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Knowledge-Aided Iterative Detection and Decoding for Multiuser Multiple-Antenna Systems
IET Communications
Abstract
In this work, the authors assess the performance and latency of a receiver design for multiuser multiple-antenna systems using low-density parity-check (LDPC) codes with iterative detection and decoding (IDD). The proposed knowledgeaided IDD (KA-IDD) receiver employs a parallel interference cancellation detector with refined iterative processing and a reweighted belief propagation (BP) decoder. Additionally, two BP-based decoding algorithms are proposed for improved performance of the decoder. The first cycle knowledge-aided reweighted-BP decoder takes advantage of the information about the distribution of cycles in the Tanner graph and the second expansion knowledge-aided reweighted-BP decoder expands the original graph into a set of subgraphs, then locally optimises the reweighting parameters of each subgraph. Novel reweighting parameter optimisation strategies are developed for decoding regular or irregular LDPC codes. The developed schemes optimise the parameters off-line and neither of these proposed algorithms imposes extra computational complexity to the on-line decoding procedure. Furthermore, the proposed schemes reduce the decoding latency. Simulation results show that the proposed KA-IDD scheme and algorithms outperform prior art and require a reduced number of decoding iterations.
... On the other hand, a few modified versions of the BP algorithm that outperform the standard BP algorithm have been introduced in [8]- [13]. In particular, an improvement method by properly scaling down the variable to check extrinsic logarithm likelihood ratio (ex-LLR) using a (multiplicative versus additive) factor (α versus β) in the iterative process of BP algorithm has been reported [8], [9]. Another method [10] attenuates the check to variable ex-LLR, when sudden sign change happens in successive decoding iterations. ...
... For all the simulations, enough codewords are simulated to generate at least 100 codeword errors for each Fig. 3 and Fig. 4 show the block error rate (BLER) and bit error rate (BER) curves for code I and II with different decoding algorithms, respectively. It can be seen that, for both block lengths, at high SNR values, the EPEFM algorithm outperforms the standard BP algorithm, the algorithm of [9] and the edge-based probabilistic scheduling decoding [12] considerably. At lower SNR values, the proposed algorithm never performs worse than the standard BP algorithm. ...
... positive effects of the feedback messages for each variable node), edge-based probabilistic schedule decoding[12], algorithm of[9] with 65 . 0 and standard BP algorithms. ...
... It was shown in [11] that the error floor still remains after a number of iterations, especially in highly frequency selective channels. In recent years, the adoption of iteratively decodable codes such as low-density parity check (LDPC) codes and Turbo codes, have shown impressive performance gain in receivers by gradually decoding and cancelling interference in multiple iterations [12]. An LDPC-based iterative detection and decoding (IDD) receiver was proposed in [13] and [14] for SISO FBMC-OQAM and MIMO-FBMC/OQAM respectively. ...
Narrowband Internet of Things (NB-IoT) was proposed by 3GPP in Release 13 to provide low power wide area connections to a high-volume of devices. With the millions of devices expected to connect to 5G through its massive machinetype communication use case, the strict orthogonality and synchronization requirement of cyclic-prefix orthogonal division multiplexing (CP-OFDM) will demand a very large amount of control information between devices and the core network. To overcome this challenge, we study a new air interface for NBIoT, which utilizes a non-orthogonal multicarrier transmission scheme. The waveform considered in this work is filter-bank muilticarrier with quadrature amplitude modulation (FBMCQAM). The loss of orthogonality in FBMC-QAM results in severe levels of intrinsic interference. Iterative detection and decoding (IDD) using low density parity check (LDPC) encoding and decoding is implemented together with iterative interference cancellation (IIC) to remove the inherent interference and improve the BER rate performance. Simulation results indicate that the proposed IDD receiver can effectively improve BER performance under time-varying channels.
