Multiuser Decoding Research Articles

A bandwidth-efficient cooperative relaying scheme with space–time block coding and iterative decoding

We propose a coded cooperative relaying scheme in which only newly generated parity bits of users are multiplexed, space–time block coded, and forwarded simultaneously by a multi-antenna relay to a common multi-antenna destination if the relay successfully decodes their information in order to improve bandwidth efficiency. Multiplexing introduces correlation between users’ data, which offers effectively longer codes and facilitates high-performance iterative multi-user decoding at the destination. Additionally, space–time block coding makes bit-metrics calculation simple and increases spatial diversity of the received signal. Simulation results show that the proposed scheme significantly outperforms direct transmission under the same transmit power and bandwidth efficiency.

Rate optimization for IDMA systems with iterative joint multi-user decoding

In this letter, we develop a rate allocation scheme for interleave-division multiple-access (IDMA) systems with iterative decoding. We use a fully-analytical approach to predict the performance of the scheme. Then, we propose a modified linear programming method to find the best rate profile for the scheme. Numerical results show that with just repetition coding and optimal rate allocation, the performance of the scheme is only about 5 dB away from the capacity for a wide range of SNR, provided that the number of users is sufficiently large. Compared with power allocation schemes for IDMA, the proposed rate allocation scheme achieves a similar performance at a moderate spectral efficiency and the requirement of sophisticated power amplifiers can be relaxed.

Novel Low-Density Signature for Synchronous CDMA Systems Over AWGN Channel

Novel low-density signature (LDS) structure is proposed for transmission and detection of symbol-synchronous communication over memoryless Gaussian channel. Given N as the processing gain, under this new arrangement, users' symbols are spread over N chips but virtually only dv < N chips that contain nonzero-values. The spread symbol is then so uniquely interleaved as the sampled, at chip rate, received signal contains the contribution from only dc < K number of users, where K denotes the total number of users in the system. Furthermore, a near-optimum chip-level iterative soft-in-soft-out (SISO) multiuser decoding (MUD), which is based on message passing algorithm (MPA) technique, is proposed to approximate optimum detection by efficiently exploiting the LDS structure. Given beta = K/N as the system loading, our simulation suggested that the proposed system alongside the proposed detection technique, in AWGN channel, can achieve an overall performance that is close to single-user performance, even when the system has 200% loading, i.e., when beta = 2. Its robustness against near-far effect and its performance behavior that is very similar to optimum detection are demonstrated in this paper. In addition, the complexity required for detection is now exponential to dc instead of K as in conventional code division multiple access (CDMA) structure employing optimum multiuser detector.

A Divergence Minimization Approach to Joint Multiuser Decoding for Coded CDMA

In this paper, a theoretical framework of divergence minimization (DM) is applied to derive iterative receiver algorithms for coded CDMA systems. The DM receiver obtained performs joint channel estimation, multiuser decoding, and noise- covariance estimation. While its structure is similar to that of many ad-hoc receivers in the literature, the DM receiver is the result of applying a formal framework for optimization without further simplifications, namely the DM approach with a factorizable auxiliary model distribution. The well-known expectation- maximization (EM) algorithm and space-alternating generalized expectation-maximization (SAGE) algorithm are special cases of degenerate model distributions within the DM framework. Furthermore, many ad-hoc receiver structures from literature are shown to represent approximations of the proposed DM receiver. The DM receiver has four interesting properties that all result directly from applying the formal framework: (i) The covariances of all estimates involved are taken into account, (ii) The residual interference after interference cancellation is handled by the noise-covariance estimation as opposed to by LMMSE filters in other receivers, (iii) Posterior probabilities of the code symbols are employed rather than extrinsic probabilities, (iv) The iterative receiver is guaranteed to converge in divergence. The theoretical insights are illustrated by simulation results.

Reduced-Complexity Belief Propagation for System-Wide MUD in the Uplink of Cellular Networks

System-wide multiuser detection (MUD), in which all base stations (BSs) of a cellular system cooperate to detect the data of all mobile stations (MSs), has much promise. However, little is known at present about practical techniques or their performance. An attractive method is belief propagation (BP), with message exchange between nearby cooperating BSs over a backbone landline network, but its performance is known only for a greatly simplified network model and its computation load grows exponentially with the number of interfering MS symbols at each BS. In this paper, we present a reduced complexity variation of BP (RCBP) and show that its performance is close to or identical to that of BP in the simplified network. We also observe excellent performance by iterative multiuser detection and decoding of low-density parity check codes (LDPC). Furthermore, we examine RCBP performance in a realistic wireless network model, with path loss, shadowing, fading and power control. These results, though poorer than those of the simplified network, show that system-wide MUD with cooperating BSs provides great improvement compared with conventional systems.

