We also show that interleave division multiple access (IDMA) is a simple implementation technique for NOMA to facilitate RPC.

Concatenated zigzag (CZ) codes have been widely studied for practical applications due to their low encoding complexity and excellent performance. However, there still lacks rigorous analysis and optimization techniques for CZ codes. This paper presents an analysis technique for CZ codes under belief propagation (BP) decoding over the binary erasure channel (BEC). We derive a pair of closed-form density evolution (DE) equations to characterize the asymptotic behavior of a CZ code under BP decoding. We show that capacity-approaching CZ codes can be designed by matching the curves corresponding to the DE equations. We also prove that the gap between the BP threshold of a regular CZ code and the corresponding Shannon threshold diminishes when the rate approaches zero. This suggests that regular CZ codes are good candidates for low-rate communication systems, where good low-density parity-check codes are difficult to construct.

This paper develops a generalized channel-aware power control scheme to enhance the multi-packet reception (MPR) capability for random access. In the proposed scheme, each user randomly selects its transmit power with a probability in accordance with a distribution function based on its own channel state. For two-user systems, we show that the optimal power distribution function has a simple discrete structure, based on which the optimal random access strategy can be efficiently computed. Leveraging the relevant insights, we further propose a decentralized binary power control scheme for general K-user systems. It is established that such a simple scheme can asymptotically approach the performance of the optimal centralized scheme, as the system load grows large. Numerical results show that the proposed schemes obtain noticeable performance improvement over the existing alternatives.

This paper is concerned with pilot transmission schemes in a large antenna system with non-orthogonal multiple-access (NOMA). We investigate two pilot structures-orthogonal pilot (OP) and superimposed pilot (SP). In OP, pilots occupy dedicated time (or frequency) slots, while in SP, pilots are superimposed with data. We study an iterative data-aided channel estimation (IDACE) receiver, where partially decoded data are used to refine channel estimation. We analyze the achievable rates for systems with IDACE receivers for both OP and SP. We show that the optimal portion of pilot power tends to zero for SP with Gaussian signaling. This result is consistent with existing findings obtained via the replica method in statistical physics. The latter involves multiple codes, which is convenient for theoretical analysis but difficult to implement. As a comparison, IDACE is potentially implementable in practice. We demonstrate that, with code optimization, SP can outperform OP in a high mobility environment with a large number of users. We provide numerical examples to verify our analysis.

Approximate message passing (AMP) is a low-cost iterative signal recovery algorithm for compressed sensing. For sensing matrices with independent identically distributed (IID) Gaussian entries, the performance of AMP can be asymptotically characterized by a simple scaler recursion called state evolution (SE). SE analysis shows that AMP can potentially approach the optimal minimum mean squared-error (MMSE) limit. However, SE may become unreliable for other matrix ensembles, especially for ill-conditioned ones. In this paper, we propose an orthogonal AMP (OAMP) algorithm based on de-correlated linear estimation (LE) and divergence-free non-linear estimation (NLE). The Onsager term in standard AMP vanishes as a result of the divergence-free constraint on NLE. We develop an SE procedure for OAMP and show numerically that the SE for OAMP is accurate for a wide range of sensing matrices, including IID Gaussian matrices, partial orthogonal matrices, and general unitarily-invariant matrices. We further derive optimized options for OAMP and show that the corresponding SE fixed point coincides with the optimal performance obtained via the replica method.

Recently massive multi-input multi-output (MIMO) techniques have attracted growing research interest. However, most existing works assume centralized control, which may involve a heavy overhead as the number of users also becomes massive. In this paper, we focus on random-access massive MIMO systems. We first analyze the performances of two conventional schemes widely used in massive MIMO, and derive their closed-form expressions in the asymptotic case. Building on the latter, we maximize the system throughput through transmission control. To further exploit the potential benefit of massive MIMO techniques, we propose a novel multi-level transmission and grouped inter-ference cancellation (MLT-GIC) scheme, which can obtain a higher system throughput and provide a flexible tradeoff between throughput and complexity. Numerical results demonstrate the merits of the proposed scheme.

ABSTRACT Minimum transmit sum power (MTSP) is of high theoretical and practical value in multi‐user rate‐constrained systems; it is, however, quite difficult to be numerically characterized in complex channels for the prohibitively high computational power required. In this paper, we present a computationally efficient method to approximate the MTSP in multi‐user multiple‐input multiple‐output orthogonal frequency division multiplexing (MU‐MIMO‐OFDM) wireless networks. Specifically, we propose both lower and upper bounds of the MTSP, which are asymptotically accurate in the limit of large K, the number of users. Then, we develop two iterative water‐filling algorithms to numerically solve the proposed bounds. These algorithms are with low complexity, that is, linear in K, and therefore enable the analysis of MTSP in complex channels even if K is large. Numerical results demonstrate the effectiveness of the bounds in approximating the MTSP and the high computational efficiency of the proposed iterative water‐filling algorithms. With the proposed bounds, we further numerically study scheduling power gain (SPG), which is defined as MTSP reduction achieved by scheduling resources over multiple channel blocks in time domain. We simulate the SPG in different wireless environments defined in Third Generation Partnership Project spatial channel extended model and find insignificant SPG in some cases, indicating that the benefit from scheduling over multiple channel blocks is limited and simply allocating resources within the present channel is sufficient. Our analysis on the MTSP and SPG provides guidelines on the design of resource schedulers in MU‐MIMO‐OFDM networks. Copyright © 2014 John Wiley & Sons, Ltd.

This paper studies the capacity scaling law of the multi-pair relay network with K source-destination pairs and M relays, where each node is equipped with a single antenna and works in half duplex mode. With the conventional two-slot relaying, the capacity was found to scale as K/2 log (M)+O(1) for fixed K and M → ∞. This paper shows that the capacity scaling law can be further improved to K log (M)+O(1) with successive relaying, as if the relays were full duplex. This scaling law can be achieved by a distributed coherent amplify-and-forward scheme, which only requires local channel state information (CSI) at each relay and statistical CSI at the sources and destinations.

Consider a parallel two-way relaying orthogonal frequency division multiple access (PTWR-OFDMA) scheme in which mobile terminals (MTs) are divided into near-nodes (NNs) and far-nodes (FNs). An NN communicates with the base station (BS) directly while an FN communicates indirectly via NNs. We study the design and analysis issues for PTWR-OFDMA. The scheme has some noticeable advantages. First, its throughput increases like XaK, much higher than that of lnlnK in conventional OFDMA (K being the number of MTs). Second, PTWR-OFDMA can provide much better fairness than conventional OFDMA. Third, the power overhead per NN reduces quickly when K increases if there is a peak rate limitation, implying that there is no strong incentive for some users to avoid providing relaying.

The distribution of information bits and frozen bits on the decoder graph can be exploited to simplify the successive‐cancellation (SC) decoding of polar codes. In this study, the authors establish a general simplified SC decoding framework for polar codes with arbitrary block‐length, which is independent of any specific or explicit generator matrices and considerably reduces decoding complexity while retaining the same error performance. Then, based on the fact that the complexity reduction depends on the distribution of information bits, a so‐called m ‐radius reselection scheme is proposed to construct multiple feasible information sets which are different from the original one defined by Arıkan. In this way, flexible tradeoffs between performance and complexity could be achieved.

In this letter, we propose a turbo compressed sensing algorithm with partial discrete Fourier transform (DFT) sensing matrices. Interestingly, the state evolution of the proposed algorithm is shown to be consistent with that derived using the replica method. Numerical results demonstrate that the proposed algorithm outperforms the well-known approximate message passing (AMP) algorithm when a partial DFT sensing matrix is involved.

This letter is on the performance of the turbo signal recovery (TSR) algorithm for partial discrete Fourier transform (DFT) matrices based compressed sensing. Based on state evolution analysis, we prove that TSR with a partial DFT sensing matrix outperforms the well-known approximate message passing (AMP) algorithm with an independent identically distributed (IID) sensing matrix.