In this paper we study widely-linear precoding techniques to mitigate in-phase/quadrature-phase (IQ) imbalance (IQI) in the downlink of large-scale multiple-input multiple-output (MIMO) systems. We adopt a real-valued signal model which takes into account the IQI at the transmitter and then develop widely-linear zero-forcing (WL-ZF), widely-linear matched filter (WL-MF), widely-linear minimum mean-squared error (WL-MMSE) and widely-linear block-diagonalization (WL-BD) type precoding algorithms for both {\color{red} single- and multiple-antenna users.} We also present a performance analysis of WL-ZF and WL-BD. It is proved that without IQI, WL-ZF has exactly the same multiplexing gain and power offset as ZF, while when IQI exists, WL-ZF achieves the same multiplexing gain as ZF with ideal IQ branches, but with a minor power loss which is related to the system scale and the IQ parameters. We also compare the performance of WL-BD with BD. The analysis shows that with ideal IQ branches, WL-BD has the same data rate as BD, while when IQI exists, WL-BD achieves the same multiplexing gain as BD without IQ imbalance. Numerical results verify the analysis and show that the proposed widely-linear type precoding methods significantly outperform their conventional counterparts with IQI and approach those with ideal IQ branches.
This paper jointly optimizes the precoding matrices and the set of active remote radio heads (RRHs) to minimize the network power consumption (NPC) for a user-centric cloud radio access network (C-RAN), where both the RRHs and users have multiple antennas and each user is served by its nearby RRHs. Both users' rate requirements and per-RRH power constraints are considered. Due to these conflicting constraints, this optimization problem may be infeasible. In this paper, we propose to solve this problem in two stages. In Stage I, a low-complexity user selection algorithm is proposed to find the largest subset of feasible users. In Stage II, a low-complexity algorithm is proposed to solve the optimization problem with the users selected from Stage I. Specifically, the re-weighted -norm minimization method is used to transform the original problem with non-smooth objective function into a series of weighted power minimization (WPM) problems, each of which can be solved by the weighted minimum mean square error (WMMSE) method. The solution obtained by the WMMSE method is proved to satisfy the Karush-Kuhn-Tucker (KKT) conditions of the WPM problem. Moreover, a low-complexity algorithm based on Newton's method and the gradient descent method is developed to update the precoder matrices in each iteration of the WMMSE method. Simulation results demonstrate the rapid convergence of the proposed algorithms and the benefits of equipping multiple antennas at the user side. Moreover, the proposed algorithm is shown to achieve near-optimal performance in terms of NPC.
Channel coding lies at the heart of digital communication and data storage, and this detailed introduction describes the core theory as well as decoding algorithms, implementation details, and performance analyses. Known for their writing clarity, Professors Ryan and Lin provide the latest information on modern channel codes, including turbo and low-density parity-check (LDPC) codes. They also present detailed coverage of BCH codes, Reed-Solomon codes, convolutional codes, finite geometry codes, and product codes, providing a one-stop resource for both classical and modern coding techniques. Assuming no prior knowledge in the field of channel coding, the opening chapters begin with basic theory to introduce newcomers to the subject. Later chapters then extend to advanced topics such as code ensemble performance analyses and algebraic code design. 250 varied and stimulating end-of-chapter problems are also included to test and enhance learning, making this an essential resource for students and practitioners alike.
This paper considers base station cooperation (BSC) strategies for the uplink
of a multi-user multi-cell high frequency reuse scenario where distributed
iterative detection (DID) schemes with soft/hard interference cancellation
algorithms are studied. The conventional distributed detection scheme exchanges
{soft symbol estimates} with all cooperating BSs. Since a large amount of
information needs to be shared via the backhaul, the exchange of hard bit
information is preferred, however a performance degradation is experienced. In
this paper, we consider a reduced message passing (RMP) technique in which each
BS generates a detection list with the probabilities for the desired symbol
that are sorted according to the calculated probability. The network then
selects the best {detection candidates} from the lists and conveys the index of
the constellation symbols (instead of double-precision values) among the
cooperating cells. The proposed DID-RMP achieves an inter-cell-interference
(ICI) suppression with low backhaul traffic overhead compared with {the
conventional soft bit exchange} and outperforms the previously reported
hard/soft information exchange algorithms.