Boosts to LDPC-coded IDMA systems

A node-by-node joint multi-user iterative decoding strategy, instead of the detector-decoder loop strategy, is proposed based on the factor graph representation of the LDPC-coded IDMA system. To analyse the proposed iterative decoding process, a Gaussian approximation based density evolution algorithm is designed. The degree distributions of LDPC codes are optimised for the IDMA system when the system bandwidth efficiency is 1.

Optimum linear decoding of vector quantisation transmitted over a CDMA channel

The problem of joint source–channel and multiuser decoding for code division multiple access channels is considered. The block source–channel encoder is defined by a vector quantiser (VQ). The jointly optimum solution to such a problem has been considered before, but its extremely high complexity makes it impractical for systems with medium to large number of users and/or medium to large size of VQ codebook. Instead, the optimum linear decoder with a much lower complexity that minimises the mean-squared error is introduced. The optimum linear decoder is soft in the sense that it utilises all the soft information available at the receiver. Analytical and simulation results show that at low channel signal-to-noise ratio region, the proposed decoder&apos;s performance is almost the same as that of the jointly optimum decoder and significantly better than that of the tandem approaches that use separate multiuser detection and table-lookup decoding.

Characterization and Optimization of LDPC Codes for the 2-User Gaussian Multiple Access Channel

We address the problem of designing good LDPC codes for the Gaussian multiple access channel (MAC). The framework we choose is to design multiuser LDPC codes with joint belief propagation decoding on the joint graph of the 2-user case. Our main result compared to existing work is to express analytically EXIT functions of the multiuser decoder with two different approximations of the density evolution. This allows us to propose a very simple linear programming optimization for the complicated problem of LDPC code design with joint multiuser decoding. The stability condition for our case is derived and used in the optimization constraints. The codes that we obtain for the 2-user case are quite good for various rates, especially if we consider the very simple optimization procedure.

Joint Channel Estimation, Partial Successive Interference Cancellation, and Data Decoding for DS-CDMA Based on the SAGE Algorithm

This paper deals with the derivation and optimization of an iterative receiver architecture performing joint multiuser decoding and channel estimation. We consider an asynchronous multirate convolutional coded DS-CDMA system that communicates over quasi-static flat Rayleigh fading channels. The proposed receiver is derived within the space-alternating generalized expectation-maximization (SAGE) framework in connection with the noise-splitting approach. The used theoretical framework guarantees convergence of the receiver, as opposed to many other iterative receiver structures. Furthermore, the noise-splitting approach provides a set of noise-weighting coefficients that can be optimized under weak constraints. The inputs to the single-user decoders are linear combinations of two kinds of soft values with weights determined by the noise-weighting coefficients. These two kinds of soft values can be interpreted as a priori information and extrinsic information, respectively, if the channels are known. In the case of unknown channels, they are asymptotically a priori and asymptotically extrinsic, i.e., they become a priori and extrinsic when the length of the observed frame tends to infinity. In most cases, the optimum coefficients lead to extrinsic or asymptotically extrinsic values fed to the input of the single-user decoders. Monte Carlo simulations show that the proposed receiver is resistant to channel estimation errors and supports high system loads.

Asymptotically optimal nonlinear MMSE multiuser detection based on multivariate Gaussian approximation

In this paper, a class of nonlinear minimum mean-squared error multiuser detectors is derived based on a multivariate Gaussian approximation of the multiple-access interference for large systems. This approach leads to expressions identical to those describing the probabilistic data association (PDA) detector, thus providing an alternative analytical justification for this structure. A simplification to the PDA detector based on approximating the covariance matrix of the multivariate Gaussian distribution is suggested, resulting in a soft interference-cancellation scheme. Corresponding multiuser soft-input, soft-output detectors delivering extrinsic log-likelihood ratios are derived for application in iterative multiuser decoders. Finally, a large-system performance analysis is conducted for the simplified PDA, showing that the bit-error rate (BER) performance of this detector can be accurately predicted and related to the replica method analysis for the optimal detector. Methods from statistical neurodynamics are shown to provide a closely related alternative large-system prediction. Numerical results demonstrate that for large systems, the BER is accurately predicted by the analysis and found to be close to optimal performance

Low-complexity iterative multiuser detection and decoding for real-time applications

This paper presents a low-complexity multiuser decoding technique that can be implemented in real time for a convolutionally coded direct sequence code division multiple access (DS-CDMA) system. The main contribution, denoted here as the iterative prior update (IPU), consists of iterative interference cancellation and prior updates on sequences of coded bits combined with M-algorithm and list decoding. We illustrate performance gains over other low-complexity sequence detection and decoding strategies and argue that the algorithm converges within a few iterations and requires only a small size buffer for keeping track of the priors along iterations. The fact that the we can use existing available architectures for Viterbi decoding with slight modifications and can meet the real-time processing constraints makes the IPU algorithm an attractive alternative for cellular systems.

