Mobile/wireless virtual reality (VR) services, especially immersive 360° VR videos, have advanced unprecedentedly in recent years. However, the high bandwidth requirement of VR services has compounded the burden on wireless networks. Multicast is a high potential technique for alleviating the bandwidth requirement of 360° VR video streaming, but the multicast capacity is still constrained by the users with poor channel conditions, and it vanishes when the number of users increases while the number of the base station (BS) antennas is fixed. To overcome the drawbacks of multicast, sidelink, which is an adaptation of the core LTE standard that allows the device-to-device (D2D) communications without going through a BS, can be utilized. In this article, two sidelink-aided multicast scenarios (i.e., independent decoding and joint decoding) are studied for multiquality tiled 360° VR video transmission. We propose a utility model for each scenario, and quality level selection, sidelink sender/receiver selection, and transmission resource allocation are optimized to maximize the total utility of all users under the bandwidth constraints as well as the quality smoothness constraints for multiquality tiles. We then develop an iterative two-stage algorithm to obtain suboptimal solutions to the formulated mixed-integer nonlinear programming (MINLP) problems. Simulation results demonstrate the advantage of the proposed solutions over several baseline schemes.

In this paper, a new rate combining model for coded modulation with practical channel codes is proposed, resulting in a novel utility function. The mathematical properties of the new utility function, such as convexity, are studied. This utility function generalizes the harmonic mean function and demon-strates great potential in various applications in communication and learning problems. The proposed rate combining model is applied to the power allocation problem for parallel Gaussian channels with coded modulation inputs. Our results show that the optimal power allocation based on the new rate combining model outperforms other well known schemes such as mercury water-filling in parallel channels or multiple-input and multiple-output (MIMO) channels.

In this paper, we first define a high dimensional (HiDi) channel characteristics, i.e., space-frequency covariance, for wideband MIMO-OFDM systems. We then design the conversion of the HiDi covariance in frequency domain from one carrier frequency to another, e.g., for FDD systems. Specifically, we apply the projection method in a Hilbert space to estimate the power angle delay spectrum and form the frequency domain conversion of the space-frequency covariance. We also obtain the asymptotic solutions when considering the infinite delay spread, which significantly reduces the complexity. Moreover, we generalize the conversions of space-frequency covariance in both spatial and frequency domains with two exemplary multi-panel scenarios. We then apply the general solutions to a specific antenna array configuration, i.e., uniform linear array (ULA), and obtain the explicit expressions of conversions. Numerical simulations demonstrate the efficiency of the designed conversions.

In this paper, we consider an adaptive grouped physical layer multicasting for large-scale multi-antenna wireless systems in which a set of users are divided into several groups and each user group are assigned with a unique beamforming vector for multicast transmissions on the orthogonal resources. Based on the adaptive grouped multicast framework, we consider the joint design of user grouping and multicast beamforming adapted to the user channels. Two design objectives are studied, i.e., the average-rate maximization and the max-min fairness. We propose an iterative user grouping and beamforming design method for both optimization objectives. For iterative user grouping, we present a method for selecting better initial grouping centers. Moreover, to overcome the issue of converging to a local optimum for the iterative approach, we propose a novel enhancement scheme via user grouping perturbation, which performs very close to the exhaustive grouping search. Simulation results demonstrate the efficacy of the proposed designs.

In this paper, we consider the design of multiuser (MU) massive multiple-input and multiple-output (MIMO) employing hybrid beamforming, i.e., an analog radio frequency (RF) beamforming at the front end concatenated with a digital baseband precoding. We present several RF beam feedback protocols with small overhead, i.e. the RF beam indices with or without channel quality index (CQI). Based on the beam feedback schemes, we design novel algorithms to jointly select the transmit RF beams and schedule the users to improve the system throughput. Specifically, when the users feed back multiple candidate RF beams, the new algorithms resolve the conflicts when different users feedback some same RF beams. The simulation results demonstrate the efficacy of the proposed algorithms.

In cellular communications, deploying a larger number of antennas at the base station, also called massive multiple-input multiple-output (MIMO), can offer a significant improvement in system throughput. In this paper, we exploit the spatial fading correlations in massive MIMO to reduce the downlink training and the corresponding feedback overhead in frequency division duplexing systems. We first study the user clustering, where the users with similar spatial channel correlations are clustered together. In the study, we provide the optimal metric and prove the convergence of the user clustering. Then, we propose an efficient eigenspace training and precoding (EETP) framework, where two different prebeamforming matrices are designed to minimize the channel estimation error and to manage the inter-user interference, respectively. In the results, we show that the channel estimation error for EETP decreases monotonically when either the number of prebeamforming vectors or the number of clusters increases. The spectral efficiency of the new algorithms is evaluated extensively with different user distributions, errors in channel correlations, different numbers of clusters, and different coherence block lengths, as well as with dynamic user scheduling for a large number of users. The new EETP not only achieves significant savings in the downlink training and the corresponding feedback, but also offers significantly higher system throughput compared with the existing schemes in the literature.

We consider the problem of downlink multicast transmission of user data in massive MIMO systems. Due to the nature of multicast transmission, the common data rate in a multicast group is constrained by that of the user with the worst Signal-to-Noise-Ratio (SNR). As a consequence, serving a large number of users in a single multicast group might degrade the system performance. To overcome this drawback, utilizing spatial degrees of freedom offered by a large number of transmit antennas, we propose to dynamically divide the set of serving users into multiple multicast groups and jointly design the user grouping pattern and co-channel beamforming vectors of these groups. Given the NP-hardness of the considered problem, we decompose it into a multi-group multicast beamforming subproblem and a user grouping subproblem. We proposed several low-complexity methods to iteratively solve these subproblems in order to obtain a suboptimal solution to the original problem. Simulation results show that our proposed GRouping And Beamforming (GRAB) scheme achieve significantly higher average sum-rate performance compared to that of the existing multicast schemes.