A novel low-complexity decision-feedback detection algorithm with constellation constraints (DFCC) is proposed for multi-input–multi-output (MIMO) systems. An enhanced interference cancellation is achieved by introducing multiple constellation points as decision candidates. A complexity reduction strategy is also developed to avoid redundant processing with reliable decisions. For time-varying channels, the proposed receiver updates the filter weights using a recursive least-squares (RLS)-based algorithm. This efficient detector is also incorporated in a multiple-branch (MB) structure to achieve a higher detection diversity order. A soft-output DFCC detector is also proposed as a component of an iterative detection and decoding receiver scheme. Simulations show that the proposed DFCC technique has complexity as low as the adaptive decision-feedback (DF) detector while it significantly outperforms ordered successive interference cancellation (OSIC) processing.
In this paper, we propose a new inference algorithm, suitable for distributed processing over wireless networks. The algorithm, called uniformly reweighted belief propagation (URW-BP), combines the local nature of belief propagation with the improved performance of tree-reweighted belief propagation (TRW-BP) in graphs with cycles. It reduces the degrees of freedom in the latter algorithm to a single scalar variable, the uniform edge appearance probability ρ. We provide a variational interpretation of URW-BP, give insights into good choices of ρ, develop an extension to higher-order potentials, and complement our work with numerical performance results on three inference problems in wireless communication systems: spectrum sensing in cognitive radio, cooperative positioning, and decoding of a low-density parity-check (LDPC) code.
In this paper, a low-complexity multiple feedback successive interference cancellation (MF-SIC) strategy is proposed for the uplink of multiuser multiple-input multiple-output (MU-MIMO) systems. In the proposed MF-SIC algorithm with shadow area constraints (SAC), an enhanced interference cancellation is achieved by introducing {constellation points as the candidates} to combat the error propagation in decision feedback loops. We also combine the MF-SIC with multi-branch (MB) processing, which achieves a higher detection diversity order. For coded systems, a low-complexity soft-input soft-output (SISO) iterative (turbo) detector is proposed based on the MF and the MB-MF interference suppression techniques. The computational complexity of the MF-SIC is comparable to the conventional SIC algorithm since very little additional complexity is required. Simulation results show that the algorithms significantly outperform the conventional SIC scheme and approach the optimal detector.
A novel algorithm to design Root-Check LDPC codes based on Progressive Edge Growth (PEG) techniques for block-fading channels is proposed. The performance of the new codes is investigated in terms of the Frame Error Rate (FER) and the Bit Error Rate (BER). Numerical results show that the codes constructed by the proposed algorithm outperform codes constructed by the existing methods by 0.5dB.
Long-Term Evolution (LTE) is the new standard recently specified by the 3GPP on the way towards fourth-generation mobile. This paper presents the main technical features of this standard as well as its performance in terms of peak bit rate and average cell throughput, among others. LTE entails a big technological improvement as compared with the previous 3G standard. However, this paper also demonstrates that LTE performance does not fulfil the technical requirements established by ITU-R to classify one radio access technology as a member of the IMT-Advanced family of standards. Thus, this paper describes the procedure followed by the 3GPP to address these challenging requirements. Through the design and optimization of new radio access techniques and a further evolution of the system, the 3GPP is laying down the foundations of the future LTE-Advanced standard, the 3GPP candidate for 4G. This paper offers a brief insight into these technological trends.
