Optimal Maximum-likelihood Decoding Research Articles

Probabilistic Searching for MIMO Detection Based on Lattice Gaussian Distribution

In this paper, a deterministic sampling decoding strategy for multiple-input multiple output (MIMO) systems is studied, which performs probabilistic searching according to a probability threshold in the lattice Gaussian distribution. Motivated by model probabilistic twin (MPT), the randomness in obtaining the target decoding solution is overcome by the proposed probabilistic searching decoding (PSD) algorithm, which brings considerable decoding gains in both performance and complexity. Specifically, the decoding radius of PSD is derived while the decoding complexity in terms of the number of visited nodes during the searching is also upper bounded, leading to an explicit decoding trade-off. Meanwhile, we generalize PSD by the mechanism of candidate protection so that it enjoys a flexible performance between the suboptimal successive interference cancelation (SIC) decoding and the optimal maximum likelihood (ML) decoding by adjusting the initial search size <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> . Methods for further optimization and complexity reduction of the proposed PSD algorithm are also given. Finally, simulation results based on MIMO detection are presented to confirm the tractable and flexible decoding trade-off of the proposed PSD algorithm.

Universal Decoding for the Typical Random Code and for the Expurgated Code

We provide two results concerning the optimality of the stochastic-mutual information (SMI) decoder, which chooses the estimated message according to a posterior probability mass function, which is proportional to the exponentiated empirical mutual information induced by the channel output sequence and the different codewords. First, we prove that the error exponents of the typical random codes under the optimal maximum likelihood (ML) decoder and the SMI decoder are equal. As a corollary to this result, we also show that the error exponents of the expurgated codes under the ML and the SMI decoders are equal. These results strengthen the well-known result due to Csiszár and Körner, according to which, the ML and the maximum-mutual information (MMI) decoders achieve equal random-coding error exponents, since the error exponents of the typical random code and the expurgated code are strictly higher than the random-coding error exponents, at least at low coding rates. The universal optimality of the SMI decoder, in the random-coding error exponent sense, is easily proven by commuting the expectation over the channel noise and the expectation over the ensemble. This commutation can no longer be carried out, when it comes to typical and expurgated exponents. Therefore, the proof of the universal optimality of the SMI decoder must be completely different and it turns out to be highly non-trivial.

Universal Sparse Superposition Codes With Spatial Coupling and GAMP Decoding

Sparse superposition codes, or sparse regression codes, constitute a new class of codes, which was first introduced for communication over the additive white Gaussian noise (AWGN) channel. It has been shown that such codes are capacity-achieving over the AWGN channel under optimal maximum-likelihood decoding as well as under various efficient iterative decoding schemes equipped with power allocation or spatially coupled constructions. Here, we generalize the analysis of these codes to a much broader setting that includes all memoryless channels. We show, for a large class of memoryless channels, that spatial coupling allows an efficient decoder, based on the generalized approximate message-passing (GAMP) algorithm, to reach the potential (or Bayes optimal) threshold of the underlying (or uncoupled) code ensemble. Moreover, we argue that spatially coupled sparse superposition codes universally achieve capacity under GAMP decoding by showing, through analytical computations, that the error floor vanishes and the potential threshold tends to capacity, as one of the code parameters goes to infinity. Furthermore, we provide a closed-form formula for the algorithmic threshold of the underlying code ensemble in terms of Fisher information. Relating an algorithmic threshold to a Fisher information has theoretical as well as practical importance. Our proof relies on the state evolution analysis and uses the potential method developed in the theory of low-density parity-check (LDPC) codes and compressed sensing.

Deep Learning-Based Sphere Decoding

In this paper, a deep learning (DL)-based sphere decoding algorithm is proposed, where the radius of the decoding hypersphere is learned by a deep neural network (DNN). The performance achieved by the proposed algorithm is very close to the optimal maximum likelihood decoding (MLD) over a wide range of signal-to-noise ratios (SNRs), while the computational complexity, compared to existing sphere decoding variants, is significantly reduced. This improvement is attributed to the DNN’s ability of intelligently learning the radius of the hypersphere used in decoding. The expected complexity of the proposed DL-based algorithm is analytically derived and compared with existing ones. It is shown that the number of lattice points inside the decoding hypersphere drastically reduces in the DL-based algorithm in both the average and worst-case senses. The effectiveness of the proposed algorithm is shown through the simulation for high-dimensional multiple-input multiple-output (MIMO) systems, using high-order modulations.