In this paper, a new approach to the wireless link adaptation based on theoretical results from the finite blocklength analysis is proposed. Theoretical bounds on parallel complex AWGN channels with coded modulation inputs are studied. A model based on these theoretical bounds is provided for the application of link adaptation. The proposed approach to link adaption only requires a significantly small number of simulations to tune the model and is able to predict the performance of parallel channels with arbitrary combinations of SNRs without referring to any lookup table as in the traditional approach. The model is tested with turbo and polar codes. The result demonstrates significant improvement over the traditional methods in link adaptation in terms of accuracy and the amount of computation.

In this article, we propose a novel cooperative hierarchical caching framework in a Cloud Radio Access Network (C-RAN), in which a new cloud-cache at Cloud Processing Unit (CPU) is envisioned to bridge the storage-capacity/delay-performance gap between the traditional edge-based and core-based caching paradigms. A delay-cost model is introduced and the cache placement problem is formulated that aims at minimizing the average delay-cost of content delivery in the network. Given the NP-completeness of the cache placement problem, we propose a low-complexity heuristic cache-management strategy comprising of a proactive cache-distribution algorithm and a reactive cache-replacement algorithm. Furthermore, a Cache-Aware Request Scheduling (CARS) algorithm is devised in order to optimize online the tradeoff between content download rate and content access delay. Via extensive numerical simulations-carried out using both real-world YouTube video requests and synthetic content requests-it is demonstrated that the proposed cache-management strategy outperforms traditional caching strategies in terms of cache hit ratio, average content access delay, and backhaul traffic load. Additionally, it is shown that the proposed CARS algorithm achieves superior tradeoff performance over traditional approaches that optimize either users' rate or access delay alone.

This paper considers the design of network coding schemes for reliable wireless broadcast and multicast transmissions, in which the same packet is broadcast to a group of receivers. Network coding across multiple broadcasted packets is employed to generate redundant packets for the broadcast retransmissions so that the lost packets can be recovered. It is assumed that optimal decoders are employed at the receivers and the focus is on the design of short block codes with small numbers of redundant bits. To this end, use if first made of the residual graph representation to calculate the error probability of the optimal decoder. Then two code design schemes are proposed to minimize the error probability, including a low-complexity deterministic greedy code design algorithm as well as a stochastic code construction algorithm inspired by the simulated annealing technique. Extensive simulation studies have been carried out to assess the performance of the proposed schemes. It is seen that for a given number of retransmissions, the proposed network coding schemes can considerably increase the average number of recovered packages per user at the receivers and thereby improve the spectral efficiency over traditional coding methods.

In this paper, we consider the design of user grouping and scheduling for large-scale multiple-input multiple-output (MIMO) frequency-division-duplexing (FDD) systems. Based on a recently proposed two-stage precoding framework, we first propose an improved K-means user grouping scheme which allocates the users to different pre-beamforming groups using the second-order channel statistics, and then a user grouping scheme that considers both load balancing and precoding design. After user groups are so determined, we present a dynamic user scheduling scheme where second-stage precoding is designed based on instantaneous channel conditions. We demonstrate the efficacy of the proposed schemes through simulations.

Heterogeneous wireless networks are formed when a set of disparate transmission points serve a multitude of users over an available spectrum. In order to enable efficient resource allocation over such networks, the set of transmission points is partitioned into multiple clusters and each cluster is assigned a set of users that it must serve. Our contribution in this paper is the design of an approximation algorithm for the resource allocation in each cluster. We show that this resource allocation problem is strongly NP-hard and that our algorithm yields a constant factor approximation, for a fixed cluster size. Our evaluations over a realistic heterogeneous network model show that significant gains can be realized by our algorithm, provided the feedback available from the users is fully exploited.

In this paper, we consider the design of a scheduling algorithm for downlink multiuser systems with a finite-buffer traffic model to reduce average packet delay, while maintaining the stability condition of the networks. We propose a new Buffer-Aware Adaptive (BAA) scheduler which considers both channel state and buffer conditions for resource allocation. The generalized form of the proposed algorithm is also established. Stability considerations of the proposed algorithm are provided, along with the average throughput lower bound and approximation. Both single-link and system-level simulation results demonstrate that the proposed scheduler appears to outperform existing scheduling algorithms in terms of average packet delay.

We propose a robust close-to-capacity dirty-paper coding (DPC) design framework in which multi-level low density parity check (LDPC) codes and trellis coded quantization (TCQ) are employed as the channel and source coding components, respectively. The proposed design framework is robust in the sense that it yields close to capacity solutions in the high-, medium-, and low-rate regimes. This is in contrast to existing practical DPC schemes that perform well only in one or two of these regimes, but not all three. We design codes for transmission rates of 0.5, 1.0, 1.5, and 2.0 bits/sample (b/s) using one, two, three, and four LDPC levels; at a block length of 2×105, the codes perform 0.95, 0.58, 0.55, and 0.54 dB from the corresponding information theoretic limits, respectively. We also propose a low-complexity decoding scheme that does not involve iterative message passing between the source and channel decoders; the low-complexity scheme performs only 1.08, 0.85, and 0.79 dB away from the theoretical limits at transmission rates of 1.0, 1.5, and 2.0 b/s, respectively.