In this letter, we revisit the pre-coder design problem for the amplify-and-forward two-way relay channel with multiple antennas equipped at each node. Based on generalized singular value decomposition (GSVD), we propose a novel pre-coding technique named Hermitian Relay Pre-coding (HRP) with a relatively low design complexity. Compared with the existing GSVD pre-coding method, HRP can achieve a higher rate by avoiding zero-forcing operation but keeping the same design complexity.

We study the uplink transmission in multiple-input multiple-output (MIMO) systems with antenna correlation. We focus on schemes that require only channel covariance information at the transmitter (CCIT), which involves lower cost than full channel state information at the transmitter (CSIT). We start from mutual information analysis and show that a simple CCIT-based scheme, referred to as statistical water-filling (SWF), can perform close to the optimal full CSIT-based one in MIMO systems with more receive antennas than transmit ones. We then focus on the implementation of SWF in practically coded systems. An iterative linear minimum mean squared error (LMMSE) receiver is assumed and an extrinsic information transfer (EXIT) chart type curve matching technique is developed based on Hadamard precoding techniques. Simulation results show that the proposed scheme can obtain significant performance improvement compared to the conventional equal power transmission. Finally, we show that the proposed scheme is also very efficient in multi-user uplink MIMO systems with distributed channel information.

We consider a parallel multiple-input multiple-output (MIMO) relay network, in which a source node communicates with a destination node assisted by multiple parallel relays. In such a network, it is costly to acquire global channel state information (CSI) at every relay node. In this regard, we assume local CSI, i.e., each node in the network knows perfect CSI of the links from and to this node, but only has some statistical information of the other links. We propose an amplify-and-forward relaying strategy, termed doubly Hermitian precoding to efficiently exploit the potential benefit of local CSI. We show that the proposed relaying strategy is asymptotically capacity-approaching as the number of relays tends to infinity. Numerical results demonstrate that the proposed scheme performs close to the performance upper bound obtained by assuming global CSI.

This paper is concerned with the uplink in a multi-cell large antenna system. We study a channel estimation scheme where partially decoded data is used to estimate the channel. We show that there are two types of interference components in this scheme that do not vanish even when the number of antennas grows to infinity: cross-contamination and self-contamination. Cross contamination is in principle similar to pilot contamination in a conventional pilot-based channel estimation scheme, while self-contamination is unique for the data-aided scheme. The data-aided scheme can effectively suppress the contamination effect by increasing the data frame length without causing rate loss. This is confirmed by both analysis and simulation results.

We establish area theorems for iterative detection and decoding (or simply, iterative detection) over coded linear systems, including multiple-input multiple-output channels, intersymbol interference channels, and orthogonal frequency-division multiplexing systems. We propose a linear precoding technique that asymptotically ensures the Gaussianness of the messages passed in iterative detection, as the transmission block length tends to infinity. Area theorems are established to characterize the behavior of the iterative receiver. We show that, for unconstrained signaling, the proposed single-code scheme with linear precoding and iterative linear minimum mean-square error (LMMSE) detection is potentially information lossless, under various assumptions on the availability of the channel state information at the transmitter. We further show that, for constrained signaling, our proposed single-code scheme considerably outperforms the conventional multicode parallel transmission scheme based on singular value decomposition and water-filling power allocation. Numerical results are provided to verify our analysis.

In this paper, we develop a novel iterative equalization algorithm for energy-spreading-transform (EST) based multiple-input multiple-output (MIMO) systems. We show that the proposed scheme significantly outperforms the existing non-linear MIMO equalizers in various system setups. We further investigate the precoder design based on the signal-to-interference-plus-noise-ratio (SINR) variance evolution technique, so as to exploit the available channel state information at the transmitter (CSIT). We derive the optimal precoding directions, and show that the precoder optimization then boils down to a simple power allocation problem that is solvable using convex programming. Numerical results demonstrate that the optimized precoder can achieve a significant power gain, as compared with the non-optimized scheme.

This paper is concerned with precoder design for multiple-input multiple-output (MIMO) systems with iterative equalization. We first consider the case of no channel state information at the transmitter (CSIT). Based on evolution analysis, we derive the optimized precoder that minimizes the bit error rate (BER) of the system. We show that, with the optimized precoder, the linear precoding and iterative equalization scheme can achieve a genie-aided performance upper bound at high signal-to-noise ratio (SNR). We further consider the precoder design with perfect CSIT. We show that the precoder design problem reduces to a convex power-allocation problem that can be efficiently solved using standard convex programming tools. Numerical results are provided to demonstrate the performance advantages of the proposed scheme over its counterparts.

This paper is concerned with the decentralized power allocation problem in random access systems. We propose a scheme that is especially suitable for systems requiring high throughput but with difficulty in establishing centralized control, such as cognitive radio environments. Specifically, we assume successive interference cancellation (SIC) at the receiver for multi-packet reception (MPR). We consider a decentralized random power transmission strategy where each user selects its transmitted power level randomly according to a power distribution conditioned on its own channel state. Our focus is on the design of this distribution such that the system packet throughput is maximized under rate and power constraints. We start from a two-user system. A main finding of this paper is that the supports of the optimal power distributions are of discrete nature. This finding greatly simplifies the distribution optimization problem. We also discuss a sub-optimal solution to systems with more than two users. Numerical results demonstrate that the proposed scheme can achieve noticeable performance improvement compared with conventional single-user detection (SUD) based ones and offer a flexible tradeoff between the system throughput and power consumption.

We consider a distributed multiple-input multiple-output (MIMO) system in which multiple transmitters cooperatively serve a common receiver. It is usually very costly to acquire full channel state information at the transmitter (CSIT) in such a scenario, especially for large-scale antenna systems. In this paper, we assume individual CSIT (I-CSIT), i.e., each transmitter has perfect CSI of its own link but only slow fading factors of the others. A linear Hermitian precoding technique is proposed to enhance the system performance. The optimality of the proposed precoding technique is analyzed. Numerical results demonstrate that the performance loss incurred by the I-CSIT assumption is negligible as compared to the full-CSIT case.

We investigate efficient communication over multiple-input multiple-output (MIMO) two-way relay channels (TWRCs), where two multi-antenna users exchange information via a multi-antenna relay. We propose a new MIMO physical-layer network coding (PNC) scheme that includes novel eigen-direction alignment (EDA) precoding. The proposed EDA precoding efficiently aligns the two-user's eigen-modes into the same set of orthogonal directions, and multiple independent PNC streams are implemented over the aligned eigen-modes. We derive an achievable rate-pair of the proposed scheme, for given EDA precoding parameters, over a MIMO TWRC. To maximize the achievable rate-region, we formulate a design criterion for the EDA precoding parameters, and present solutions to the formulation. Closed-form bounds on the sum-rates of the designed EDA-PNC schemes are derived. Numerical results show that there is only a small gap between the achievable rate of the proposed scheme and the capacity upper bound of the MIMO TWRC. It is shown that the proposed scheme can significantly outperforms existing schemes in the literature.

In this paper, we consider multi-user multiple-input multiple-output (MIMO) systems over either multiple access channels (MACs) or broadcast channels (BCs). Contrary to common views, we show that antenna correlation at the mobile unit (MU), the base station (BS) or both sides can be potentially beneficial for such systems. Both asymptotic analysis and numerical results indicate that antenna correlation can provide a significant capacity gain in multi-user environments.

In this paper, we consider a distributed MIMO communication network in which multiple transmitters cooperatively send common messages to a single receiver. In this scenario, it is usually costly to acquire full channel state information at the transmitters (CSIT), i.e., every transmitter perfectly knows the overall channel state information (CSI) of the network. Hence, we assume individual CSIT (I-CSIT), i.e., each transmitter only knows its own CSI. We propose a novel precoding technique, named Hermitian precoding, to enhance the system performance under the constraint of I-CSIT. We show that the proposed scheme can perform close to the system capacity with full CSIT. This reveals that the amount of CSI required at the transmitters can be significantly reduced without considerably compromising performance.