Universal Decoding Using a Noisy Codebook

We consider the topic of universal decoding with a decoder that does not have direct access to the codebook, but only to noisy versions of the various randomly generated codewords, a problem motivated by biometrical identification systems. Both the source that generates the original (clean) codewords, and the channel that corrupts them in generating the noisy codewords, as well as the main channel for communicating the messages, are all modeled by non–unifilar, finite–state systems (hidden Markov models). As in previous works on universal decoding, here too, the average error probability of our proposed universal decoder is shown to be as small as that of the optimal maximum likelihood (ML) decoder, up to a multiplicative factor that is a sub–exponential function of the block length. It therefore has the same error exponent, whenever the ML decoder has a positive error exponent. The universal decoding metric is based on Lempel–Ziv incremental parsing of each noisy codeword jointly with the given channel output vector, but this metric is somewhat different from the one proposed in earlier works on universal decoding for finite–state channels, by Ziv (1985) and by Lapidoth and Ziv (1998). The reason for the difference is that here, unlike in those earlier works, the probability distribution that governs the (noisy) codewords is, in general, not uniform across its support. This non–uniformity of the codeword distribution also makes our derivation more challenging. Another reason for the more challenging analysis is the fact that the effective induced channel between the noisy codeword of the transmitted message and the main channel output is not a finite–state channel in general.

Interference Management via Sliding-Window Coded Modulation for 5G Cellular Networks

SWCM aims to mitigate the adverse effects of interference at the physical layer by tracking the optimal maximum likelihood decoding performance with low-complexity decoding and minimal coordination overhead. This article reviews the basic structure of the SWCM scheme built on the principles of network information theory, and discusses how it can be extended and implemented in practical wireless communication systems. Using a representative implementation based on LTE OFDM MIMO systems, extensive link-level and system-level performance simulations are carried out, which demonstrate that SWCM offers significant gains for all users over conventional interference-aware communication schemes. Network operating prerequisites for SWCM are also discussed to facilitate the standardization effort for its adoption in the fifth generation cellular network.

Antenna Beam Pattern Modulation With Lattice-Reduction-Aided Detection

This paper introduces a novel transmission design for antenna beam pattern modulation (ABPM) with a low-complexity decoding method. The concept of ABPM was first presented with optimal maximum-likelihood (ML) decoding. However, an ML detector may not be viable for practical systems when the constellation size or the number of antennas is large, such as in massive multiple-input–multiple-output (MIMO) systems. Linear detectors, on the other hand, have lower complexity but inferior performance. In this paper, we present the antenna pattern selection with a lattice-reduction-aided linear detector for ABPM to reduce the detection complexity with the bit error rate (BER) performance approaching that of ML while conserving low complexity. Simulation results show that even with this suboptimal detection, performance gain is achieved by the proposed scheme compared with different spatial modulation techniques using ML detection. In addition, to validate the results, an upper bound expression for the BER is provided for ABPM with ML detection.

Optimal Achievable Rates for Interference Networks With Random Codes

The optimal rate region for interference networks is characterized when encoding is restricted to random code ensembles with superposition coding and time sharing. A simple simultaneous nonunique decoding rule, under which each receiver decodes for the intended message as well as the interfering messages, is shown to achieve this optimal rate region regardless of the relative strengths of signal, interference, and noise. This result implies that the Han-Kobayashi bound, the best known inner bound on the capacity region of the two-user-pair interference channel, cannot be improved merely by using the optimal maximum likelihood decoder.

Universal Decoding for Gaussian Intersymbol Interference Channels

A universal decoding procedure is proposed for the intersymbol interference (ISI) Gaussian channels. The universality of the proposed decoder is in the sense of being independent of the channel parameters, and at the same time, attaining the same random coding error exponent as the optimal maximum-likelihood decoder, which utilizes full knowledge of these unknown parameters. The proposed decoding rule can be regarded as a frequency domain version of the universal maximum mutual information decoder. Contrary to previously suggested universal decoders for ISI channels, our proposed decoding metric can easily be evaluated.

Optimal Prediction Likelihood Tree Based Source- Channel ML Decoder for Wireless Sensor Networks

In this work, we develop a framework for optimal joint Source-Channel Maximum Likelihood (SCML) decoding in Wireless Sensor Networks (WSNs). The proposed scheme employs a novel Generalized Likelihood Ratio Test based Prediction Likelihood Tree (PLT) approach to exploit the spatio-temporal narrowband properties of the sensor data for sequence detection in wireless sensor networks. Further, analytical bounds are derived to characterize the performance of the low complexity decision feedback and optimal Viterbi based Maximum Likelihood Sequence Detection (MLSD) for joint decoding over fading wireless channels, where only ad hoc schemes exist in current literature. The PLT based SCML scheme, which has a low complexity, is ideally suited for implementation in practical wireless sensor networks with limited computational power and achieves a performance close to the optimal MLSD bound. Simulation results are presented to validate the performance of the SCML algorithm and the proposed analytical bounds for sensor data reception in WSNs.

