Large-system performance of iterative multiuser decision-feedback detection

An iterative receiver with soft decision feedback is derived to yield a maximum a posteriori (MAP) estimate of fast Rayleigh flat fading channels. The derivation is based on the expectation-maximization (EM) algorithm. Simulation results indicate that the derived receiver performs better than an iterative receiver with hard decision feedback, for both uncoded data and convolutionally coded data. The combination with turbo codes is also investigated. Three kinds of decision feedback are proposed and compared namely, re-encoder, soft decision feedback and quantizer. It is shown via simulation that soft decision feedback is the best while the quantizer has similar performance. The re-encoder, on the other hand has performance degradation.

In this paper, an integrated Orthogonal Frequency Division Multiplexing (OFDM) system is developed to improve Bit Error Rate (BER) performance of communication systems in order to meet the requirements of advanced communication systems like long term evaluation advanced (LTE –A). The proposed OFDM system consists of channel estimation using comb type pilot arrangement and convolution encoder with the best known Coding Bounds and Maximum A Posteriori (MAP) decoder. Using pilot symbols, the channel quality is estimated. The BER performance of OFDM system is improved using pilot carriers, channel estimation schemes and MAP decoder at the best known coding bounds. The system performance is analyzed with recursive systematic and non-systematic convolution codes, ML and MAP decoders. From the results, it is evident that the proposed OFDM system with channel estimation and MAP decoder at the best known coding bounds improves the system performance significantly.

In this paper, we develop a detection algorithm at the receiver, for a wireless system employing multiple antennas at both the transmitter and receiver, where the knowledge of channel is not available at the transmitter (a.k.a open-loop system). The proposed algorithm offers a very good trade-off between implementation complexity and bit-error-rate (BER) performance. In the literature, the fixed complexity sphere decoding (FSD) is known to be state-of-the art decoding algorithm for open-loop multiple input and multiple output (MIMO) systems. The reduced state maximum aposteriori (RS-MAP) algorithm is an extension of FSD where reduced state (RS) receiver delivers bit level soft decisions using maximum aposteriori (MAP) Bahl, Cocke, Jelinek and Raviv (BCJR) recursions that are implemented on the reduced state tree. While RS-MAP employs state dependent hard decision feedback, the proposed algorithm uses a) a state dependent soft/hard symbol feedback b) a scaling of the branch metric with the assumption that soft decision feedback is employed, to obtain a performance improvement over standard RS-MAP algorithm. The proposed modifications to the branch metric are general and can be applied to a number of other sequence estimators such as maximum likelihood soft output viterbi algorithm (ML-SOVA), FSD-SOVA, RS-MAP with forward only recursion etc.

A number of authors have sought to combine equalization and decoding in an iterative system in order to reduce the effects of frequency and temporal dispersiveness of time-varying frequency-selective channels. In the recent literature, several architectures based on these iterative systems have been proposed. One can note architectures which combine a maximum a posteriori (MAP) equalizer and decoder, architectures formed by an interference canceller and MAP decoder, architectures implementing a decision feedback equalizer and a MAP decoder, etc. Most of these architectures require accurate channel estimation to adapt the equalizer filters or to execute the MAP equalizers. This article presents a turbo equalizer architecture for time-varying frequency-selective channels without channel estimators. The proposed turbo equalizer consists of an interference canceller in direct-adaptation mode and a turbo decoder. In order to reduce noise correlation, the addition of a transverse filter to the interference-canceller architecture is proposed. The reliability factor for variable time-varying frequency-selective channels is also redefined in order to improve the performance of the turbo decoder. The architecture of the proposed turbo equalizer reduces considerably the effects of frequency and temporal dispersiveness of time-varying frequency-selective channels depending on the normalized Doppler frequency range.