We consider a two-way relay channel (TWRC) in which two terminals exchange messages with the help of a relay between them. The two terminals transmit messages to the relay through the Multiple Access Channel (MAC) and the relay transmits messages to the two terminals through the Broadcast Channel (BC). We assume that the MAC and the BC do not interfere with each other, and each terminal receives signals only from the relay but not the other terminal. All the nodes are assumed to be full-duplex, which means that they can transmit and receive information at the same time. A transmission scheme for the Gaussian TWRC is said to be analog-relaying if the relay does not need any codebook for encoding. The simplest analog-relaying scheme is amplify-and-forward (AF), under which the relay amplifies the received codeword and forwards the resultant codeword to the two terminals. In this paper, we propose a new analog-relaying scheme called amplify-and-modulo (AM) based on lattice operations. AM is a slight modification of AF. Under AM, the relay first amplifies the received codeword followed by reducing the power of the amplified codeword using the modulo-lattice operation, and then forwards the resultant codeword to the two terminals. After receiving the codeword transmitted by the relay, each terminal subtracts its own information before decoding. We prove an achievable rate region for AM, and obtain a necessary and sufficient condition under which AM outperforms AF. In addition, we show by graph that AM can achieve a strictly higher equal-rate than AF and another existing analog-relaying scheme together under some scenario.

We propose a new joint channel coding and physical layer network coding (CPNC) scheme for multiple-input multiple-output (MIMO) two-way relay channels (TWRCs). At the heart of the scheme lies a key technique referred to as eigen-direction alignment (EDA) precoding. This technique efficiently creates multiple aligned parallel channels which facilitates the deployment of multi-stream CPNC. Our analysis shows that the achievable rate of the scheme can approach the capacity upper bound in the median to high signal-to-noise (SNR) region when nT> nR, where nTand nRdenote the number of antennas of each user and that of relay, respectively. The gap to the capacity upper bound diminishes as nT/nRincreases. Numerical results demonstrate that the proposed scheme significantly outperform other well-known schemes in the literature.

We propose a space-time coding scheme for efficient transmission over multiple-input multiple-output (MIMO) channels without channel state information at the transmitter (CSIT). The proposed scheme involves linear precoding (LP) at the transmitter and iterative linear minimum mean-square error (LMMSE) detection at the receiver. We develop a procedure to jointly optimize the forward-error-control (FEC) coding and LP, taking into consideration of the iterative detection process. Our analysis shows that the proposed scheme can perform close to the outage capacity of MIMO channels.

In this paper, we consider the performance analysis of multiple-input multiple-output (MIMO) inter-symbol interference (ISI) systems involving linear-precoding (LP) and iterative linear minimum mean-square error (ILMMSE) detection. The main contribution of this paper is an area theorem to evaluate the achievable rate of the proposed LP-ILMMSE scheme. Based on this area theorem, we further optimize the linear precoder to maximize the achievable rate. Numerical results are provided to verify our analysis.

In this paper, we propose an analytical model for evaluating the MAC throughput in an unsaturated IEEE 802.11 wireless local area network (WLAN) where multiple packets reception (MPR) is possible using multiuser detection techniques. In particular, a recently proposed successive interference cancellation (SIC) scheme for MPR is considered where users can randomly choose the transmission power from a set of discrete power levels. We derive an explicit expression for throughput of the WLAN based on such an SIC scheme and validate the accuracy of the model via ns-2 simulation results. We show that the throughput is significantly improved compared to the conventional 802.11 MAC protocol just by resolving collisions between two packets with different transmission power levels. In addition, we provide the optimal power distribution to maximize the throughput achievable in an SIC-enabled WLAN.

This paper is concerned with the advantages of multi-user concurrent transmission in multiple-input multiple-output (MIMO) systems with rate constraints. We first study a maximum eigenmode beamforming (MEB) strategy for fading multiple access channels (MACs). This strategy allows each user to transmit only in its maximum eigenmode direction and applies a suboptimal matched-filter receiver with successive interference cancellation at the base station (BS). We derive a closed-form expression for the average minimum transmitted sum power required by MEB. Based on this, we show that: a) the MEB strategy is asymptotically optimal when the number of simultaneous users is sufficiently large; b) multi-user concurrent transmission has a power advantage, referred to as multi-user gain, over orthogonal transmission approaches such as time-division multiple-access; c) the number of antennas at the BS has a far stronger impact on the system performance than that at each user side. These properties are verified by simulation. Both numerical analyses and simulation results show that a major part of multi-user gain can be achieved in practical environments even with a quite small number of simultaneous users. We also study the MEB strategy for MIMO broadcast channels (BCs). The dirty paper coding (DPC) technique is necessary in this case. It is analytically shown that most observations made for MIMO MACs are extendable to MIMO BCs.

This paper is concerned with the capacity of multiple-input multiple-output (MIMO) cellular systems. We assume an equal rate constraint for all users and adopt a realistic channel model that incorporates path loss, lognormal fading and Rayleigh fading. Several bounds are derived for the minimum transmission power of such rate-constrained MIMO cellular systems with various base station (BS) cooperation strategies. In particular, the upper power bound is based on the maximum eigenmode beamforming (MEB) scheme. These power bounds are then used to obtain the corresponding cellular capacity bounds when partial BS cooperation strategies are adopted. Our results show that, allowing more users to transmit simultaneously, introducing cooperation among BSs and increasing the number of antennas (especially at each BS) are efficient ways to improve system performance.

Asymptotic analysis of the dual-diagonal (DD) linear-minimum-mean-square-error (LMMSE) channel estimation for orthogonal frequency-division multiplexing (OFDM) systems is presented. We prove that the DD-LMMSE estimator is asymptotically optimal among all DD estimators as the number of subcarriers tends to infinity. Based on the asymptotic analysis, we propose an evolution tool to predict the performance of iterative OFDM systems. Numerical results are presented to verify our analysis.

In this paper, we present a joint forward-error-correction (FEC) coding and linear precoding scheme for multiple-input multiple-output (MIMO) and inter-symbol interference (ISI) channels with imperfect channel state information at the transmitter (CSIT). We first study the performance of ideally coded systems. We focus on an average power gain (APG) method that can achieve capacity in the two extreme cases of no CSIT and perfect CSIT. In the more general case, the performance of the APG method improves progressively with the CSIT quality. We then consider the implementation of this APG method in a practically coded system. We propose a unified scheme involving beamforming, water-filling, and diversity coding. The core of the new scheme is a joint FEC coding and linear precoding strategy at the transmitter and an iterative detection process at the receiver. Simulation results demonstrate that the proposed scheme can achieve significant performance gain by efficiently utilizing the available CSIT.

We propose a dual diagonal linear-minimum-mean-square-error (DD-LMMSE) channel estimation algorithm for orthogonal frequency division multiplexing (OFDM) systems involving joint channel estimation and signal detection. Computational complexity and mean-square-error (MSE) analysis are presented to evaluate the efficiency of the proposed algorithm. Compared with the optimal LMMSE method, the proposed DD-LMMSE method can achieve significant complexity reduction without compromising much performance.

This paper deals with the clipping method used in orthogonal frequency-division multiplexing (OFDM) systems to reduce the peak-to-average power ratio (PAPR). An iterative soft compensation method is proposed to mitigate the clipping distortion, which can outperform conventional treatments. The impact of signaling schemes on the residual clipping noise power is studied via the symbol variance analysis. It is found that superposition coded modulation (SCM) can minimize the residual clipping noise power among all possible signaling schemes. This indicates that SCM-based OFDM systems are more robust to clipping effect than other alternatives when soft compensation is applied. It is also shown that a multi-code SCM scheme can further reduce the clipping effect and its overall performance can be quickly evaluated using a semi-analytical evolution method. Numerical examples are provided to verify the analysis.