Information theory research has shown that the rich-scattering
wireless channel is capable of enormous theoretical capacities if the
multipath is properly exploited. In this paper, we describe a wireless
communication architecture known as vertical BLAST (Bell Laboratories
Layered Space-Time) or V-BLAST, which has been implemented in real-time
in the laboratory. Using our laboratory prototype, we have demonstrated
spectral efficiencies of 20-40 bps/Hz in an indoor propagation
environment at realistic SNRs and error rates. To the best of our
knowledge, wireless spectral efficiencies of this magnitude are
unprecedented and are furthermore unattainable using traditional
techniques
In this paper we propose minimum mean squared error (MMSE) iterative successive parallel arbitrated decision feedback (DF) receivers for direct sequence code division multiple access (DS-CDMA) systems. We describe the MMSE design criterion for DF multiuser detectors along with successive, parallel and iterative interference cancellation structures. A novel efficient DF structure that employs successive cancellation with parallel arbitrated branches and a near-optimal low complexity user ordering algorithm are presented. The proposed DF receiver structure and the ordering algorithm are then combined with iterative cascaded DF stages for mitigating the deleterious effects of error propagation for convolutionally encoded systems with both Viterbi and turbo decoding as well as for uncoded schemes. We mathematically study the relations between the MMSE achieved by the analyzed DF structures, including the novel scheme, with imperfect and perfect feedback. Simulation results for an uplink scenario assess the new iterative DF detectors against linear receivers and evaluate the effects of error propagation of the new cancellation methods against existing ones.
A coding and modulation technique is studied where the coded bits of an irregular low-density parity-check (LDPC) code are passed directly to a modulator. At the receiver, the variable nodes of the LDPC decoder graph are connected to detector nodes, and iterative decoding is accomplished by viewing the variable and detector nodes as one decoder. The code is optimized by performing a curve fitting on extrinsic information transfer charts. Design examples are given for additive white Gaussian noise channels, as well as multiple-input, multiple-output (MIMO) fading channels where the receiver, but not the transmitter, knows the channel. For the MIMO channels, the technique operates within 1.25 dB of capacity for various antenna configurations, and thereby outperforms a scheme employing a parallel concatenated (turbo) code by wide margins when there are more transmit than receive antennas.
The presence of both multiple-access interference (MAI) and
intersymbol interference (ISI) constitutes a major impediment to
reliable communications in multipath code-division multiple-access
(CDMA) channels. In this paper, an iterative receiver structure is
proposed for decoding multiuser information data in a convolutionally
coded asynchronous multipath DS-CDMA system. The receiver performs two
successive soft-output decisions, achieved by a soft-input soft-output
(SISO) multiuser detector and a bank of single-user SISO channel
decoders, through an iterative process. At each iteration, extrinsic
information is extracted from detection and decoding stages and is then
used as a priori information in the next iteration, just as in turbo
decoding. Given the multipath CDMA channel model, a direct
implementation of a sliding-window SISO multiuser detector has a
prohibitive computational complexity. A low-complexity SISO multiuser
detector is developed based on a novel nonlinear interference
suppression technique, which makes use of both soft interference
cancellation and instantaneous linear minimum mean-square error
filtering. The properties of such a nonlinear interference suppressor
are examined, and an efficient recursive implementation is derived.
Simulation results demonstrate that the proposed low complexity
iterative receiver structure for interference suppression and decoding
offers significant performance gain over the traditional noniterative
receiver structure. Moreover, at high signal-to-noise ratio, the
detrimental effects of MAI and ISI in the channel can almost be
completely overcome by iterative processing, and single-user performance
can be approached
We introduce a simple technique for analyzing the iterative
decoder that is broadly applicable to different classes of codes defined
over graphs in certain fading as well as additive white Gaussian noise
(AWGN) channels. The technique is based on the observation that the
extrinsic information from constituent maximum a posteriori (MAP)
decoders is well approximated by Gaussian random variables when the
inputs to the decoders are Gaussian. The independent Gaussian model
implies the existence of an iterative decoder threshold that
statistically characterizes the convergence of the iterative decoder.