In this paper, we consider the downlink (DL) multiuser (MU) multi-input-multi-output (MIMO) scheduling for the fourth generation LTE Advanced (LTE-A) cellular networks. The DL MU-MIMO scheduling can be posed as an optimization problem to maximize the weighted sum rate subject to several practical constraints, such as a per-user rank constraint. Due to these constraints finding the optimal solution becomes an NP-hard problem. Consequently, we propose an efficient albeit sub-optimal rank balancing approach that enforces the peruser rank constraint and present several rank balancing based scheduling algorithms. We show that the proposed algorithms are guaranteed to yield constant-factor approximations. Simulation results demonstrate that the proposed rank balancing based scheduling algorithms outperform other competing schemes over various relevant system scenarios.

Discrete Fourier transform (DFT) based channel estimation (CE) has been widely studied as a practical CE scheme over the OFDM based wireless systems. The conventional DFT-based channel estimation utilizes a transform domain cut-off filter to suppress the noise in the time domain. However, this method can suffer significant performance loss due to the channel impulse response (CIR) energy leakage, especially when the available pilot sub-carriers are confined to a small portion of the system bandwidth. In this paper, we propose an enhanced DFT-based channel estimation technique for the long term evolution (LTE) based cellular uplink. A sinc-null based noise power estimation method in conjunction with a dynamic noise removal technique is proposed to suppress the noise in the time domain and achieve better performance while keeping the complexity in check. Simulation results show that the proposed scheme not only achieves better mean square error (MSE) and block error rate (BLER) performance but also exhibits robustness to timing offsets compared to existing DFT based CE schemes.

We consider a downlink multi-user multi-input-multi-output (MU-MIMO) fading channel wherein the base station can schedule several user terminals on the same time-frequency resource. A severe practical problem in MU-MIMO is that when computing its feedback report, a user does not have an accurate estimate of the interference it might see (if scheduled) from the signals intended for the other co-scheduled users. This results in a mismatch between the user reported signal-to-interference-plus-noise-ratio (SINR) and the one it actually observes in the aftermath of scheduling. To alleviate this problem we propose to inform each user (in a slow or semi-static manner) about the rank of the precoding matrix that it should report, along with an estimate of the total number of streams that the base station expects to co-schedule on a time-frequency resource. The suggested rank and the expected total number of streams can be user-specific and together convey the expected total number of co-scheduled interfering streams to the intended user. Each user then computes one or more SINRs for all the precoding matrices having the suggested rank and reports its preferred precoding matrix along with the corresponding SINRs. The SINRs are computed after assuming that the co-scheduled interfering streams will be transmitted along vectors isotropically distributed in the orthogonal complement of the range of the precoding matrix being examined. Alternatively, the SINRs can be computed after assuming that the co-scheduled interfering streams will be transmitted along the worst-case choice of mutually orthogonal vectors that lie in the orthogonal complement. We show that the proposed solutions, while requiring negligible additional signalling overhead, mitigate the mismatch problem to a large extent and result in significant improvements in system throughput.

In this paper, we consider resource allocation in the the fourth generation multi antenna (4G MIMO) cellular uplink. In particular, we consider the two 4G standards, IEEE 802.16m and 3GPP LTE-A, that have recently been approved. We show that the uplink resource allocation problems in both 802.16m and LTE-A networks are NP-hard. We then propose constant-factor polynomial-time approximation algorithms for both these problems. We also provide linear programming (LP) based upper bounds to benchmark the performance of our proposed approximation algorithms. Simulations reveal that the proposed algorithms have excellent performance, much superior to their worst-case guarantees.

We propose a close-to-capacity dirty-paper coding framework which employs multi-level low density parity-check (LDPC) and trellis coded quantization. The proposed coding framework is robust in the sense that it performs close to capacity in the high as well as the low rate regimes. This is in contrast to existing practical DPC schemes which perform well at one of these regimes, but never both. In order to evaluate the performance of our scheme, we consider its application to a cognitive radio channel. At a block length of 2 × 105, the designed dirty-paper coding scheme operates within 0.95, 0.58 and 0.6 dB of the theoretical limit at transmission rates of 0.5, 1.0 and 1.5 bits/sample, respectively. As far as the authors are aware, this is the best performance reported in the literature so far.

In this paper, we consider the design of a binary network coding scheme for the wireless broadcast, in which the same packet sequence is broadcasted to multiple receivers. In the proposed coding scheme, a short block code is employed for the coding across the broadcasted packets to generate redundant packets to recover the lost packets for all terminals in the service. In particular, we assume the optimal decoder and consider the design of short block codes with a small number of redundancy. We present a residual graph based code design method and propose an iterative design algorithm with stochastic update. The short block code is then extended with an improved pseudo-random code to achieve the flexibility on redundancy. Numerical results show that the proposed coding scheme provides superior performance over other coding schemes.

In this paper, an efficient closed-loop link adaption scheme consisting of adaptive modulation and coding as well as adaptive precoding is proposed for the 3GPP LTE-A uplink. The uplink envisaged in the LTE-A cellular network will support precoded multi-rank transmission from the users and have base stations with advanced non-linear receivers. Our proposed scheme considers one such advanced receiver, namely, the turbo successive interference cancelation (Turbo-SIC) receiver. The main difficulty in designing link adaptation schemes for these advanced non-linear receivers is that the soft-outputs of such receivers cannot be simply modeled using a scalar Gaussian channel characterized by a signal-to-interference-plus-noise ratio (SINR). To circumvent this difficulty, we employ SINRs corresponding to an ordered hard-decision SIC receiver, that can be explicitly expressed in closed form. The proposed scheme accurately predicts the turbo SIC performance and results in a perfect match between the predicted and actually simulated performance in terms of block error rate (BLER) and the spectrum efficiency. Realistic and extensive simulations reveal that it provides the highest actual spectrum efficiency compared to other competing schemes.