This paper is concerned with a simple binary erasure-recovery coding scheme that falls into the family of so-called semi-random low-density-parity-check (SR-LDPC) codes. Based on a constrained random-scrambling technique, the proposed coding scheme is systematic, rateless, and capacity-achieving. We provide simulation examples comparing the new scheme with the well-known Luby transform (LT) and raptor codes. It is shown that the new scheme has advantages in complexity and performance over its counterparts especially in channels with a relatively low erasure rate.

In this paper, we present a practical approach to the iterative decoding of Reed-Solomon (RS) codes. The presented methodology utilizes an architecture in which the output produced by steps of belief-propagation (BP) is successively applied to a legacy decoding algorithm. Due to the suboptimal performance of BP conducted on the inherently dense RS parity-check matrix, a method is first provided for the construction of reduced-density, binary, parity-check equations. Iterative decoding is then conducted utilizing a subset of a redundant set of parity-check equations to minimize the number of connections into the least-reliable bits. Simulation results show that performance comparable to (and exceeding) the best known practical RS decoding techniques is achievable with the presented methodology. The complexity of the proposed algorithm is significantly lower than these existing procedures and permits a practical implementation in hardware.

In this paper, we study the impact of antenna correlation at mobile units (MUs) on the capacity of multi-user multiple-input multiple-output (MIMO) systems with rate constraints. Both numerical results and asymptotic analyses show that antenna correlation can actually be regarded as a beneficial factor for such systems. It is also shown that the maximum eigenmode beamforming (MEB) based interleave-division multiple-access (IDMA) system is an effective platform to exploit the potential gain provided by antenna correlation at MUs.

We extend the area property to more general linear channel models (including inter-symbol-interference (ISI) and multiple-input multiple-output (MIMO) systems) with arbitrary input constellations. We show that the theoretical limit of a channel (i.e., the mutual information) can be achieved under some assumptions. Several engineering techniques are examined to ensure these assumptions. It is shown that the required assumptions can be approximately materialized using superposition coded modulation (SCM) and a preceding technique.

We propose a family of binary erasure codes, namely, quasi-systematic doped LT (QS-DLT) codes that are almost systematic, universal, and asymptotically capacity-achieving with encoding and decoding complexity O(K log(1/epsiv)), where K is the information length, and e is the overhead. Finite-length analysis is carried out to study the error-floor behavior of our proposed codes. Numerical results verify that our proposed codes provide a low-complexity alternative to systematic Raptor codes with comparable performance.

We study superposition coded modulation (SCM) with iterative linear minimum-mean-square-error (LMMSE) detection. We show that SCM offers an attractive solution for highly complicated transmission environments with severe interference. We analyze the impact of signaling schemes on the performance of iterative LMMSE detection. We prove that among all possible signaling methods, SCM maximizes the output signal-to-noise/ interference ratio (SNIR) in the LMMSE estimates during iterative detection. Numerical examples are used to demonstrate that SCM outperforms other signaling methods when iterative LMMSE detection is applied to multi-user/multi-antenna/multipath channels.

We propose a family of binary erasure codes, namely, quasi-systematic doped Luby-Transform (QS-DLT) codes, that are rate-less, almost systematic, and universally capacity-achieving without the prior knowledge of channel erasure rate. The encoding and decoding complexities of QS-DLT codes are O(Klog(1/epsiv)), where K is the information length, and epsiv is the overhead. Stopping-set analysis is carried out to study the error-floor behavior of QS-DLT codes. Analysis and numerical results demonstrate that QS-DLT codes provide a low-complexity alternative to systematic Raptor codes with comparable performance.

We apply clipping to superposition coded modulation (SCM) systems to reduce the peak-to-average power ratio (PAPR) of the transmitted signal. The impact on performance is investigated by evaluating the mutual information driven by the induced peak-power-limited input signals. It is shown that the rate loss is marginal for moderate clipping thresholds if optimal encoding/decoding is used. This fact is confirmed in examples where capacity-approaching component codes are used together with the maximumaposterioriprobability (MAP) detection. In order to reduce the detection complexity of SCM with a large number of layers, we develop a suboptimal soft compensation (SC) method that is combined with soft-input soft-output (SISO) decoding algorithms in an iterative manner. A variety of simulation results for additive white Gaussian noise (AWGN) and fading channels are presented. It is shown that with the proposed method, the effect of clipping can be efficiently compensated and a good tradeoff between PAPR and bit-error rate (BER) can be achieved. Comparisons with other coded modulation schemes demonstrate that SCM offers significant advantages for high-rate transmissions over fading channels.

In this paper, we propose a low-complexity iterative joint channel estimation, detection and decoding technique for doubly selective channels. The key to the proposed technique is a segment-by-segment processing strategy under the assumption that the channel is approximately static within a short segment of a data block. Through a virtual zero-padding technique, the proposed segment-by-segment equalization approach inherits the low-complexity advantage of the conventional frequency domain equalization (FDE), but does not need the assistance of guard interval (for cyclic-prefixing or zero-padding), thereby avoiding the spectral and power overheads. Furthermore, we develop a low-complexity bidirectional channel estimator, where the Gaussian message passing (GMP) technique is used to exploit the channel correlation information, and the intermediate channel estimation results in the iterative process are employed to perform inter-tap interference cancellation. Simulation results demonstrate the effectiveness of the proposed detection and channel estimation algorithms.

Equal power allocation (EPA) has been truly successful when applied in IS-95 CDMA. It is therefore worthwhile to see whether EPA is also applicable in IDMA systems, which can be considered as a special case of the direct-sequence CDMA. However, the applicability of EPA in IDMA systems must be considered in light of two fundamental problems. First, EPA is not efficient in suppressing multi-user interference and hence often results in severe performance degradation (infeasibility). Second, EPA schemes often require higher received power than other schemes that allow unequal received powers (sub-optimality). In this paper, we derive the necessary and sufficient conditions for the feasibility and optimality of IDMA systems having equal received powers. The conditions show how feasibility and optimality are related to system parameters such as number of users, code rate and bit-error rate target. The conditions also suggest an upper limit on the throughput of IDMA systems with equal received powers. The results obtained in this paper may provide a theoretical foundation for designing future EPA schemes for IDMA.

In this paper, we propose a low-complexity iterative joint channel estimation, detection and decoding technique for doubly selective channels. The key is a segment-by-segment frequency domain equalization (FDE) strategy under the assumption that channel is approximately static within a short segment. Guard gaps (for cyclic prefixing or zero padding) are not required between adjacent segments, which avoids the power and spectral overheads due to the use of cyclic prefix (CP) in the conventional FDE technique. A low-complexity bi-directional channel estimation algorithm is also developed to exploit correlation information of time-varying channels. Simulation results are provided to demonstrate the efficiency of the proposed algorithms.

In this paper, we study the iterative detection problem for a coded system with multi-ary modulation. We show that, with iterative linear minimum-mean-square-error (LMMSE) detection, superposition coded modulation (SCM) can provide performance superior to that with other traditional signaling schemes used in trellis coded modulation (TCM) and bit-interleaved coded modulation (BICM). This finding provides a useful guideline for system design considering inter-symbol interference (ISI) and other forms of interference. Simulation results are provided to illustrate the efficiency of the iterative LMMSE detection with different signaling schemes.

This paper is concerned with cellular systems with rate constraints in fading environments. We consider a simple but asymptotically optimal matched filtering/successive interference cancellation (MF-SIC) scheme. We derive several concise and closed-form bounds for the power and spectral efficiencies of various base station cooperation strategies, which provide some useful insights into cellular systems.

This paper studies orthogonal frequency-division multiplexing (OFDM) systems employing coded modulation. Clipping is applied to reduce the peak-to-average-power-ratio (PAPR) of the transmit signal. A soft compensation method is proposed to combat the clipping effect. It is shown that the proposed method can outperform conventional clipping effect mitigation methods. The impact of signaling schemes of the coded modulation on system performance is investigated. The average variance analysis and numerical results demonstrate that superposition coded modulation (SCM) together with the proposed detection technique provides a simple and efficient solution to clipped OFDM transmission.