Fast Sparse Superposition Codes Have Near Exponential Error Probability for &lt;formula formulatype="inline"&gt;&lt;tex Notation="TeX"&gt;$R&amp;lt;{\cal C}$&lt;/tex&gt;&lt;/formula&gt;

For the additive white Gaussian noise channel with average codeword power constraint, sparse superposition codes are developed. These codes are based on the statistical high-dimensional regression framework. In a previous paper, we investigated decoding using the optimal maximum-likelihood decoding scheme. Here, a fast decoding algorithm, called the adaptive successive decoder, is developed. For any rate R less than the capacity C, communication is shown to be reliable with nearly exponentially small error probability. Specifically, for blocklength n, it is shown that the error probability is exponentially small in n/logn.

Robust Decoding for Convolutionally Coded Systems Impaired by Memoryless Impulsive Noise

It is well known that communication systems are susceptible to strong impulsive noises. To combat this, convolutional coding has long served as a cost-efficient tool against moderately frequent memoryless impulses with given statistics. Nevertheless, impulsive noise statistics are difficult to model accurately and are typically not time-invariant, making the system design challenging. In this paper, because of the lack of knowledge regarding the probability density function of impulsive noises, an efficient decoding scheme was devised for single-carrier narrowband communication systems; a design parameter was incorporated into recently introduced joint erasure marking and Viterbi decoding algorithm, dubbed the metric erasure Viterbi algorithm (MEVA). The proposed scheme involves incorporating a well-designed clipping operation into a Viterbi algorithm, in which the clipping threshold must be appropriately set. In contrast to previous publications that have resorted to extensive simulations, in the proposed scheme, the bit error probability performance associated with the clipping threshold was characterized by deriving its Chernoff bound. The results indicated that when the clipping threshold was judiciously selected, the MEVA can be on par with its optimal maximum-likelihood decoding counterpart under fairly general circumstances.

Low-Complexity Decoding Algorithms for Distributed Space-Time Coded Regenerative Relay Systems

We examine decoding structure for distributed space-time coded regenerative relay networks. Given the possible demodulation error at the regenerative relays, we provide a general framework of error aware decoder, where the receiver exploits the demodulation error probability of relays to improve the system performance. Considering the high computational complexity of optimal Maximum Likelihood (ML) decoder, we also propose two low-complexity decoders, Max-Log decoder and Max-Log-Sphere decoder. Computational complexities of these three decoders are also analyzed. Simulation results show that error aware decoders can improve system performance greatly without high system overload and Max-Log decoder and Max-Log-Sphere decoder can drastically reduce the decoding complexity with negligible performance degradation.

Efficient blind decoders for additive spread spectrum embedding based data hiding

This article investigates efficient blind watermark decoding approaches for hidden messages embedded into host images, within the framework of additive spread spectrum (SS) embedding based for data hiding. We study SS embedding in both the discrete cosine transform and the discrete Fourier transform (DFT) domains. The contributions of this article are multiple-fold: first, we show that the conventional SS scheme could not be applied directly into the magnitudes of the DFT, and thus we present a modified SS scheme and the optimal maximum likelihood (ML) decoder based on the Weibull distribution is derived. Secondly, we investigate the improved spread spectrum (ISS) embedding, an improved technique of the traditional additive SS, and propose the modified ISS scheme for information hiding in the magnitudes of the DFT coefficients and the optimal ML decoders for ISS embedding are derived. We also provide thorough theoretical error probability analysis for the aforementioned decoders. Thirdly, sub-optimal decoders, including local optimum decoder (LOD), generalized maximum likelihood (GML) decoder, and linear minimum mean square error (LMMSE) decoder, are investigated to reduce the required prior information at the receiver side, and their theoretical decoding performances are derived. Based on decoding performances and the required prior information for decoding, we discuss the preferred host domain and the preferred decoder for additive SS-based data hiding under different situations. Extensive simulations are conducted to illustrate the decoding performances of the presented decoders.