In this paper, we consider the doped decoder for Luby-Transform (LT) codes, where based on the decoder feedback, the decoding process is revived by retransmission of the in formation packet. We propose several improved doping methods to reduce the average doping rate. We then provide an analysis of the proposed doping methods based on the study of the decoding ripple evolution. Both analytical and simulation results show that the proposed doping approaches provide significant performance gain over the existing random doping strategy. We then apply the doped LT decoding to the wireless broadcast system in which limited feedback is allowed. We propose a majority vote based doping selection and demonstrate the efficiency of the proposed doping selection through simulations.

In this paper, we consider a downlink (DL) multiuser (MU) multi-input-multi-output (MIMO) channel with linear precoding where the base station simultaneously schedules several user terminals on the same frequency sub-band. We assume imperfect (or quantized) per-user channel state information at the base station and present two types of channel state information (CSI) reports from user terminals, namely, the CSI report that assumes the single-user (SU) MIMO transmissions and the enhanced CSI feedback report that assumes the MU-MIMO transmissions, and in the latter case we consider both uniform and nonuniform power allocations. To improve the MU-MIMO system performance, we propose signal-to-interference-plus-noise ratio (SINR) approximation techniques that utilize the quantized CSI available at the base station and improve the rate matching. We also introduce user pooling techniques which enable a reduction in feedback signaling overhead via per-user feedback mode selection. The proposed techniques also allow unconstrained user pairing at the base station scheduler and hence enable dynamic switching between SU and MU MIMO transmissions. The simulation results demonstrate the efficiency of the proposed MU-MIMO enhancement techniques.

We consider the problem of maximizing the weighted sum rate (WSR) in MIMO broadcast channel where the number of transmitted streams (ranks) is constrained. The problem is treated both with or without interference pre-compensation also known as dirty paper coding (DPC). The rank constrained problem is highly motivated by the practical consideration on the receiver complexity in current wireless systems such as LTE. We propose a unified algorithm based on fixed point iteration. The proposed approach has very fast convergence rate that usually converges to the minimal number of streams for each user and finds the corresponding optimal precoding matrix. Rank minimization is particularly desirable in practice. The order in which the users' streams are encoded is crucial when dirty paper coding is allowed. We prove that the optimal user ordering does not depend on the transmission rank constraints and is given only by the weight vector. Using simulations, we compare the performance of our proposed scheme with the best known algorithms in the literature and demonstrate the effect of rank constraints.

We propose a practical message-wise unequal error protection (UEP) scheme using low-density parity-check (LDPC) codes, where one or more special messages are more protected than other ordinary messages. In contrast to the information theoretic cavity coding scheme, which discards the codewords of ordinary messages near those of special messages, the proposed coding scheme performs codeword flipping to separate the codewords of special and ordinary messages without discarding any codewords. To better distinguish the original and flipped codewords, the LDPC codes with all-odd degree check nodes are employed. The decoder performs message type detection and codeword flipping detection based on the unsatisfied check nodes in iterative decoding. We provide performance analysis for both the message type detection and the codeword flipping detection. Moreover, we provide an asymptotic analysis on the detection error exponent to reveal the relationship between the proposed practical coding scheme and the information theoretically optimal cavity coding. Simulation results are provided to show that the proposed practical message-wise UEP schemes offer capacity-approaching protections to both types of messages as if only one type is transmitted.

In this paper, we propose a practical and systematic approach to implement the MIMO transmission with rank adaptation for 60 GHz systems. In the 60 GHz system with multiple antennas, the transmit and receive (Tx-Rx) antenna arrays are grouped into a number of subarrays with a predetermined subarray separation based on the derived geometrical criteria of creating high rank MIMO in LoS environments. We first apply an enhanced blind beamforming technique based on a stochastic gradient algorithm (SGA) for the inner-subarray antennas, which does not require channel state information (CSI) at either the transmitter or the receiver. Secondly, the composite MIMO channel, as a joint effect of Tx-Rx beamforming and the channel impulse response, can be estimated with much reduced complexity. Finally, the MIMO transmission with rank adaptation is performed by adaptively selecting the better scheme out of the high-rank spatial multiplexing and the rank-1 beamforming whichever gives higher system throughput. Simulation results show that high-rank spatial multiplexing and rank-1 beamforming outperform each other at different geometrical placements and transmit power settings. The proposed MIMO transmission with rank adaptation offers significant performance gain especially at high signal-to-noise ratio (SNR) regions.

In a cognitive radio (CR) network, secondary users (SUs) are allowed to opportunistically access a licensed spectrum that is not currently being occupied by primary users. This paper is concerned with the problem of how to quickly and accurately locate an unoccupied channel or determine that there is no unoccupied channel, from multiple (yet finite) candidate channels for a SU with a single detector. To design channel search algorithms, we propose a design criterion that minimizes average searching time subject to constraints on the error probabilities for a multichannel system. Relying on the proposed design criterion, we develop two efficient channel search algorithms that are based on a sequential application of the sequential probability ratio test and energy detection to the candidate channels.

We consider the joint channel and network code design for a half-duplex 4-node multiple-access relay system with two sources, one relay, and one destination. The relay combines the information from both sources and transmits it to the destination together with both sources. We consider two network coding schemes for information combining at the relay, namely, the superposition coding (SC) and the Raptor coding (RC). For both SC and RC, the profiles for joint channel and network coding are optimized based on the extrinsic information transfer (EXIT) function analysis. For both additive white Gaussian noise (AWGN) and block fading channels, the multiple-access relay system with optimized profiles exhibits significant performance gains over that employing the code profile optimized for either the single-user AWGN channel or the 2-user multiple-access channel.