Specifically, the iterative decoder converges to zero probability of
error as the number of iterations increases if and only if the channel E
b/N0 exceeds the threshold. Despite the
idealization of the model and the simplicity of the analysis technique,
the predicted threshold values are in excellent agreement with the
waterfall regions observed experimentally in the literature when the
codeword lengths are large. Examples are given for parallel concatenated
convolutional codes, serially concatenated convolutional codes, and the
generalized low-density parity-check (LDPC) codes of Gallager and
Cheng-McEliece (1996). Convergence-based design of asymmetric parallel
concatenated convolutional codes (PCCC) is also discussed
We study a serially interleaved concatenated code construction,
where the outer code is a standard convolutional code, and the inner
code is a recursive convolutional code of rate 1. We focus on the
ubiquitous inner differential encoder (used, in particular, to resolve
phase ambiguities), double differential encoder (used to resolve both
phase and frequency ambiguities), and another rate 1 recursive
convolutional code of memory 2. We substantiate analytically the rather
surprising result, that the error probabilities corresponding to a
maximum-likelihood (ML) coherently detected antipodal modulation over
the additive white Gaussian noise (AWGN) channel for this construction
are advantageous as compared to the stand-alone outer convolutional
code. This is in spite of the fact that the inner code is of rate 1. The
analysis is based on the tangential sphere upper bound of an ML decoder,
incorporating the ensemble weight distribution (WD) of the concatenated
code, where the ensemble is generated by all random and uniform
interleavers. This surprising result is attributed to the WD thinning
observed for the concatenated scheme which shapes the WD of the outer
convolutional code to resemble more closely the binomial distribution
(typical of a fully random code of the same length and rate). This gain
is maintained regardless of a rather dramatic decrease, as demonstrated
here, in the minimum distance of the concatenated scheme as compared to
the minimum distance of the outer stand-alone convolutional code. The
advantage of the examined serially interleaved concatenated code, given
in terms of bit and/or block error probability which is decoded by a
practical suboptimal decoder, over the optimally decoded standard
convolutional code is demonstrated by simulations, and some insights
into the performance of the iterative decoding algorithm are also
discussed. Though we have investigated only specific constructions of
constituent inner (rate 1) and outer codes, we trust, hinging on the
rational of the arguments here, that these results extend to many other
constituent convolutional outer codes and rate 1 inner recursive
convolutional codes
In this paper, we consider the problem of iterative detection and decoding (IDD) for multi-antenna systems using low-density parity-check (LDPC) codes. The proposed IDD system consists of a soft-input soft-output parallel interference (PIC) cancellation scheme with linear minimum mean-square error (MMSE) receive filters and two novel belief propagation (BP) decoding algorithms. The proposed BP algorithms exploit the knowledge of short cycles in the graph structure and the reweighting factors derived from the hypergraph's expansion. Simulation results show that when used to perform IDD for multi-antenna systems both proposed BP decoding algorithms can consistently outperform existing BP techniques with a small number of decoding iterations.
A multiplicity of autonomous terminals simultaneously transmits data streams to a compact array of antennas. The array uses imperfect channel-state information derived from transmitted pilots to extract the individual data streams. The power radiated by the terminals can be made inversely proportional to the square-root of the number of base station antennas with no reduction in performance. In contrast if perfect channel-state information were available the power could be made inversely proportional to the number of antennas. Lower capacity bounds for maximum-ratio combining (MRC), zero-forcing (ZF) and minimum mean-square error (MMSE) detection are derived. An MRC receiver normally performs worse than ZF and MMSE. However as power levels are reduced, the cross-talk introduced by the inferior maximum-ratio receiver eventually falls below the noise level and this simple receiver becomes a viable option. The tradeoff between the energy efficiency (as measured in bits/J) and spectral efficiency (as measured in bits/channel use/terminal) is quantified for a channel model that includes small-scale fading but not large-scale fading. It is shown that the use of moderately large antenna arrays can improve the spectral and energy efficiency with orders of magnitude compared to a single-antenna system.
Toward the fifth generation (5G) of wireless/mobile broadband, numerous devices and networks will be interconnected and traffic demand will constantly rise. Heterogeneity will also be a feature that is expected to characterize the emerging wireless world, as mixed usage of cells of diverse sizes and access points with different characteristics and technologies in an operating environment are necessary. Wireless networks pose specific requirements that need to be fulfilled. In this respect, approaches for introducing intelligence will be investigated by the research community. Intelligence shall provide energy- and cost-efficient solutions at which a certain application/service/quality provision is achieved. Particularly, the introduction of intelligence in heterogeneous network deployments and the cloud radio-access network (RAN) is investigated. Finally, elaboration on emerging enabling technologies for applying intelligence will focus on the recent concepts of software-defined networking (SDN) and network function virtualization (NFV). This article provided an overview for delivering intelligence toward the 5G of wireless/mobile broadband by taking into account the complex context of operation and essential requirements such as QoE, energy efficiency, cost efficiency, and resource efficiency.