On Pseudocodewords and Decision Regions of Linear Programming Decoding of HDPC Codes

In this paper we explore the decision regions of Linear Programming (LP) decoding. We compare the decision regions of an LP decoder, a Belief Propagation (BP) decoder and the optimal Maximum Likelihood (ML) decoder. We study the effect of minimal-weight pseudocodewords on LP decoding. We present global optimization as a method for finding the minimal pseudoweight of a given code as well as the number of minimal-weight generators. We present a complete pseudoweight distribution for the [24, 12, 8] extended Golay code, and provide justifications of why the pseudoweight distribution alone cannot be used for obtaining a tight upper bound on the error probability.

Monotonic optimization based decoding for linear codes

New efficient methods are developed for the optimal maximum-likelihood (ML) decoding of an arbitrary binary linear code based on data received from any discrete Gaussian channel. The decoding algorithm is based on monotonic optimization that is minimizing a difference of monotonic (d.m.) objective functions subject to the 0---1 constraints of bit variables. The iterative process converges to the global optimal ML solution after finitely many steps. The proposed algorithm's computational complexity depends on input sequence length k which is much less than the codeword length n, especially for a codes with small code rate. The viability of the developed is verified through simulations on different coding schemes.

A Low Complexity Decoder for Quasi-Orthogonal Space Time Block Codes

In this paper, a low-complexity suboptimal decoder for coherent and non-coherent quasi-orthogonal space time block codes with three and four transmit antennas is proposed. Our decoder enjoys a nearly linear complexity and approximately the same performance as the optimal maximum-likelihood (ML) decoder. Simulations show the advantages of the proposed decoder with respect to several other popular approaches to the coherent and non-coherent decoding.

EM‐based noise plus interference estimation for OFDM‐based cognitive radio systems

ABSTRACTIn this paper, we consider the narrowband interference problem for orthogonal frequency division multiplexing (OFDM)‐based cognitive radio (CR) systems, in which parts of the OFDM subcarriers and parts of the data frame can be seriously interfered, resulting in significant performance degradation. We propose a scheme of iterative noise plus interference estimation and decoding (IED) to mitigate the performance degradation caused by the narrowband interference, which is based on expectation maximization (EM) algorithm. To reduce the number of OFDM symbols for time domain averaging required in the proposed scheme, and adapt the proposed scheme to rapid changing narrowband interference conditions, we also propose an IED scheme with frequency domain partial averaging (IED‐FPA). Moreover, we derive the Cramér‐Rao lower bounds for unbiased noise plus interference variance estimations, and they can be achieved via the proposed IED schemes. Simulation results show that the proposed IED‐FPA scheme can effectively achieve the same performance as that of the optimal maximum likelihood decoder with full knowledge of the power plus interference variances, and the proposed IED‐FPA scheme is very robust with respect to the number of the interfered subcarriers and positive errors of the knowledge of the interfered subcarriers' number. Copyright © 2010 John Wiley &amp; Sons, Ltd.

Approximate Performance Analysis for Linear Codes in Superposition Schemes over Gaussian Broadcast Channels

Unequal error-protection schemes obtained by means of two-level superposition coding are considered. Their performance over Gaussian broadcast channels (GBCs) is investigated with optimal maximum-likelihood decoding as well as with a suboptimal decoding strategy based on interference cancellation. We focus on GBCs without fading and, assuming that linear codes are used, we evaluate, for both decoding strategies, analytical approximations of the word-error rate based on a suitable application of the union bound. As in the case of turbo codes and turbo-coded modulations in schemes without superposition, the derivation of the approximations exploits the concept of uniform interleaving. The analytical expressions obtained are in excellent agreement with the simulation results, and thus provide a useful tool for analysis and design of practical superposition-coding schemes. Unlike the existing design tools, which rely on the assumption of infinite-length superposition codes, the proposed approach allows us to study the effectiveness of finite-length coding schemes with known distance spectrum.

A comparative study of heuristic algorithms: GA and UMDA in spatially multiplexed communication systems

A performance comparison of genetic algorithm (GA) and the univariate marginal distribution algorithm (UMDA) as decoders in multiple input multiple output (MIMO) communication system is presented in this paper. While the optimal maximum likelihood (ML) decoder using an exhaustive search method is prohibitively complex, simulation results show that the GA and UMDA optimized MIMO detection algorithms result in near optimal bit error rate (BER) performance with significantly reduced computational complexity. The results also suggest that the heuristic based MIMO detection outperforms the vertical bell labs layered space time (VBLAST) detector without severely increasing the detection complexity. The performance of UMDA is found to be superior to that of GA in terms of computational complexity and the BER performance.