We implement a dirty-paper coded framework for the cognitive radio channel. We assume that the cognitive user has non-causal knowledge about the primary user's transmissions. Thus the secondary receiver can employ dirty-paper coding to counter the effect of any interference from the primary user. In addition, we consider a situation where the introduction of the cognitive user should not affect the performance of the primary system -- nor should the primary system have to change its encoding/decoding process. For the primary user we use a low-density parity-check code and a 4-ary pulse amplitude modulation format. For the cognitive user, we propose a dirty-paper coding scheme which employs trellis-coded quantization as the source code and an irregular repeat-accumulate code as the channel code. At a transmission rate of 1.0 bits/sample, the designed dirty-paper coding scheme operates within 1.23 dB of the theoretical limit.

We propose a practical message-wise unequal error protection (UEP) scheme using low-density parity-check (LDPC) codes, where one or more special messages are more protected than other ordinary messages, which performs codeword flipping to separate the codewords of special and ordinary messages. To better distinguish the original and flipped codewords, the LDPC codes with all-odd degree check nodes are employed. The decoder performs message type detection and codeword flipping detection by tracking the number of unsatisfied check nodes in iterative decoding. We provide both finite-length and asymptotic performance analysis for the proposed coding scheme. Simulation results are provided to show that the proposed practical message-wise UEP schemes offer capacity-approaching protections to both types of messages as if only one type of message is transmitted.

We propose a rateless coded protocol for a half-duplex wireless relay channel where all links experience independent quasi-static Rayleigh fading. The protocol utilizes a combination of rateless coded decode-forward and compress-forward relaying schemes. Assuming very limited feedback from the destination, we derive the theoretical performance limits specifically with BPSK modulation. We then implement the rateless coded relaying protocol using carefully designed Raptor codes.

We introduce an implementation-friendly binary message-passing decoding method for low-density parity-check (LDPC) codes that does not require the degree information of variable nodes or degree dependent parameters. For hard decision decoding, given its low-complexity, the implementation cost for variable node degree information is an important consideration. We develop an estimation method for the extrinsic error probability (EEP) as well as its analysis. The proposed method offers similar performance as the existing methods for time-invariant decoding in most cases, while it facilitates efficient circuit implementations of the LDPC decoder.

We consider the code design for a half-duplex 4-node joint relay system with two sources, one relay, and one destination. The relay combines the information from both sources and transmits it to the destination together with both sources. We consider two coding schemes for information combining at the relay, namely, the superposition coding (SC) and the Raptor coding (RC). The Raptor codes are employed at the sources as well as the relay. The relay and the destination perform iterative a posteriori probability (APP) detection and soft Raptor decoding. For both SC and RC, the profiles for Raptor codes are optimized based on the extrinsic information transfer (EXIT) function analysis. For both the additive white Gaussian noise (AWGN) and block fading channels, the joint relay system with optimized profiles exhibits significant performance gains over that employing the code profile optimized for either the singleuser AWGN channel or the 2-user multiple-access channel.

We present a multilayer space-time-frequency (STF) coding scheme for wideband multiple-input multiple-output (MIMO) systems employing orthogonal frequency-division multiplexing (OFDM). With multiple receive antennas, we employ an iterative demodulator consisting of a low-complexity multilayer detector and a simple soft combiner. The system performance is optimized by efficient power allocation among layers, as well as interleaver design and extrinsic scaling. The results show that the proposed multilayer STF coding scheme performs close to or even better than the optimized linear dispersion (LD) STF codes with maximum likelihood (ML) decoding. Unlike the existing STF codes, the proposed multilayer STF strategy is a universal scheme that exhibit excellent performance under various system configurations and channel statistics.

We introduce simple yet efficient ARQ protocols in conjunction with two types of anti-jamming coding techniques - rateless coding and piecewise coding - for cognitive radios. For piecewise coding, we propose to employ systematic codes to facilitate efficient selected retransmissions and design short codes to maximize secondary user throughput. For rateless coding, we consider a protocol that transmits new parity packets during retransmission and show that this scheme is stable if the jamming rate of the system is within a certain range. For both anti-jamming coding schemes, the corresponding simple ARQ protocols provide significant improvement in secondary user throughput. Moreover, the piecewise coding together with its ARQ protocol offers similar or better throughput performance compared with the rateless coding counterpart, without incurring the stability issue.

In this paper, we consider the design of efficient anti-jamming coding techniques for recovering lost packets transmitted through parallel channels. We present two coding schemes with small overhead and low complexity, namely, rateless coding and piecewise coding. For piecewise coding, we propose the optimal as well as several suboptimal design methods to build short block codes with small number of parity checks. One application of the anti-jamming coding techniques is in a cognitive radio system to protect the secondary users from the interference by the primary users. For such application, we consider two types of subchannel selections, i.e., the single uniform and general non-uniform subchannel selections. Throughput and the goodput performance of the secondary users employing either anti-jamming coding technique is analyzed under both subchannel selection strategies. The results show that both coding techniques provide reliable transmissions with high throughput and small redundancy. The piecewise coding using the designed short codes provides better performance with smaller overhead under low to medium jamming rate. For non-uniform subchannel selection, the designed short code improves the throughput and goodput performance of secondary transmission with antijamming piecewise coding while the rateless coding provides similar or worse performance than that in the uniform case.

We present a multilayer space-time-frequency (STF) coding scheme for wideband multiple-input multiple-output (MIMO) systems employing orthogonal frequency-division multiplexing (OFDM). With multiple receive antennas, we employ an iterative demodulator consisting of a low-complexity multilayer detector and a simple soft extrinsic combiner. The system performance is optimized by efficient power allocation among layers, as well as interleaver design and extrinsic scaling to reduce the extrinsic correlation. Simulation results demonstrate that the proposed multilayer STF coding scheme performs close to or even better than the optimized linear dispersion (LD) STF codes with maximum likelihood (ML) decoding. Unlike the existing STF codes, which need to be designed for different system configurations and channel statistics, the proposed multilayer STF strategy is a universal scheme that exhibit excellent performance under various conditions.