We study the maximum a posteriori (MAP) decoding of memoryless non-uniform sources over multiple-antenna channels. Our model is general enough to include space-time coding, BLAST architectures, and single-transmit multi-receive antenna systems which employ any type of channel coding. We derive a closed-form expression for the codeword pairwise error probability (PEP) of general multi-antenna codes using moment generating function and Laplace transform arguments. We then consider space-time orthogonal block (STOB) coding and prove that, similar to the maximum likelihood (ML) decoding case, detection of symbols is decoupled in MAP decoding. We also derive the symbol PEP in closed-form for STOB codes. We apply these results in several scenarios. First, we design a binary antipodal signaling scheme which minimizes the system bit error rate (BER) under STOB coding. At a BER of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> , this constellation has a channel signal-to-noise ratio (CSNR) gain of 4.7 dB over conventional BPSK signaling for a binary nonuniform source with p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> Delta <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">=</sub> P(0) = 0.9. We next design space-time linear dispersion (LD) codes which are optimized for the source distribution under the criterion of minimizing the union upper bound on the frame error rate (FER). Two codes are given here: one outperforms V-BLAST by 3.5 dB and Alamouti's code by 12.3 dB at an FER of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> for a binary source with p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> = 0.9, and the other outperforms V-BLAST by 4.2 dB at an FER of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> for a uniform source. These codes also outperform the LD codes of constructed under a different criteria. Finally, the problem of bit-to-signal mapping is studied. It is shown that for a binary source with p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> = 0.9, 64-QAM signaling, and SER = 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> , a gain of 3.7 dB can be achieved using a better-than-Gray mapping. For a system with one transmit and two receive antennas that uses trellis coding with 16-QAM signaling, a 1.8 dB gain over quasi-Gray mapping and ML decoding is observed when MAP decoding is used for binary sources with p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> = 0.9.

This paper compares a number of decision feedback schemes that improve the initial channel estimates provided by the pilot symbols alone. The decision feedback scheme that feeds back the systematic bits achieves about the same performance as feeding back both the systematic and parity bits at the low fading rate. Its performance is slightly degraded at the higher fading rate. The advantage of this scheme is its lower complexity as the LLRs of the systematic bits are readily available in the turbo decoding process. Soft decision feedback does not always provide large improvement in performance. Noticeable gain in performance using soft decision feedback is seen only when the bits to be fed back are not reliable during the first few iterations.

This paper considers the joint design of bit loading, precoding and receive filters for a multiple-input multiple-output (MIMO) digital communication system employing decision feedback (DF) detection at the receiver. Both the transmitter as well as the receiver are assumed to know the channel matrix perfectly. It is well known that, for linear MIMO transceivers, a diagonal transmission (i.e., orthogonalization of the matrix channel) is optimal for some criteria. Surprisingly, it was shown five years ago that for the family of Schur-convex functions an additional rotation of the symbols is necessary. However, if the bit loading is optimized jointly with the linear transceiver, then the rotation is unnecessary. Similarly, for DF MIMO transceivers, a rotation of the symbols is sometimes needed. The main result of this paper shows that for a DF MIMO transceiver where the bit loading is jointly optimized with the transceiver filters, the rotation of the symbols becomes unnecessary and, consequently, also the DF part of the receiver is not required.

In this correspondence, we study algorithmic approach to solving the problem of maximum a posteriori (MAP) estimation of Markov sequences transmitted over noisy channels, which is also known as the MAP decoding problem. For the class of memoryless binary channels that produce independent substitution and erasure errors, the MAP sequence estimation problem can be formulated and solved as one of the longest path in a weighted directed acyclic graph. But for algorithm efficiency, we transform the graph problem to one of matrix search. If the underlying matrix is totally monotone, then the complexity of MAP sequence estimation can be greatly reduced. We give a sufficient condition for the matrix induced by MAP sequence estimation to be totally monotone, which is indeed the case if the input sequence is Gaussian Markov. Under this condition, the complexity of MAP decoding can be reduced from O(N/sup 2/M) to O(NM), where N is the size of source alphabet and M is the length of input sequence. Furthermore, for Markov sequences of fixed-length code we propose a block parsing strategy to reduce the complexity of MAP sequence estimation to O(M+N/sup 2/M/logM) or to O(M+NM/logM), depending on if the total monotonicity holds. Another significance of this correspondence lies in the applicability of the presented algorithmic approach, which has been thoroughly studied in computer science literature, to many other discrete optimization problems encountered in both source and channel coding, ranging from optimal multiresolution and multiple-description quantizer design, to context quantization for minimum conditional entropy, and to optimal packetization with uneven error protection.