In this paper we propose a novel message passing algorithm which exploits the existence of short cycles to obtain performance gains by reweighting the factor graph. The proposed decoding algorithm is called variable factor appearance probability belief propagation (VFAP-BP) algorithm and is suitable for wireless communications applications with low-latency and short blocks. Simulation results show that the VFAP-BP algorithm outperforms the standard BP algorithm, and requires a significantly smaller number of iterations when decoding either general or commercial LDPC codes.
This paper addresses digital communication in a Rayleigh fading environment when the channel characteristic is unknown at the transmitter but is known (tracked) at the receiver. Inventing a codec architecture that can realize a significant portion of the great capacity promised by information theory is essential to a standout long-term position in highly competitive arenas like fixed and indoor wireless. Use (nT, nR) to express the number of antenna elements at the transmitter and receiver. An (n, n) analysis shows that despite the n received waves interfering randomly, capacity grows linearly with n and is enormous. With n = 8 at 1% outage and 21-dB average SNR at each receiving element, 42 b/s/Hz is achieved. The capacity is more than 40 times that of a (1, 1) system at the same total radiated transmitter power and bandwidth. Moreover, in some applications, n could be much larger than 8. In striving for significant fractions of such huge capacities, the question arises: Can one construct an (n, n) system whose capacity scales linearly with n, using as building blocks n separately coded one-dimensional (1-D) subsystems of equal capacity? With the aim of leveraging the already highly developed 1-D codec technology, this paper reports just such an invention. In this new architecture, signals are layered in space and time as suggested by a tight capacity bound.
The extrinsic information transfer (EXIT) chart pioneered by Stephan ten Brink is introduced in a tutorial way for readers not yet familiar with this powerful technique which is used to analyze the behavior of iterative so-called turbo techniques. Simple examples and preliminary analytical results are given as well as some typical applications.
We investigate the use of multiple transmitting and/or receiving antennas for single user communications over the additive Gaussian channel with and without fading. We derive formulas for the capacities and error exponents of such channels, and describe computational procedures to evaluate such formulas. We show that the potential gains of such multi-antenna systems over single-antenna systems is rather large under independenceassumptions for the fades and noises at different receiving antennas.
A cellular base station serves a multiplicity of single-antenna terminals over the same time-frequency interval. Time-division duplex operation combined with reverse-link pilots enables the base station to estimate the reciprocal forward- and reverse-link channels. The conjugate-transpose of the channel estimates are used as a linear precoder and combiner respectively on the forward and reverse links. Propagation, unknown to both terminals and base station, comprises fast fading, log-normal shadow fading, and geometric attenuation. In the limit of an infinite number of antennas a complete multi-cellular analysis, which accounts for inter-cellular interference and the overhead and errors associated with channel-state information, yields a number of mathematically exact conclusions and points to a desirable direction towards which cellular wireless could evolve. In particular the effects of uncorrelated noise and fast fading vanish, throughput and the number of terminals are independent of the size of the cells, spectral efficiency is independent of bandwidth, and the required transmitted energy per bit vanishes. The only remaining impairment is inter-cellular interference caused by re-use of the pilot sequences in other cells (pilot contamination) which does not vanish with unlimited number of antennas.
We propose an improved minimum mean square error (MMSE) vertical Bell Labs layered space-time (V-BLAST) detection technique, called a soft input, soft output, and soft feedback (SIOF) V-BLAST detector, for turbo multi-input multioutput (turbo-MIMO) systems. We derive a symbol estimator by minimizing the power of the interference plus noise, given a priori probabilities of undetected layer symbols and a posteriori probabilities for past detected layer symbols. For a low-complexity implementation, an approximate SIOF algorithm is presented, which allows for a time-invariant realization of the symbol ordering and an MMSE filtering process. Another implementation, referred to as the iterative SIOF algorithm is introduced, which decides on symbol detection order based on a posteriori symbol probabilities to improve the detection performance. Simulations performed on a space-time bit-interleaved coded modulation (STBICM) architecture over quasi-static MIMO fading channels demonstrate that the SIOF V-BLAST detector provides performance gains over previous turbo-BLAST detectors, most notably when more transmit antennas are used.