Abstract We introduce simple yet efficient automatic retransmission request (ARQ) protocols in conjunction with two types of anti‐jamming coding techniques—rateless coding and piecewise coding—for protecting secondary users' data transmissions in cognitive radio systems. For piecewise coding, we propose to employ systematic codes to facilitate efficient selected retransmissions and design short codes to maximize secondary user throughput. For rateless coding, we consider a protocol that transmits new parity packets during retransmission and show that this scheme is stable if the jamming rate of the system is within a certain range. It is seen that for both anti‐jamming coding schemes, the corresponding simple ARQ protocols provide significant improvement in secondary user throughput. Moreover, the piecewise coding together with its ARQ protocol offers similar or better throughput performance compared with the rateless coding counterpart, without incurring the stability issue. Copyright © 2009 John Wiley & Sons, Ltd.

We consider the design of adaptive hybrid automatic retransmission request (ARQ) with incremental redundancy (IR) in which the transmission rates of different blocks in one hybrid ARQ process can be different. The throughput of adaptive IR hybrid ARQ in block fading channels is formed based on the renewal-reward theorem. Two types of input signals are considered, namely, Gaussian inputs and practical turbo coded modulation. For Gaussian inputs, the error probability after each transmission is obtained from the outage rate. For turbo coded modulation, we obtain the error rate after each transmission block by applying union-Bhattacharyya (UB) bound for parallel channels. The throughput optimization is then formed to seek the optimal transmission rates. The results show that adaptive IR HARQ provides higher throughput than non-adaptive IR HARQ and chase combining in the moderate-to-high SNR region.

The authors propose a concatenated scheme to reduce the peak-to-average power ratio (PAPR) in coded orthogonal frequency-division multiplexing (OFDM) systems. First, they employ a label-bits-inserted encoder of a random-like code to achieve selected mapping (SLM). Then they set a threshold at the selector to limit the number of candidate sequences. Both analytical and numerical results show that the complexity of the SLM implemented by the label-bit-inserted encoder can be significantly reduced by threshold limited selection. With the same complexity, the performance of PAPR reduction is improved. The proposed concatenated PAPR reduction scheme enjoys many advantages including low-complexity, small overhead, no side information transmission and no performance loss or additional complexity at the receiver.

We treat the problem of designing low-density parity-check (LDPC) codes to approach the capacity of relay channels. We consider an efficient analysis framework that decouples the factor graph (FG) of aB-block transmission into successive partial FGs, each of which denotes a two-block transmission. We develop design methods to find the optimum code ensemble for the partial FG. In particular, we formulate the relay operations and the destination operations as equivalent virtual MISO and MIMO systems, and employ a binary symmetric channel (BSC) model for the relay node output. For AWGN channels, we further develop a Gaussian approximation for the detector output at the destination node. Jointly treating the relay and the destination, we analyze the performance of the LDPC-coded relay system using the extrinsic mutual information transfer(EXIT) chart technique. Furthermore, differential evolution is employed to search for the optimum code ensemble. Our results show that the optimized codes always outperform the regular LDPC codes with a significant gain; in the AWGN case, when Protocol-II is employed and the relay is close to the source, the optimized code performs within 0.1dB to the capacity bound.

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.

We consider a slow-fading narrowband multiple-input multiple-output (MIMO) multiple-access channel (MAC) in which multiple users, each equipped with multiple transmit antennas, communicate to a receiver equipped with multiple receive antennas. The users are unaware of the channel state information (CSI) whereas the receiver has perfect CSI and employs a successive group decoder (SGD). We obtain achievable outage probabilities for the case where an outage must be declared simultaneously for all users (common outage) as well as the case where outages can be declared individually for each user (individual outage). We then derive the optimum successive group decoder (OSGD) that simultaneously minimizes the common outage probability and the individual outage probability of each user, over all SGDs of permissible decoding complexity. For each channel realization, the OSGD is also shown to maximize the error exponent of the decodable set of users. An adaptive SGD is derived which not only retains the outage optimality of the OSGD but also minimizes the expected decoding complexity. Asymptotically tight (in the limit of high signal-to-noise ratio (SNR)) affine approximations are then obtained for the weighted sum common and individual outage capacities and the symmetric outage capacity yielded by the OSGD. Limiting expressions for the relevant capacities as the number of users and the number of receive antennas approach infinity are also obtained and it is shown that the OSGD yields symmetric capacity gains commensurate with the decoding complexity allowed. Simulation results with practical low-density parity-check (LDPC) outer codes show that the OSGD offers significantly improved performance at low decoding complexity.

We treat the problem of outage minimization via power control in MIMO systems with quantized feedback. We formulate the optimal quantized power control design for a general MIMO system and provide the numerical procedure for finding the optimal solution. Our results not only extend but also show the deficiency of the existing quantized power control schemes for MISO systems. We further propose a design based on the pre-evaluation of the packet error rate performance of practical MIMO systems employing short-length LDPC codes and QAM modulations and with possibly unreliable feedback links. It is demonstrated that with only a few bits of feedback, the resulting quantized power control strategy achieves considerable gain over a system without power control.