A systematic approach to decision feedback multiuser detection is introduced for the joint detection of symbols of K simultaneously transmitting users of a synchronous correlated waveform multiple-access (CWMA) channel with Gaussian noise. A new performance criterion called symmetric energy is defined which is a low-noise indicator of the joint error rate that at least one user is detected erroneously. Even the best linear detectors can perform poorly in terms of symmetric energy compared to the maximum-likelihood detector. A general class of decision feedback detectors (DFDs) is defined with O(K) implementational complexity per user. The symmetric energy of arbitrary DFD and bounds on their asymptotic effective energy (AEE) performance are obtained along with an exact bit-error rate and AEE analysis for the decorrelating DFD. The optimum DFD that maximizes symmetric energy is obtained. Each one of the K! optimum, decorrelating, and conventional DFDs, that correspond to the K! orders in which the users can be detected, are shown to outperform the linear optimum, decorrelating, and conventional detectors, respectively, in terms of symmetric energy. Moreover, algorithms are obtained for determining the choice of order of detection for the three DFDs which guarantee that they uniformly (user-wise) outperform their linear counterparts. In addition to optimality in symmetric energy, it is also shown that under certain conditions, the optimum DFD achieves the AEE performance of the exponentially complex maximum-likelihood detector for all users simultaneously. None of the results of this paper make the perfect feedback assumption. The implications of our work on power control for multiuser detection are also discussed.

This paper investigates the performance of various “turbo” receivers for serially concatenated turbo codes transmitted through intersymbol interference (ISI) channels. Both the inner and outer codes are assumed to be recursive systematic convolutional (RSC) codes. The optimum turbo receiver consists of an (inner) channel maximum a posteriori (MAP) decoder and a MAP decoder for the outer code. The channel MAP decoder operates on a “supertrellis” which incorporates the channel trellis and the trellis for the inner error-correcting code. This is referred to as the MAP receiver employing a SuperTrellis (STMAP). Since the complexity of the supertrellis in the STMAP receiver increases exponentially with the channel length, we propose a simpler but suboptimal receiver that employs the predictive decision feedback equalizer (PDFE). The key idea in this paper is to have the feedforward part of the PDFE outside the iterative loop and incorporate only the feedback part inside the loop. We refer to this receiver as the PDFE-STMAP. The complexity of the supertrellis in the PDFE-STMAP receiver depends on the inner code and the length of the feedback part. Investigations with Proakis B, Proakis C (both channels have spectral nulls with all zeros on the unit circle and hence cannot be converted to a minimum phase channel) and a minimum phase channel reveal that at most two feedback taps are sufficient to get the best performance. A reduced-state STMAP (RS-STMAP) receiver is also derived which employs a smaller supertrellis at the cost of performance.

Recent studies have revealed a number of pathologies of neural machine translation (NMT) systems. Hypotheses explaining these mostly suggest there is something fundamentally wrong with NMT as a model or its training algorithm, maximum likelihood estimation (MLE). Most of this evidence was gathered using maximum a posteriori (MAP) decoding, a decision rule aimed at identifying the highest-scoring translation, i.e. the mode. We argue that the evidence corroborates the inadequacy of MAP decoding more than casts doubt on the model and its training algorithm. In this work, we show that translation distributions do reproduce various statistics of the data well, but that beam search strays from such statistics. We show that some of the known pathologies and biases of NMT are due to MAP decoding and not to NMT's statistical assumptions nor MLE. In particular, we show that the most likely translations under the model accumulate so little probability mass that the mode can be considered essentially arbitrary. We therefore advocate for the use of decision rules that take into account the translation distribution holistically. We show that an approximation to minimum Bayes risk decoding gives competitive results confirming that NMT models do capture important aspects of translation well in expectation.

Motivated by the structure of basic sensor networks, we study an optimal joint decoding problem in which the real-valued outputs of two correlated Gaussian sources are scalar quantized, bit assigned, and transmitted, without applying channel coding or interleaving, over a multiple-access channel that consists of two orthogonal point-to-point time-correlated Rayleigh fading subchannels used with soft-decision demodulation. Each fading subchannel is modeled by a nonbinary Markov noise discrete channel that was recently shown to effectively represent it. The correlated sources have memory captured by a time-varying correlation coefficient governed by a two-state first-order Markov process. At the receiver side, we design a joint sequence maximum a posteriori (MAP) decoder to exploit the correlation between the two sources, their temporal memory, and the redundancy left in the quantizers' indexes, the channels' soft-decision outputs, and noise memory. Under the simple practical case of using two-level source quantization, we propose a Markov model to estimate the joint behavior of the quantized sources. We then establish necessary and sufficient conditions under which the delay-prone joint sequence MAP decoder can be reduced to a simple instantaneous symbol-by-symbol decoder. We illustrate our analytical results by system simulation and demonstrate that joint MAP decoding can appropriately harness source and channel characteristics to achieve improved signal-to-distortion ratio performance for a wide range of system conditions.