Let G=(U∪W, E) be a bipartite graph with disjoint vertex sets U and W, edge set E, and girth g. This correspondence presents an algorithm for counting the number of cycles of length g, g+2, and g+4 incident upon every vertex in U∪W. The proposed cycle counting algorithm consists of integer matrix operations and its complexity grows as O(gn3) where n=max(|U|,|W|).
A low-density parity-check code is a code specified by a parity-check matrix with the following properties: each column contains a small fixed number j geq 3 of l's and each row contains a small fixed number k > j of l's. The typical minimum distance of these codes increases linearly with block length for a fixed rate and fixed j . When used with maximum likelihood decoding on a sufficiently quiet binary-input symmetric channel, the typical probability of decoding error decreases exponentially with block length for a fixed rate and fixed j . A simple but nonoptimum decoding scheme operating directly from the channel a posteriori probabilities is described. Both the equipment complexity and the data-handling capacity in bits per second of this decoder increase approximately linearly with block length. For j > 3 and a sufficiently low rate, the probability of error using this decoder on a binary symmetric channel is shown to decrease at least exponentially with a root of the block length. Some experimental results show that the actual probability of decoding error is much smaller than this theoretical bound.
Multiple-input-multiple-output (MIMO) systems provide a very promising means to increase the spectral efficiency for wireless systems. By using orthogonal frequency-division multiplexing (OFDM), wideband transmission can be achieved over frequency-selective fading radio channels. First, in this paper, we introduce an improved vertical Bell Labs layered space-time (V-BLAST) receiver which takes the decision errors into account. Second, we propose an iterative detection and decoding (IDD) scheme for coded layered space-time architectures in MIMO-OFDM systems. For the iterative process, a low-complexity demapper is developed by making use of both nonlinear interference cancellation and linear minimum mean-square error filtering. Also, a simple cancellation method based on hard decision is presented to reduce the overall complexity. Simulation results demonstrate that the proposed IDD scheme combined with the improved V-BLAST performs almost as well as the optimal turbo-MIMO approach, while providing tremendous savings in computational complexity.
We consider a low-density parity-check (LDPC)-coded modulation scheme in multi-input multi-output (MIMO) multiple-access systems. The receiver can be regarded as a serially concatenated iterative detection and decoding scheme, where the LDPC decoders perform the role of outer decoder and the multiuser demapper does that of the inner decoder. In this paper, we investigate the performance of the scheme with simulation results and bounds. Union upper bounds are derived, which can be used as additional means to evaluate the performance of the MIMO multiple-access system.
We design serial concatenated multi-input multi-output systems based on low-density parity-check (LDPC) codes. We employ a receiver structure combining the demapper/detector and the decoder in an iterative fashion. We consider the a posteriori probability (APP) demapper, as well as a suboptimal demapper incorporating interference cancellation with linear filtering. Extrinsic information transfer (EXIT) chart analysis is applied to study the convergence behavior of the proposed schemes. We show that EXIT charts match very well with the simulated decoding trajectories, and they help explain the impact of different mappings and different demappers. It is observed that if the APP demapper transfer characteristics are almost flat, the LDPC codes optimized for binary-input channels are good enough to achieve performance close to the channel capacity. We also present a simple code-optimization method based on EXIT chart analysis, and we design a rate-1/2 LDPC code that achieves very low bit-error rates within 0.15 dB of the capacity of a two-input two-output Rayleigh fading channel with 4-pulse amplitude modulation. We next propose to use a space-time block code as an inner code of our serial concatenated coding scheme. By means of a simple example scheme, using an Alamouti inner code, we demonstrate that the design/optimization of the outer code (e.g., LDPC code) is greatly simplified.