This paper is concerned with the transmission strategies and relay selection for decode-and-forward parallel relay networks (PRNs) based on superposition coding. Our focus is on the minimization of the aggregate transmission power that supports a given transmission rate. In this paper, two transmission strategies are investigated, i.e., an optimal- cooperation (OC) strategy requiring strict synchronization at the destination/relay nodes and a no-information-overlapping (NIO) strategy with no synchronization requirement for the ease of implementation using current technologies such as interleave- division multiple-access (IDMA). Furthermore, a reduced-relay-selection (RRS) strategy involving only 2-level superposition coding is given to trade off between complexity and performance. Numerical results show that the performance gap between OC and NIO is negligible, and selecting the best two relay nodes is adequate to achieve most performance gain even when the number of relay nodes is large.

In this paper, a vector-form factor graph representation is derived for intersymbol interference (ISI) channels. The resultant graphs have a tree-structure that avoids the short cycle problem in existing graph approaches. Based on a joint Gaussian approximation, we establish a connection between the LLR (log-likelihood ratio) estimator for a linear system driven by binary inputs and the LMMSE (linear minimum mean-square error) estimator for a linear system driven by Gaussian inputs. This connection facilitates the application of the recently proposed Gaussian message passing technique to the cycle-free graphs for ISI channels. We also show the equivalence between the proposed approach and the Wang-Poor approach based on the LMMSE principle. An attractive advantage of the proposed approach is its intrinsic parallel structure. Simulation results are provided to demonstrate this property.

This paper is concerned with the low-cost iterative equalization/detection principles for coded linear systems with cyclic prefixes. Turbo frequency-domain-equalization (FDE) is applied to systems that may contain the joint effect of multiple-access interference (MAI), cross-antenna interference (CAI) and inter-symbol interference (ISI). We develop an SNR-variance evolution technique for the performance evaluation of the proposed systems. Numerical results in various channel environments demonstrate excellent agreement between the predicted and simulated system performance.

We propose a low-cost detection strategy for multi-user multiple-input-multiple-output (MIMO) systems with inter-symbol interference (ISI). The cyclic prefix (CP) technique is assumed. The proposed detection algorithm is derived in a very concise manner based on some elegant properties of circulant matrices. We show that multi-user detection and equalization can be carried out jointly and efficiently.

We investigate spectrum shaping based on cyclic filtering for coded single-carrier transmission over intersymbol interference (ISI) channels. An optimized precoder is derived for coded single-carrier systems using an iterative linear-minimum-mean-square-error (LMMSE) frequency-domain-equalization (FDE) receiver. Numerical results show that this precoder can provide considerable spectrum-shaping gain.

In this paper, we propose a new class of low-rate error correction codes called repeat-zigzag-Hadamard (RZH) codes featuring simple encoder and decoder structures, and flexible coding rate. RZH codes are serially concatenated turbo-like codes where the outer code is a repetition code and the inner code is a punctured zigzag-Hadamard (ZH) code. By analyzing the code structure of RZH codes, we prove that both systematic and nonsystematic RZH codes are good codes, in the sense that for an RZH code ensemble, there exists a positive number gamma0such that for any binary-input memoryless channel whose Bhattacharyya noise parameter is less than , the average block error probability of maximum-likelihood (ML) decoding approaches zero. Two decoding algorithms-serial and parallel decoders for RZH codes-are proposed. We then employ the extrinsic information transfer (EXIT) chart technique to design irregular RZH codes. Results show that the optimized irregular RZH codes exhibit a performance that is very close to capacity in the low-rate regime.

This paper presents a quasi-random approach to space–time (ST) codes. The basic principle is to transmit randomly interleaved versions of forward error correction (FEC)-coded sequences simultaneously from all antennas in a multilayer structure. This is conceptually simple, yet still very effective. It is also flexible regarding the transmission rate, antenna numbers, and channel conditions (e.g., with intersymbol interference). It provides a unified solution to various applications where the traditional ST codes may encounter difficulties. We outline turbo-type iterative joint detection and equalization algorithms with complexity (per FEC-coded bit) growing linearly with the transmit antenna number and independently of the layer number. We develop a signal-to-noise-ratio (SNR) evolution technique and a bounding technique to assess the performance of the proposed code in fixed and quasi-static fading channels, respectively. These performance assessment techniques are very simple and reasonably accurate. Using these techniques as a searching tool, efficient power allocation strategies are examined, which can greatly enhance the system performance. Simulation results show that the proposed code can achieve near-capacity performance with both low and high rates at low decoding complexity.

In this paper, we study the advantages of multi-user concurrent transmission, measured using the multi-user gain (MUG), in multiple-input multiple-output (MIMO) systems with rate constraints. Our focus is on a maximum eigenmode beamforming (MEB) strategy. We derive a closed-form expression for the transmitted sum power required by the MEB strategy and prove that this strategy is asymptotically optimal. The simple closed-form expression for the MEB sum-power provides many useful insights into the asymptotic behavior of multi-user MIMO systems. Interleave-division multiple-access is adopted as a platform for implementing the proposed MEB scheme. Both numerical and simulation results show that a major part of MUG can be achieved with a quite small number of users.

The recent investigations on interleave-division multiple-access (IDMA) have demonstrated its advantage in supporting high-data-rate and multi-rate services over wireless fading channels. This paper focuses on quality of service (QoS) guarantee in IDMA-based multi-service wireless networks. We propose a QoS architecture which addresses the key issues of QoS guarantee for multi-service in IDMA, including medium access control (MAC), admission control, power control, and rate allocation. The proposed IDMA QoS architecture avoids complex packet scheduling at the MAC layer which is however required in other existing multiple access systems. Data packets can be transmitted in IDMA without scheduling delay. Additionally, to improve the efficiency of random access, an interleave- division slotted-ALOHA (IDSA) access method is proposed for the IDMA MAC protocol. We derive the relationship between the arrival rate of access requests and the number of access interleavers allocated to an IDMA system for a given access success probability. Based on this relationship, we can adaptively adjust the number of access interleavers according to the traffic load of access requests, so as to ensure a satisfactory probability of successful access as well as low complexity of request detection at the receiver.

For real-time wireless communications, short forward error-correcting (FEC) codes are indispensable due to the strict delay requirement. In this paper we study the performance of short FEC codes. Reed-Solomon (RS) codes and concatenated zigzag (CZ) codes are chosen as representatives of classical algebraic codes and modern simple iterative decodable codes, respectively. Additionally, we use random binary linear codes as a baseline reference for comparison. Our main results (demonstrated by both simulation and ensemble distance spectrum analysis) are as follows: 1) Short RS codes are as good as random binary linear codes; 2) Carefully designed short low-density parity-check (LDPC) codes are almost as good as random binary linear codes when high decoding complexity can be tolerated; 3) Low complexity belief propagation decoders incur considerable performance loss at short coding lengths.

We introduce a family of rateless codes, namely the doped accumulate LT (DALT) codes, that are capacity-approaching on a binary erasure channel (BEC) with bounded encoding and decoding complexity. DALT codes can be either systematic or non-systematic. Non-systematic DALT codes are very similar to raptor codes, except that joint optimization on the full coding graph can be applied to DALT codes, and thus they can be optimized to have better asymptotic performance than raptor codes. Systematic DALT codes, with the proposed protocol, exhibit better performance and lower complexity than their non-systematic counterparts.

This paper is concerned with the iterative detection principles for coded linear systems with cyclic prefixes. We derive a matrix-form low-cost fast Fourier transform (FFT) based iterative LMMSE-APP detector and propose an evolution technique for the performance evaluation of the proposed detector. Numerical results show a good match between simulation and evolution prediction.

We consider the sum-power minimization problem for multi-user multiple-input multiple-output (MIMO) systems with rate constraints. We show that significant performance improvements, qualified by multiuser gain (MUG), can be achieved by allowing multiple users to transmit simultaneously on their individual maximum eigenmodes. We also show that a major part of MUG can be achieved even with quite a small number of users and increasing the number of antennas at the base station is an efficient method for maximizing MUG.