The authors consider the design of LDPC codes for cooperative relay systems in the half-duplex mode. The capacity of halfduplex relay channels has been studied previously but the design of good channel codes for such channels remains a challenging problem. Employing an efficient relay protocol, we transform the half-duplex relay code design problem into a problem of ratecompatible LDPC code design where different code segments experience different SNRs. The density evolution with conventional Gaussian approximation for single user channels, which assumes invariant SNR within one codeword, is not capable of accurately predicting the code performance for this system. Here we develop a density evolution with a modified Gaussian approximation that takes into account the SNR variation in one received codeword as well as the rate-compatibility constraint. We then optimize the code ensemble using a modified differential evolution procedure. Extensive simulations are carried out to demonstrate that the proposed algorithm offers more accurate prediction of code performance in half-duplex relay channels than the conventional methods, and the optimized codes achieve a significant gain over existing codes.

We consider the design of efficient anti-jamming coding techniques for secondary usage of spectrum in cognitive radio. Specifically, we consider two coding schemes, rateless coding and piecewise coding. Both coding schemes have small overhead, as well as low-complexity encoding and decoding. The proposed piecewise coding also enjoys the advantages of parallel decoding and fast response to packet loss. For piecewise coding, we propose two design methods to build short block codes with small number of parity checks by incorporating the jamming rate. We analyze the throughput performance of the secondary users systems employing either anti-jamming coding technique. The performance results demonstrate that both coding techniques provide reliable transmission with high throughput and small redundancy. The piecewise coding using the designed short codes provides better performance with smaller overhead if the jamming rate is not high.

In this study, we consider the design of LDPC codes for cooperative relay systems in half-duplex mode (namely, "cheap" relay) that are of practical interest. We transform the code design problem into the design of rate-compatible LDPC codes where the SNRs in different parts of one codeword are different. Due to the SNR variation, the conventional density evolution (DE) or extrinsic-mutual-information-transfer (EXIT) is not capable of accurately predicting the code performance. We develop a more refined definition of code ensembles and present a modified DE based algorithm related to the new relay code structure. Our results show that the proposed algorithm is more accurate than the conventional DE or EXIT in this case. We further employ the code optimization based on differential evolution. The optimized "cheap" relay code significantly outperforms existing codes.

We consider the design of efficient rate-compatible (RC) irregular repeat accumulate (IRA) codes over a wide code rate range. The goal is to provide a family of RC codes to achieve high throughput in hybrid automatic repeat request (ARQ) scheme for high-speed data packet wireless systems. As a subclass of low-density parity-check codes, IRA codes have an extremely simple encoder and a low-complexity decoder while providing capacity approaching performance. We focus on a hybrid design method which employs both puncturing and extending. We propose a simple puncturing method based on minimizing the maximal recoverable step of the punctured nodes. We also propose a new extending scheme for IRA codes by introducing the degree-1 parity bits for the lower rate codes and obtaining the optimal proportions of extended nodes through density evolution analysis. The throughput performance of the designed RC-IRA codes in hybrid ARQ is evaluated for both AWGN and block fading channels. Simulation results demonstrate that our designed RC codes offer good error correction performance over a wide rate range and provide high throughput, especially in the high and low signal-to-noise ratio regions.

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

We consider the multiplexed coding design for cooperative communications. The ideal multiplexed coding, which outperforms the superposition coding in theory, is difficult to implement with practical error-correction codes. We therefore introduce a partially multiplexed (PMP) coding scheme to approach the performance of fully multiplexed coding scheme. We then design the PMP coding using irregular repeat accumulate (IRA) codes. We also present a practical superposition coding scheme with two decoding methods. The outage analysis shows that all these schemes perform very close to lower cooperation bound. The simulation results demonstrate that both PMP and practical superposition block Markov coding for two-user cooperation provide significant gain over the non-cooperative system.

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 the design of efficient rate-compatible (RC) irregular repeat accumulate (IRA) codes, a subclass of LDPC codes, over a wide code rate range. The goal is to provide a family of RC codes to achieve high throughput in hybrid automatic repeat request (ARQ) scheme for high-speed data packet wireless systems. We focus on a hybrid design method which employs both puncturing and extending. We propose a simple puncturing method based on minimizing the maximal recoverable step of the punctured nodes and a new extending scheme by introducing the degree-1 parity bits for the lower rate codes and obtaining the optimal proportions of extended nodes through density evolution analysis. Simulation results show that our designed RC codes offer good error correction performance over a wide rate range and provide high throughput, especially in the high and low SNR regions

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 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.

We consider schemes for reducing the peak-to-average power ratio (PAPR) in coded orthogonal frequency-division multiplexing (OFDM) systems. We develop a new PAPR reduction technique using the label-inserted encoder of a random-like code and the soft amplitude limiter (SAL). Using this hybrid scheme provides 5.5 dB PAPR reduction in an OFDM system with 128 subcarriers, 4-bit selection and 3 dB clipping. Besides the significant PAPR reduction, the scheme also enjoys other advantages such as small overhead, low complexity, no side information transmission, and little performance loss. Among various random-like codes, the irregular repeat accumulate (IRA) code is the best choice for its simple encoder and capacity achieving performance. The scheme can be directly applied to multiple-input multiple-output (MIMO) OFDM systems. The capacity of the clipped MIMO-OFDM systems is analyzed based on a Gaussian approximation of the clipping noise. We consider an iterative receiver with soft MAP MIMO-OFDM detector. For both single antenna and multiple antenna systems, the encoder part is independent in the hybrid scheme, thus no additional constraint is applied to the IRA code optimization. The IRA codes are designed for the ergodic MIMO-OFDM systems with different PAPR reduction settings, more specifically different clipping ratios, based on the extrinsic information transfer (EXIT) charts. Simulation results show that the hybrid scheme with 3 dB clipping can achieve as good PAPR reduction performance as the simple clipping with 0 dB ratio but incurs much less performance loss at the receiver

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 consider the analysis and design of low-density parity check (LDPC) codes for intersymbol interference (ISI) channels when used with soft interference cancellation plus linear minimum mean-square error filtering (SIC-MMSE) turbo equalization. We discuss techniques to compute the probability density function (pdf) of the extrinsic information at the output of the SIC-MMSE equalizer as a function of pdf of the input extrinsic information, channel impulse response, and the signal-to-noise ratio. For static ISI channels, we show that the output pdf can be modeled as symmetric Gaussian, and show that the mean can be evaluated without simulating the equalizer. For channels with long memory, we propose to use the unscented transform technique to compute the mean, which significantly reduces the computation required. Finally, for fading channels, we model the pdf by a mixture of symmetric Gaussian densities. Using these techniques, we are able to fairly accurately compute the thresholds for LDPC codes and design good irregular LDPC codes. Simulation results are in good agreement with the computed thresholds and the designed irregular LDPC codes outperform regular ones significantly.