Reduced-Complexity MAP-Based Iterative Multiuser Detection for Coded Multicarrier CDMA Systems

In recent years, combining multiuser detection (MUD) and channel decoding has received considerable attention. The maximum a posteriori (MAP) criterion-based iterative multiuser detector greatly improves the system performance and can approach the performance of single-user coded systems. However, its complexity increases exponentially with the number of users and can become prohibitive for systems with a medium-to-large number of users. In this paper, a reduced complexity MAP-based iterative MUD based on the use of a soft sensitive bits algorithm is proposed for coded multicarrier code-division multiple-access systems. It is shown that it can greatly reduce the computational complexity with a minimal penalty in performance compared to the conventional optimal scheme.

Coding-Spreading Tradeoff in LDPC-Coded CDMA With Turbo Multiuser Detection

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.

An Extrinsic Kalman Filter for Iterative Multiuser Decoding

One powerful approach for multiuser decoding is to iterate between a linear multiuser filter (which ignores coding constraints) and individual decoders (which ignore multiple-access interference). Subject to clearly formulated statistical assumptions and the history of input signals provided by the outer decoders over all previous iterations, an extrinsic Kalman filter is suggested. This approach is motivated by the recent observation that decoder outputs are loosely correlated during initial iterations. Numerical results show that iterative decoding using this filter provides better performance in terms of the supportable load and convergence speed as compared to previously suggested linear-filter-based iterative decoders.

Low-Complexity Turbo Equalization and Multiuser Decoding for TD-CDMA

The authors propose a low complexity multiuser joint parallel interference cancellation (PIC) decoder and turbo decision feedback equalizer for code division multiple access (CDMA). In their scheme, an estimate of the interference signal (both multiple-access interference and intersymbol interference) is formed by weighting the hard decisions produced by conventional (i.e., hard-output) Viterbi decoders. The estimated interference is subtracted from the received signal in order to improve decoding in the next iteration. By using asymptotic performance analysis of random-spreading CDMA, they optimize the feedback weights at each iteration. Then, they consider two (mutually related) performance limitation factors: the bias of residual interference and the ping-pong effect. The authors show that the performance of the proposed algorithm can be improved by compensating for the bias in the weight calculation, and they propose a modification of the basic PIC algorithm, which prevents the ping-pong effect and allows higher channel load and/or faster convergence to the single-user performance. The proposed algorithm is validated through computer simulation in an environment fully compliant with the specifications of the time-division duplex mode of third-generation systems, contemplating a combination of time-division multiple access and CDMA and including frequency-selective fading channels, user asynchronism, and power control. The main conclusion of this work is that, for such application, soft-input soft-output decoders (e.g., implemented by the forward-backward BCJR algorithm) are not needed to attain very high spectral efficiency, and simple conventional Viterbi decoding suffices for most practical settings.

Soft multiuser demodulation and iterative decoding for FH/SSMA with a block turbo code

The number of users that can be supported by frequency-hopped, spread-spectrum multiple-access systems can be increased greatly by using multiuser demodulation and iterative decoding. In the receiver employed hard-decision multiuser demodulation followed by iterative decoding, users exchange decoded information with each other. Additional information from multiuser demodulation in the first decoding iteration is limited by the hard-decision output of the multiuser demodulator. The error-correction used was an errors-and-erasures Reed-Solomon (RS) decoder. We revisit hard-decision demodulation and conventional RS decoding. Hard-decision multiuser demodulation is modified to provide a soft output, which is then given to a nonbinary block turbo code with shortened RS codes as the constituent codes. An iterative multiuser decoding algorithm is developed to do soft multiuser interference cancellation. This soft receiver with soft demodulation and decoding is shown to be more resistant to multiuser interference and channel noise, especially at lower values of signal-to-noise ratio. The results show a great improvement in the ability of the system to support more users (more than three times in some cases), as compared with systems that erase all hits or employ hard-decision multiuser demodulation followed by RS code. We examine the proposed method for synchronous as well as asynchronous frequency-hopped systems in both AWGN and fading channels.