The message-passing approach to model-based signal processing is developed with a focus on Gaussian message passing in linear state-space models, which includes recursive least squares, linear minimum-mean-squared-error estimation, and Kalman filtering algorithms. Tabulated message computation rules for the building blocks of linear models allow us to compose a variety of such algorithms without additional derivations or computations. Beyond the Gaussian case, it is emphasized that the message-passing approach encourages us to mix and match different algorithmic techniques, which is exemplified by two different approaches—steepest descent and expectation maximization—to message passing through a multiplier node.

In this paper, we consider the design and analysis of generalized low-density parity-check (GLDPC) codes in AWGN channels. The GLDPC codes are specified by a bipartite Tanner graph, as with standard LDPC codes, but with the single parity-check constraints replaced by general coding constraints. In particular, we consider imposing Hadamard code constraints at the check nodes for a low-rate approach, termed LDPC-Hadamard codes. We introduce a low-complexity message-passing based iterative soft-input soft-output (SISO) decoding algorithm, which employs the a posteriori probability (APP) fast Hadamard transform (FHT) for decoding the Hadamard check codes at each decoding iteration. The achievable capacity with the GLDPC codes is then discussed. A modified LDPC-Hadamard code graph is also proposed. We then optimize the LDPC-Hadamard code ensemble using a low-complexity optimization method based on approximating the density evolution by a one-dimensional dynamic system represented by an extrinsic mutual information transfer (EXIT) chart. Simulation results show that the optimized LDPC-Hadamard codes offer better performance in the low-rate region than low-rate turbo-Hadamard codes, but also enjoy a fast convergence rate. A rate-0.003 LDPC-Hadamard code with large block length can achieve a bit-error-rate (BER) performance of 10-5at -1.44 dB, which is only 0.15 dB away from the ultimate Shannon limit (-1.592 dB) and 0.24 dB better than the best performing low-rate turbo-Hadamard codes

A novel hybrid ARQ (HARQ) scheme using a concatenated two-state trellis-coded modulation (CT-TCM) code is proposed for improving wireless TCP throughput. A distinguished feature of the proposed scheme is that the heavily punctured TCM codes are used for retransmissions of the corrupted data block, which are combined at the receiver with the previously received sequences of the same data block for decoding. By this method, significantly improved coding gain and efficient spectrum utilization can be achieved with very low complexity. A Markov model is developed to evaluate TCP throughput over the proposed HARQ in wireless link. By both analysis and simulation, we demonstrate that compared with other existing TCM-based ARQ schemes, significant improvement of TCP throughput over wireless links is achieved by the proposed CT-TCM HARQ while smaller buffer size is required at the access point.

The recently proposed interleave-division multiple-access (IDMA) system is a flexible spread-spectrum air-interface technique featuring low receiver complexity and high spectral efficiency. In IDMA, each user's chip sequence is interleaved by a distinct chip-level interleaver. The receiver employs a simple chip-level iterative multiuser detector to decode the user's data. Here we focus on the analysis and optimization of such an IDMA system. We show that IDMA can be viewed as a limit case of the conventional CDMA employing repetition code and random spreading. Two analytical tools, namely, the large-system performance approximation and the EXIT chart technique are tailored in the context of IDMA chip-level iterative detector to facilitate the system performance analysis and optimization. The spectral efficiencies of a low-rate coded IDMA system with equal power setting in both single-cell and multi-cell scenarios are then analyzed, from which it is seen that the coded IDMA system with turbo receiver is a spectral efficient multiple-access scheme. Finally, we consider optimal power allocation among users in IDMA to maximize the spectral efficiency with finite-alphabet constellation. The differential evolution technique for nonlinear optimization is adopted to solve the power profile optimization problem. With optimized power profiles, the low-rate coded IDMA system can approach the optimal spectral efficiency with finite input constellations

In this paper, we compare different low-cost detection techniques for multiple access systems. The per-user complexities of these techniques are independent of the number of users. We demonstrate that the chip extrinsic information (CEI) method achieves the best performance, and the a posteriori probability information (APPI) and bit extrinsic information (BEI) methods provide different tradeoffs between performance, complexity and storage requirements. These low-cost multiuser detectors are applicable to a variety of systems, including interleave-division multiple-access (IDMA) and code-division multiple-access (CDMA) systems. Both analysis and simulation demonstrate that interleaving can greatly improve the effectiveness of the low-cost algorithms. In the presence of chip interleavers, the CEI method slightly outperforms the more complex minimum mean square error (MMSE) method.

We consider the design of practical interleavers for interleaver division multiple access (IDMA) systems. A set of interleavers is considered to be practical if it satisfies two criteria: 1) It is easy to generate (i.e., the transmitter and receiver need not store or communicate many bits in order to agree upon an interleaver), and 2) no two interleavers in the set "collide". We show that a properly defined correlation between interleavers can be used to formulate a collision criterion, where zero-correlation (i.e., orthogonality) implies no collision. Computing the correlation among non-orthogonal interleavers is generally computationally very expensive, so we also design an upper-bounding technique to efficiently check whether two interleavers have low correlation. We then go on to propose several methods to design practical interleavers for IDMA: one method to design orthogonal interleavers, and two methods to design non-orthogonal interleavers (where the upper-bounding technique is used to verify their cross-correlation is low). Simulation results are presented to show that the designed practical interleavers perform as well as random interleavers in an IDMA system.

This paper presents a peak-power-limited superposition coding scheme based on clipping. A low-complexity soft compensation algorithm (SCA) for combating the clipping effect is investigated. It can be easily combined with soft-input soft-output (SISO) decoding algorithms in an iterative manner. Various numerical results show that the SCA can effectively mitigate the performance loss due to clipping.

This paper is concerned with the power allocation problem for practically coded interleave-division multiple-access (IDMA) systems with iterative multi-user detection (MUD) over multiple access channels (MACs). Both Additive White Gaussian Noise (AWGN) and fading channels are considered. For AWGN channels, two power allocation methods based on linear programming are discussed and compared with an interior-point method (IPM). These techniques are extended to power allocation over fading channels. Numerical results show that, with power optimization, IDMA can achieve significant performance improvements over TDMA in fading environments.

This paper is concerned with signal estimation over general multiple-input-multiple-output (MIMO) channels based on a jointly Gaussian (JG) approach. We show that the proposed method is equivalent to the LMMSE approach, but is conceptually more concise and computationally more efficient. A 2×2 multi-antenna system with multipath effect is considered as an example to illustrate the advantages of the JG method. Also, a simple SNR-bounding evolution tool, similar to EXIT chart technique, is developed for fast assessment of the JG method. Compared with the optimal MAP algorithm, the JG method can achieve almost the same performance with greatly reduced complexity.

We introduce a new class of low-rate error correction codes called concatenated zigzag Hadamard (ZH) codes which are specified by a highly structured zigzag graph with each segment being a Hadamard codeword. The ZH codes enjoy extremely simple encoding and very-low-complexity soft-input soft-output (SISO) decoding. We present an asymptotic performance analysis of the proposed codes using the extrinsic mutual information transfer (EXIT) chart for infinite-length codes. We also provide a union bound analysis of the error performance for finite-length codes.