Recent advancements in iterative processing of channel codes and the development of turbo codes have allowed the communications industry to achieve near-capacity on a single-antenna Gaussian or fading channel with low complexity. We show how these iterative techniques can also be used to achieve near-capacity on a multiple-antenna system where the receiver knows the channel. Combining iterative processing with multiple-antenna channels is particularly challenging because the channel capacities can be a factor of ten or more higher than their single-antenna counterparts. Using a "list" version of the sphere decoder, we provide a simple method to iteratively detect and decode any linear space-time mapping combined with any channel code that can be decoded using so-called "soft" inputs and outputs. We exemplify our technique by directly transmitting symbols that are coded with a channel code; we show that iterative processing with even this simple scheme can achieve near-capacity. We consider both simple convolutional and powerful turbo channel codes and show that excellent performance at very high data rates can be attained with either. We compare our simulation results with Shannon capacity limits for ergodic multiple-antenna channel.
Mutual information transfer characteristics of soft in/soft out
decoders are proposed as a tool to better understand the convergence
behavior of iterative decoding schemes. The exchange of extrinsic
information is visualized as a decoding trajectory in the extrinsic
information transfer chart (EXIT chart). This allows the prediction of
turbo cliff position and bit error rate after an arbitrary number of
iterations. The influence of code memory, code polynomials as well as
different constituent codes on the convergence behavior is studied for
parallel concatenated codes. A code search based on the EXIT chart
technique has been performed yielding new recursive systematic
convolutional constituent codes exhibiting turbo cliffs at lower
signal-to-noise ratios than attainable by previously known constituent
codes
We introduce a new class of upper bounds on the log partition function of a Markov random field (MRF). This quantity plays an important role in various contexts, including approximating marginal distributions, parameter estimation, combinatorial enumeration, statistical decision theory, and large-deviations bounds. Our derivation is based on concepts from convex duality and information geometry: in particular, it exploits mixtures of distributions in the exponential domain, and the Legendre mapping between exponential and mean parameters. In the special case of convex combinations of tree-structured distributions, we obtain a family of variational problems, similar to the Bethe variational problem, but distinguished by the following desirable properties: i) they are convex, and have a unique global optimum; and ii) the optimum gives an upper bound on the log partition function. This optimum is defined by stationary conditions very similar to those defining fixed points of the sum-product algorithm, or more generally, any local optimum of the Bethe variational problem. As with sum-product fixed points, the elements of the optimizing argument can be used as approximations to the marginals of the original model. The analysis extends naturally to convex combinations of hypertree-structured distributions, thereby establishing links to Kikuchi approximations and variants.
We propose a general method for constructing Tanner graphs having a large girth by establishing edges or connections between symbol and check nodes in an edge-by-edge manner, called progressive edge-growth (PEG) algorithm. Lower bounds on the girth of PEG Tanner graphs and on the minimum distance of the resulting low-density parity-check (LDPC) codes are derived in terms of parameters of the graphs. Simple variations of the PEG algorithm can also be applied to generate linear-time encodeable LDPC codes. Regular and irregular LDPC codes using PEG Tanner graphs and allowing symbol nodes to take values over GF(q) (q>2) are investigated. Simulation results show that the PEG algorithm is a powerful algorithm to generate good short-block-length LDPC codes.
In this note, we apply a hierarchical identification principle to study solving the Sylvester and Lyapunov matrix equations. In our approach, we regard the unknown matrix to be solved as system parameters to be identified, and present a gradient iterative algorithm for solving the equations by minimizing certain criterion functions. We prove that the iterative solution consistently converges to the true solution for any initial value, and illustrate that the rate of convergence of the iterative solution can be enhanced by choosing the convergence factor (or step-size) appropriately. Furthermore, the iterative method is extended to solve general linear matrix equations. The algorithms proposed require less storage capacity than the existing numerical ones. Finally, the algorithms are tested on computer and the results verify the theoretical findings.