Asynchronous multicarrier multiple access: Optimal and sub-optimal detection and decoding

In this paper, we describe multicarrier multiple access architectures that are based on combining filtered multicarrier modulation with multiplexing of sub-carriers across distinct users. These architectures can be deployed for both uplink and downlink wireless communications. We focus on the more critical uplink where multiple users share an asynchronous channel. Signals belonging to distinct users experience time and carrier frequency asynchronism and propagate through independent frequency-selective fading channels. In such a scenario the receiver sees intersymbol interference, intercarrier interference, and multiple access interference components that are a function of the propagation conditions, the design of the sub-channel transmit filters, and the tone allocation strategy. We formulate the optimal multicarrier multiuser detector that yields minimum probability of error. Then, we devise sub-optimal (simplified) detection approaches. These detectors are soft-in soft-out modules that can be concatenated with the channel decoders when the users' information signals are channel encoded. In such a case, practical decoding can be performed by the iterative concatenation of multicarrier detection and decoding (turbo multiuser decoding).

The throughput of some wireless multiaccess systems

We compute the throughput of some multiaccess wireless systems for delay-tolerant data communications, characterized by an infinite population of uncoordinated users accessing a common channel. The channel is affected by block fading, and the channel state is perfectly known to the receiver but unknown to the transmitters. To cope with multiaccess interference (MAI) and fading, the users employ retransmission of erroneously received packets. We consider unspread and randomly spread (code-division multiple-access (CDMA)) systems with decentralized (single-user) decoding and a system where the receiver employs joint multiuser decoding. The following conclusions can be drawn from our analysis: (a) unspread systems with packet retransmission outperforms CDMA systems with conventional detection, but are outperformed by CDMA with linear minimum mean-square error (MMSE) detection. (b) For all systems based on single-user decoding (SUD), there exists a threshold value of (E/sub b//N/sub o/) below which the throughput is maximized by an infinite number of users per dimension transmitting at vanishing rate, and above which the throughput is maximized by a finite average number of users per dimension transmitting at nonvanishing rate. Moreover, as (E/sub b//N/sub o/) increases, the optimal average number of users per dimension tends to one. In this sense, we say that the optimized systems self-orthogonalize. (c) For the system based on joint multiuser decoding, a simple slotted ALOHA strategy is able to recover the throughput penalty due to fading in the limit for high (E/sub b//N/sub o/), while an incremental redundancy (INR) strategy recovers the fading penalty for any (E/sub b//N/sub o/).

Multistage decoding for internally bandwidth efficient coded Poisson fiber-optic CDMA communication systems

We consider the structure and performance of a multistage decoding scheme for an internally bandwidth efficient convolutionally coded Poisson fiber-optic code division multiple access (CDMA) communication system. The decoder is implemented electronically in several stages in which in each stage, the interfering users' coded bit decisions obtained in the previous stage is applied for computing the likelihood of the coded symbols of the desired user. The first stage is a soft-input Viterbi decoder for the internally coded scheme, in which the soft-input coded symbol likelihood values are computed by considering the multiuser interference as a noise signal. The likelihood of coded symbol computed in each stage is then entered into the convolutional decoder for the next bit decisions. The convolutional codes that are used for demonstrating the performance of the multistage decoder are super orthogonal codes (SOCs). We derive the bit error rates (BERs) of the proposed decoder for internally coded Poisson fiber-optic CDMA systems using optical orthogonal codes (OOCs) along with both ON-OFF keying (OOK) and binary pulse position modulation (BPPM) schemes. Our numerical results indicate that the proposed decoding scheme substantially outperforms the single-stage soft-input Viterbi decoder. We also derive the upper bound on the probability of error of a decoder for the known interference case, which is the ultimate performance of a multiuser decoder, and compare the result with that of the soft-input Viterbi decoder.

Low Complexity Receiver Structures for Space-Time Coded Multiple-Access Systems

Multiuser detection for space-time coded synchronous multiple-access systems in the presence of independent Rayleigh fading is considered. Under the assumption of quasi-static fading, it is shown that optimal (full diversity achieving) space-time codes designed for single-user channels, can still provide full diversity in the multiuser channel. The joint optimal maximum likelihood multiuser detector, which can be implemented with a Viterbi-type algorithm, is derived for such space-time coded systems. Low complexity, partitioned detector structures that separate the multiuser detection and space-time decoding into two stages are also developed. Both linear and nonlinear multiuser detection schemes are considered for the first stage of these partitioned space-time multiuser receivers. Simulation results show that these latter methods achieve performance competitive with the single-user bound for space-time coded systems.