We propose a new class of low-rate error correction codes called repeat-zigzag-Hadamard (RZH) codes. RZH codes are serially concatenated turbo-like codes where the outer code is a repetition code and the inner code is a punctured zigzag-Hadaniard (ZH) code. We prove that RZH codes are good in the sense that for an RZH code ensemble, there exists a positive number 70 such that for any binary-input memoryless channel whose Bhattacharyya noise parameter is less than 70, the average maximum-likelihood (ML) decoder block error probability approaches zero. EXIT charts are used to design irregular codes

We consider a code-spread and chip-interleaved time-hopping (TH) multiple-access scheme for multiuser ultra-wideband (UWB) communications. In such a system, each user's chip sequence is interleaved by a user-specific distinct random interleaver, and the receiver is a low-complexity chip-level iterative multiuser detector (MUD) which performs simple Rake-type combining to collect the energy dispersed in multipath UWB channels. To further reduce the receiver complexity, time reversal (TR), a transmitter preprocessing technique, is also considered. When power control is employed along with TR, a single-tap receiver can be utilized which offers a desirable bit error rate (BER) performance with a significantly reduced sampling rate. Furthermore, the zigzag Hadamard (ZH) code is proposed as the low-rate code for both channel coding and spreading in the code-spread TH-UWB system. With its capacity-approaching capability and low encoding/decoding complexity, the parallel concatenated ZH code is a promising coding scheme for UWB applications.

In this paper, we present an unequal power allocation technique to increase the throughput of code-division multiple-access (CDMA) systems with chip-level interleavers. Performance is optimized, respectively, based on received and transmitted power allocation. Linear programming and power matching techniques are developed to provide solutions to systems with a very large number of users. Various numerical results are provided to demonstrate the efficiency of the proposed techniques and to examine the impact of system parameters, such as iteration number and interleaver length. We also show that with some very simple forward error correction codes, such as repetition codes or convolutional codes, the proposed scheme can achieve throughput reasonably close to that predicted by theoretical limit in multiple access channels.

In this correspondence, we introduce a new class of low-rate error correction codes called zigzag Hadamard (ZH) codes and their concatenation schemes. Each member of this class of codes is specified by a highly structured zigzag graph with each segment being a Hadamard codeword. The ZH codes enjoy extremely simple encoding and very low-complexity soft-input-soft-output (SISO) decoding based on a posteriori probability (APP) fast Hadamard transform (FHT) technique. We present an asymptotic performance analysis of the proposed concatenated ZH codes using the extrinsic mutual information transfer (EXIT) chart for infinite-length codes. We also provide a union bound analysis of the error performance for finite-length codes. Furthermore, the concatenated ZH codes are shown to be a good class of codes in the low-rate region. Specifically, a rate-0.0107 concatenated code with three ZH components and an interleaver size of 65536 can achieve the bit error rate (BER) performance of 10/sup -5/ at -1.15dB, which is only 0.44 dB away from the ultimate Shannon limit. The proposed concatenated ZH codes offer similar performance as another class of low-rate codes-the turbo-Hadamard codes, and better performance than superorthogonal turbo codes, with much lower encoding and decoding complexities.

This paper provides a comprehensive study of interleave-division multiple-access (IDMA) systems. The IDMA receiver principles for different modulation and channel conditions are outlined. A semi-analytical technique is developed based on the density evolution technique to estimate the bit-error-rate (BER) of the system. It provides a fast and relatively accurate method to predict the performance of the IDMA scheme. With simple convolutional/repetition codes, overall throughputs of 3 bits/chip with one receive antenna and 6 bits/chip with two receive antennas are observed for IDMA systems involving as many as about 100 users.

In this paper, we focus on the analysis and optimization of the interleave-division multiple-access (IDMA) system. The spectral efficiencies of the coded IDMA system are analyzed. Optimal power allocation among users in IDMA, to maximize the spectral efficiency with a finite-alphabet constellation, is also considered. Differential evolution is adopted to solve the power profile optimization problem.

This paper presents a factor graph approach to turbo equalization. Unlike the existing linear MMSE turbo equalization methods, which operate with truncated windows (sliding or extending window), the proposed is a full-window approach with low complexity. This approach supports a high-speed parallel implementation technique, which makes it an attractive option in practice

We consider the design and analysis of generalized low-density parity-check (GLDPC) codes specified by a bipartite Tanner graph, as with standard LDPC codes, but with the single parity-check constraints replaced by general coding constraints. In particular, we consider imposing Hadamard code constraints at the check nodes for a low-rate approach, termed LDPC-Hadamard codes. The achievable capacity with the GLDPC codes is then discussed. A modified LDPC-Hadamard code graph is also proposed. We then optimize the LDPC-Hadamard code ensemble using a low-complexity optimization method based on approximating the density evolution by a one-dimensional dynamic system represented by an extrinsic mutual information transfer (EXIT) chart. Simulation results show that a rate-0.003 LDPC-Hadamard code with large block length can achieve a bit-error-rate (BER) performance of 10-5at -1.44 dB, only 0.15 dB away from the ultimate Shannon limit (-1.592 dB)

We study a multi-layer space-time code, based on random interleaving and proper power allocation. We show that, theoretically, the proposed code can achieve capacity for any transmission rate by superimposing many ideal low-rate codes. We also show that, with practically available codes, the proposed scheme can achieve performance close to the theoretical limit.

This work provides a comprehensive study of IDMA systems. We first outline the basic IDMA principles in single-path and multi-path environments. We then describe a simple semi-analytical technique to assess the performance of IDMA systems, based on which we develop a power allocation scheme for performance optimization. We also discuss the use of low-rate codes to further enhance the power efficiency of IDMA systems. Simulation results demonstrate the advantages of the IDMA scheme in terms of both bandwidth and power efficiencies. For example, with simple convolutional/repetition codes an overall throughput of 8 bits/chip is achieved in single antenna systems. With turbo-Hadamard codes, performance at 1.4 dB away from the theoretical limit is demonstrated in a Gaussian MAC.

We employ the extrinsic information transfer (EXIT) chart technique to assess the limiting performance of turbo-Hadamard codes and identify the optimized design parameters for such codes. It is shown that for a sufficiently long code length and a sufficiently large number of iterations, a carefully designed low-rate turbo-Hadamard code can potentially achieve successful decoding at Eb/N0≈ –1.30 dB, which is about 0.29 dB from the ultimate Shannon limit.

We present a modified turbo minimum mean-squared error (MMSE) equalization algorithm using an extending window approach. We show that the new method can achieve nearly the same performance and considerable cost reduction compared with a recently proposed sliding window MMSE equalization technique.

This letter concerns the performance assessment of cascade trellis-block space-time codes. We focus on the case where the 2/spl times/2 orthogonal block space-time code is used as the inner code. Either bounding or hybrid bounding/simulation techniques can be used. The proposed work provides some insights into the properties of such codes.

This letter presents an improved two-state turbo single-parity-check code for applications with rates around 1/3. The new code is compared with the (15,13)/sub 8/ turbo code used in the Third Generation Partnership Project. Simulation results demonstrate that the proposed code can achieve similar performance at reduced decoding complexity.

In this correspondence, we investigate in a comprehensive fashion a one-layer coding/shaping scheme resembling a perfectly cooperated multiple-access system. At the transmitter, binary data are encoded by either single-level or multilevel codes. The coded bits are first randomly interleaved and then entered into a signal mapper. At each time, the signal mapper accepts as input multiple binary digits and delivers as output an amplitude signal, where the input are first independently mapped into 2-PAM signals (possibly having different amplitudes) and then superimposed to form the output. The receiver consists of an iterative decoding/demapping algorithm with an entropy-based stopping criterion. In the special cases when all the 2-PAM signals have equal amplitudes, based on an irregular trellis, we propose an optimal soft-input-soft-output (SISO) demapping algorithm with quadratic rather than exponential complexity. In the general cases, when multilevel codes are employed, we propose power-allocation strategies to facilitate the iterative decoding/dempaping algorithm. Using the unequal power-allocations and the Gaussian-approximation-based suboptimal demapping algorithm (with linear complexity), coded modulation with high bandwidth efficiency can be implemented.

This correspondence concerns the performance analysis of turbo-single-parity-check (SPC) codes based on the union bound of bit-error rate (BER). A treatment of the special interleavers used in turbo-SPC codes is discussed. It is shown that simple two- or four-state turbo-SPC codes with multiple component codes can perform comparably as (or even better than) the 16-state standard turbo codes. Using more complex trellis codes (with state number more than 4) appears unnecessary for such codes. Instead, performance improvement can be achieved by increasing the number of component codes, which maintains the low decoding complexity property of turbo-SPC codes.