A turbo receiver combined with CFO compensation in frequency-domain for OFDMA uplink

Event Abstract Back to Event Ensemble methods for boosting the decoding performance of a hand grasping BMI Erk Subasi1*, Benjamin Townsend2 and Hans Scherberger2 1 Institute of Neuroinformatics, Computer Science, Switzerland 2 Institute of Neuroinformatics, Switzerland We are developing a brain machine interface (BMI) to decode grasp shape in macaque monkeys online. Neural activity is evaluated using chronically implanted electrodes in the anterior intraparietal cortex (AIP) and ventral premotor cortex (F5), areas known to be involved in the transformation of visual signals into hand grasping instructions. Macaque monkeys were trained in a delayed grasping task, where they first placed their hands at rest and fixated a red LED before a grasping handle was presented in one of 5 different orientations, and the color of an LED instructed the animals to grasp the handle either with a power or precision grip, respectively. After a short delay the fixation LED dimmed instructing the monkey to perform the required grasp. Correct trials were rewarded with a small amount of juice. After successful training 5 floating micro-electrode arrays (FMA; MicroProbe Inc) were implanted in AIP (2) and F5 (3) of 1 animal. Each array comprised 16 platinum-iridium electrodes (length 1.0-4.5mm, spacing 0.5 mm). This configuration was chosen to facilitate the recording of neuronal activity within cortical sulci instead of on the cortical surface. Neural signals were sampled using a Cerebus (Cyberkinetics Inc, Foxborough, MA) Neural Signal Processor (NSP) and streamed to a dedicated decoding PC via UDP. We previously reported our results using a standard maximum a posteriori (MAP) classifier where we obtained 94% performance for grasp type decoding (precision vs. power), following a mean accuracy of 91% for grasp type and 2 grasp orientations (target tilted to left or right) and finally a mean accuracy of 55% where we decode full 10 conditions (grasp type and 5 orientations). MAP decoding is one of the standard methods in BMI literature which is shown yielding robust decoding results in similar experiments before. But we make 3 common strong assumptions regarding the underlying probability distributions in MAP framework. First, we assume a Poisson probability distribution for firing rates of each individual unit. Second, in order to ease the joint probability distribution computation, it is assumed that neurons are firing in an independent fashion. And third, it is assumed that these units have stationary firing probability distributions. It is important to note that a marginal increase in the decoding performance of a neural-prosthetic device may provide substantial improvement in perceived quality of the system by the user. Here, we introduce a new approach for decoding discrete grasping postures which does not need to rely on any of these assumptions. Ensemble methods have gained popularity among the machine learning community in the last decade, both due to their strong theoretical base and practical outcomes. They mainly try to optimally utilize many weak learners on a training set for achieving better performance compared to a single strong classifier while reducing the variance of the classifier and in some cases also providing a better bias. Here, the comparative decoding analysis will be presented with adaptive bagging and boosting techniques. Conference: Neuroinformatics 2009, Pilsen, Czechia, 6 Sep - 8 Sep, 2009. Presentation Type: Poster Presentation Topic: Brain machine interface Citation: Subasi E, Townsend B and Scherberger H (2019). Ensemble methods for boosting the decoding performance of a hand grasping BMI. Front. Neuroinform. Conference Abstract: Neuroinformatics 2009. doi: 10.3389/conf.neuro.11.2009.08.056 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 22 May 2009; Published Online: 09 May 2019. * Correspondence: Erk Subasi, Institute of Neuroinformatics, Computer Science, Zurich, Switzerland, erk@ini.phys.ethz.ch Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Erk Subasi Benjamin Townsend Hans Scherberger Google Erk Subasi Benjamin Townsend Hans Scherberger Google Scholar Erk Subasi Benjamin Townsend Hans Scherberger PubMed Erk Subasi Benjamin Townsend Hans Scherberger Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Recently, it has been verified that the Reed-Muller (RM) code, which has been predicted for a long time in the field of code theory, achieves capacity in a binary erasure channel (BEC) with a MAP (maximum a posteriori) decoder. Through weight distribution interpretation, it was also discovered that the RM code achieves a binary memoryless symmetric (BMS) channel capacity. A successive cancellation list (SCL) technique has been studied as a practical decoder instead of a MAP decoder. In this paper, the performance improvement potential that can be improved when a generalized concatenated code (GCC) with an outer code is designed to improve the practical SCL decoder performance is analyzed. When information bits are used as frozen bits in these code-word designs, we analyze an inter-code-word distance and the decoding outage probability of the designed code. We expect that our results can be used as a conceptual base for improving communication methods in the future development of channel encoding technology.