This paper takes into account the design optimization of the random-like ensemble of irregular repeat accumulate (IRA) codes for multiple-input multiple-output (MIMO) communication systems employing iterative receivers. First, the density evolution-based procedure for optimizing the IRA code ensemble is presented. An approximation method based on linear programming is adopted to design an IRA code with the extrinsic information transfer (EXIT) chart matched to that of the soft MIMO demodulator. The authors then reveal the relationship between the IRA codes and the low-density parity-check (LDPC) codes. With a code ensemble mapping relationship between an IRA code and an LDPC code, a quasi-optimal IRA code can be obtained by transforming an optimal LDPC code designed for MIMO systems. Two types of soft MIMO detectors are treated, namely, the maximum a posteriori (MAP) detector and the soft interference canceller with linear MMSE filtering (SIC-MMSE). The results show that with the MAP receiver the designed IRA codes can perform within 1 dB from the ergodic capacities of the MIMO systems under consideration. The authors also treat the short-length IRA code design for block fading MIMO channels. They adopt design techniques for short-length LDPC codes to improve the performance of the short-length IRA code and to reduce the error floor.

We consider the problem of coding-spreading tradeoff in code-division multiple-access (CDMA) systems employing multiuser joint decoding. In particular, we assume the users employing the capacity-achieving low-density parity-check (LDPC) codes and at the receiver, turbo multiuser detection is used to implement joint decoding. We solve the coding-spreading optimization based on the extrinsic information signal-to-noise ratio (SNR) evolution curves for the soft-input soft-output (SISO) multiuser detectors and the SISO LDPC decoders. Two types of SISO multiuser detectors are treated, namely, the soft interference cancellation minimum mean-square-error (SIC-MMSE) detector and the soft interference cancellation matched filter (SIC-MF) detector. Moreover, both single-cell and multicell scenarios are considered. For each of these cases, we are able to characterize the extrinsic information SNR analytically, for both finite-size systems and for the so-called large systems where asymptotic performance results must be evoked. Our analysis indicates that the SIC-MMSE-based system offers a significant gain in spectral efficiency compared with the SIC-MF counterpart, in both single-cell and multicell scenarios. This is in contrast to the single-user decoding case, where it has been shown that the MMSE detector offers little advantage over the conventional matched-filter in terms of capacity in multicell scenario. Moreover, the results on coding-spreading tradeoff for finite-size systems and large systems match very well.

The problem of pilot-symbol-aided estimation of multipath fading channels in up-link code-division multiple-access (CDMA) systems is considered. The transmitted symbol streams of each user are divided into time-slots; and each time-slot contains a number of pilot-symbols followed by information data symbols. Channel estimation is based on interpolation of the channel values corresponding to the pilot symbols in adjacent time-slots. Existing channel estimation techniques, including the weighted multislot average method and the wavelet expansion method, are studied. Two new channel estimation methods, namely, the robust channel interpolator, and the polynomial channel interpolator, are developed and are compared with these techniques. It is seen that the two new channel estimation methods significantly outperform the existing methods in multipath fading CDMA systems, for a wide range of Doppler values, and under various receiver schemes (with single or multiple receive antennas), such as the RAKE receiver, the interference cancellation receiver, and a receiver which performs iterative channel estimation and interference cancellation.

The performance analysis and design optimization of low density parity check (LDPC) coded multiple-input-multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems for high speed wireless transmission is considered. The tool of density evolution with mixture Gaussian approximations is used to optimize irregular LDPC codes and to compute minimum operational signal-to-noise ratios for ergodic MIMO OFDM channels. In particular, the optimization is done for various MIMO OFDM system configurations which include different number of antennas, different channel models and different demodulation schemes; and the optimized performance is compared to the corresponding channel capacity.

We consider the analysis and design of low density parity check (LDPC) codes for turbo multiuser detection in multipath code-division multiple-access (CDMA) channels. We develop techniques to compute the probability density function (pdf) of the extrinsic information at the output of the multiuser detector. We show that the output pdf can be modeled as symmetric Gaussian for synchronous CDMA in additive white Gaussian noise (AWGN) channel and as a mixture of symmetric Gaussian densities for asynchronous CDMA system over fading channel. The expectation-maximization (EM) algorithm can be used to compute the parameters of this mixture. Using these techniques, we are able to accurately compute the thresholds for LDPC codes and design good irregular LDPC codes. Simulation results are in good agreement with the computed thresholds and the designed irregular LDPC codes outperform regular ones significantly.

We discuss techniques to characterize the probability density function of the extrinsic information at the output of a soft interference canceler based equalizer when used in a turbo equalizer. Then, we show how to use this to compute thresholds for low density parity check (LDPC) codes and to design good LDPC code ensembles for static and time-varying intersymbol interference channels. For other types of equalizers, we propose to design LDPC codes whose extrinsic information transfer (EXIT) diagram is matched to that of the equalizer.