This paper presents a family of space-time codes employing interleavers to separate signals form different antennas. Noticeable performance improvement has been observed compared with existing schemes. An interactive detection algorithm is derived. The complexity involved is very low, and increases only linearly with the number of transmit antennas.

This paper presents an asynchronous interleave-division multiple-access (IDMA) scheme, in which users are distinguished by different chip-level interleaving methods instead of by different signatures as in a conventional code-division multiple -access (CDMA) scheme. A very low-cost iterative detection algorithm is derived for the IDMA scheme based on a chip-by-chip detection principle. The proposed scheme can achieve nearly optimal performance for systems with a large number of users. Furthermore, receiver simplicity as well as high performance can be maintained in multipath environments.

This paper presents a family of concatenated two-state trellis-coded modulation (CT-TCM) schemes. Compared with the existing turbo-type bandwidth-efficient coded modulation schemes, the proposed codes have significantly reduced complexity without sacrificing performance. A joint design strategy for all component codes is established. This leads to so-called asymmetrical and time-varying trellis structures, which possess good Hamming and Euclidean distance distributions. The performance of the proposed codes is demonstrated by simulation results.

This paper is concerned with a class of low-rate codes constructed from Hadamard code arrays. A recursive encoding principle is employed to introduce an interleaving gain. Very simple trellis codes with only two or four states are sufficient for this purpose, and the decoding cost involved in the trellis part is typically negligible. Both simulation and analytical results are provided to demonstrate the advantages of the proposed scheme. The proposed scheme is of theoretical interest as it can achieve performance of BER=10/sup -5/ at E/sub b//N/sub 0//spl ap/-1.2dB (only about 0.4 dB away from the ultimate low-rate Shannon limit) with an information block size of 65534. To the authors' knowledge, this is the best result achieved to date with respect to the ultimate Shannon limit. With regard to practical issues, the decoding complexity of the proposed code is considerably lower than that of existing low-rate turbo-type codes with comparable performance.

This paper presents a simple erasure correcting coding scheme based on semi-random low-density-parity-check codes. Compared with tornado codes, the proposed scheme has much simpler encoder and decoder structures, yet still has proven capacity-achieving performance.

Techniques using interleaving as the basic means for signal separation are introduced for both multiple access systems and multiple transmit antenna systems. A very low-cost chip-by-chip iterative detection algorithm is presented. The proposed schemes can achieve nearly optimal performance for system with a large numbers of users or transmit antennas.

We report the progress in concatenated tree (CT) codes and related schemes, including low rate codes for CDMA applications and bandwidth efficient coded modulation schemes. It is shown that CT codes provide efficient solutions for various situations. Near capacity performances (within about 0.5 dB) can be achieved at significantly reduced decoding costs.

This letter is concerned with a family of modified turbo-type codes, referred to as turbo-SPC (single parity check) codes. A technique based on the SPC code is introduced to replace puncturing for rate adjustment. A noticeable feature of the proposed scheme is the significantly reduced decoding complexity compared with the standard punctured turbo code. The cost reduction factor becomes more noticeable as rate increases (over ten times for rate /spl rarr/1). The error-rate floor problem known to turbo codes can also be improved using the proposed scheme. For moderate to high rates, performances of about 0.5 dB from the theoretical limits at BER=10/sup -5/ have been observed for turbo-SPC codes.

This paper introduces a family of error-correcting codes called zigzag codes. A zigzag code is described by a highly structured zigzag graph. Due to the structural properties of the graph, very low-complexity soft-in/soft-out decoding rules can be implemented. We present a decoding rule, based on the Max-Log-APP (MLA) formulation, which requires a total of only 20 addition-equivalent operations per information bit, per iteration. Simulation of a rate-1/2 concatenated zigzag code with four constituent encoders with interleaver length 65 536, yields a bit error rate (BER) of 10/sup -5/ at 0.9 dB and 1.3 dB away from the Shannon limit by optimal (APP) and low-cost suboptimal (MLA) decoders, respectively. A union bound analysis of the bit error probability of the zigzag code is presented. It is shown that the union bounds for these codes can be generated very efficiently. It is also illustrated that, for a fixed interleaver size, the concatenated code has increased code potential as the number of constituent encoders increases. Finally, the analysis shows that zigzag codes with four or more constituent encoders have lower error floors than comparable turbo codes with two constituent encoders.

This paper is concerned with a family of concatenated tree (CT) codes. CT codes are special low-density parity check (LDPC) codes consisting of several trees with large spans. They can also be regarded as special turbo codes with hybrid recursive/nonrecursive parts and multiple constituent codes. CT codes are decodable by the belief-propagation algorithm. They combine many advantages of LDPC and turbo codes, such as low decoding cost, fast convergence speed, and good performance.

We present a combined orthogonal frequency-division multiplexing (OFDM) and code-division multiple-access cellular system. It is derived from the OFDM model by introducing an extra code-shift division multiple access layer. This mitigates intercell interference without affecting intracell orthogonality and such property can be maintained in multipath environments. The new scheme is suitable for both up and down links. It retains the low-receiver complexity property of the OFDM system.

An efficient coset based symbol-by-symbol soft in/soft-out a posteriori probability (APP) decoding algorithm is presented for the Golay code. Its application in the iterative decoding of concatenated Golay codes is examined.

We investigate the decoding technique and performance of concatenated Hadamard codes. Efficient soft-in-soft-out decoding algorithms based on the fast Hadamard transform are developed. The performance required by CDMA mobile or PCS speech services, e.g., BER=10/sup -3/, can be achieved at E/sub b//N/sub 0/=0.5 dB using short interleaver length of 198 bits.

This paper is concerned with the decoding technique and performance of multi-dimensional concatenated single-parity-check (SPC) code. A very efficient sub-optimal soft-in-soft-out decoding rule is presented for the SPC code, costing only 3 addition-equivalent-operations per information bit. Multi-dimensional concatenated coding and decoding principles are investigated. Simulation results of rate 5/6 and 4/5 3-dimensional concatenated SPC codes are provided. Performance of BER=10/sup -4/-10/sup -5/ can be achieved by the MAP and max-log-MAP decoders, respectively, with E/sub b//N/sub 0/ only 1 and 1.5 dB away from the theoretical limits.

This paper presents a symbol-by-symbol decoding method for the F/sub 24/ code. It forms the core part of an iterative Max-Log-MAP filtering algorithm for the product F/sub 24/ code and noticeable coding gain is observed by simulation The complexity of the proposed algorithm is very modest. The relatively short frame length of the product F/sub 24/ code can be an advantage for its applications in some communication systems.

This paper focuses on designing efficient multicast time slot assignment (MTSA) algorithms for TDM switching systems, Based on a packet compatibility matrix, the MTSA can be transformed to the well-known graph-coloring problem. We show that the MTSA problem is NP-complete. A lower bound on the frame length of a multicast time slot assignment is then found to be the clique number of the MTSA equivalent graph. Two efficient MTSA algorithms, called the contention-based ordering (CBO) algorithm and the hybrid ordering algorithm, are proposed. Their performance is compared with the three existing algorithms and the lower bound through extensive simulations. We found that the CBO algorithm, which has one of the lowest computational complexities, gives the best performance among all five algorithms studied. The average frame length generated by the CBO algorithm is within 1% above the lower bound. We also show that (i) the previously reported DAC algorithm has the poorest performance despite its highest complexity, and (ii) the previously reported CCBO algorithm has only a comparable performance to the simple greedy algorithm.

A unified investigation is presented for low-sensitivity, limit-cycle-free filter structures. It is shown that important properties like boundedness and pseudopassivity are closely related to the symmetry of the system matrix description. Implementations by digital circuits are considered. It is demonstrated that symmetric matrix systems can be designed for optimal circuit performance. Sensitivity can be minimized if the deviation of component values is kept symmetric, which can be achieved for a digital filter design by carefully selecting the coefficient truncations.>