Maximum A Posteriori Probability Algorithm Research Articles

GMM based low-complexity adaptive machine-learning equalizers for optical fiber communication

The demand for high-speed data transmission has increased rapidly over the past few years, leading to advanced optical communication techniques. However, most of machine learning based equalizers which are trained with offline dataset mainly focus on achieving low BER, neglecting the generalization ability when the properties of optical link change. In this paper, we propose Gaussian Mixture model (GMM) based low-complexity adaptive machine-learning equalizers. The proposed online training strategy can fine-tune the parameters in GMM with a small amount of training sequence by introducing Maximum a posteriori probability (MAP) algorithm and sliding window. The size of online training sequence can be reduced by utilizing the parameters trained from offline data as the priori information to reduce the size of online training sequence. The proposed adaptive GMM based equalizers can not only show an excellent capability of mitigating nonlinear distortions but also show the ability to update parameters automatically according to the channel conditions. In addition, experimental results show that by introducing MAP algorithm and sliding window, the convergence speed of the proposed equalizers have been accelerated by 2 times, compared with the case that the traditional Expectation Maximization (EM) algorithm is used for online parameter update. On the other hand, there is no significant increase in computational complexity during the online stage.

Attenuation Factor approach to minimize the correlation effect in Soft Output Viterbi Algorithm

Prominent turbo decoding algorithms used for wireless applications are Maximum A posteriori Probability (MAP) and Soft Output Viterbi Algorithm (SOVA). These algorithms are known for their error correcting performance close to Shannon’s limit. MAP algorithm is intense in terms of computational complexity but gives optimal performance. SOVA algorithm gives sub-optimal performance with reduced complexity and is appropriate for real time implementation. Sub-optimal performance of SOVA is attributed to correlation effect that exists between intrinsic and extrinsic information exchanged between component turbo decoders. This paper aims at reducing the correlation effect in SOVA using Attenuation Factor (AF) approach. In this approach, two AF values are selected through MATLAB simulation that minimizes the correlation between intrinsic and extrinsic information of the two constituent decoders. Acquired AF values are analysed in Additive White Gaussian Noise (AWGN) and Rayleigh fading channel. To justify the efficiency of the proposed SOVA algorithm, EXIT chart analysis, BER analysis and complexity analysis are done. The results depict that the proposed AF approach reduces the correlation effect in SOVA with nominal BER and complexity.

Sparse Channel Estimation for OFDM-Based Underwater Acoustic Systems in Rician Fading With a New OMP-MAP Algorithm

In this paper, a new channel estimation algorithm is proposed that exploits channel sparsity in the time domain for an orthogonal frequency division multiplexing (OFDM)-based underwater acoustical (UWA) communications systems in the presence of Rician fading. A path-based channel model is used, in which the channel is described by a limited number of paths, each characterized by a delay, Doppler scale, and attenuation factor. The resulting algorithm initially estimates the overall sparse channel tap delays and Doppler shifts using a compressed sensing approach, in the form of the orthogonal matching pursuit (OMP) algorithm. Then, a computationally efficient and novel channel estimation algorithm is developed by combining the OMP and maximum a posteriori probability (MAP) techniques for estimating the sparse complex channel path gains whose prior densities have complex Gaussian distributions with unknown mean and variance vectors, where a computationally efficient maximum likelihood algorithm is proposed for their estimation. Monte Carlo simulation results show that the mean square error and symbol error rate performances of the OMP–MAP algorithm uniformly outperforms the conventional OMP-based channel estimation algorithm, in case of uncoded OFDM-based UWA communications systems.

Duality of channel encoding and decoding—Part II: rate‐1 non‐binary convolutional codes

AbstractThis is the second part of a series of papers on a revisit to the bidirectional Bahl–Cocke–Jelinek–Raviv (BCJR) soft‐in‐soft‐out maximum a posteriori probability (MAP) decoding algorithm. Part I revisited the BCJR MAP decoding algorithm for rate‐1 binary convolutional codes and proposed a linear complexity decoder using shift registers in the complex number field. Part II proposes a low complexity decoder for rate‐1 non‐binary convolutional codes that achieves the same error performance as the bidirectional BCJR soft‐in‐soft‐out MAP decoding algorithm. We observe an explicit relationship between the encoding and decoding of rate‐1 convolutional codes in GF(q). Based on this relationship, the BCJR forward and backward decoding are implemented by dual encoders using shift registers whose contents are vectors of complex numbers. The input to the dual encoders is the probability mass function of the received symbols, and the output of the dual encoders is the probability mass function of the information symbols. The bidirectional BCJR MAP decoding is implemented by linearly combining the shift register contents of the dual encoders for forward and backward decoding. The proposed decoder significantly reduces the computational complexity of the bidirectional BCJR MAP algorithm from exponential to linear with constraint length of convolutional codes. To further reduce complexity, fast Fourier transform is applied. Mathematical proofs and simulation results are provided to validate our proposed decoder. Copyright © 2016 John Wiley & Sons, Ltd.

Iterative Single-Antenna Interference Cancellation: Algorithms and Results

The capacity of cellular mobile communication systems can significantly be improved using single-antenna interference cancellation (SAIC) techniques. This paper analyzes several soft-input-soft-output (SISO) detectors in iterative SAIC receivers based on the turbo principle and compares their performances and complexities. Among them, the concurrent maximum a posteriori probability (MAP) receiver, which detects single-user signals and exchanges the soft information between cochannel users, is found to provide a good balance between performance and complexity. It can perform nearly the same as the joint MAP algorithm and achieve the single-user matched-filter bound (MFB), and its complexity only linearly increases with the number of cochannel signals. Other reduced-complexity algorithms, such as the Rake Gaussian (RG) approach and soft interference cancellation with MAP equalization (SIC-MAP), also achieve satisfactory performance for binary phase-shift keying (BPSK) modulation when the cochannel interference (CCI) signal can be decoded.

Performance of Unequal Error Protection Using Maximum A- posteriori Probability Algorithm and Modified MAP in Additive White Gaussian Noise and Fading Channel

Problem statement : In this study we propose a method to improve the performance of Maximum A-Posteriori Probability Algorithm, which is used in turbo decoder. Previously the performance of turbo decoder is improved by means of scaling the channel reliability value. Approach : A modification in MAP algorithm proposed in this study, which achieves further improvement in forward error correction by means of scaling the extrinsic information in both decoders without introducing any complexity. The encoder is modified with a new puncturing matrix, which yields Unequal Error Protection (UEP). This modified MAP algorithm is analyzed with the traditional turbo code system Equal Error Protectio n (EEP) and also with Unequal Error Protection (UEP) both in AWGN channel and fading channel. Result: MAP and modified MAP achieve coding gain of 0.6 dB over EEP in AWGN channel. The MAP and modified MAP achieve coding gain of 0.4 dB and 0.9dB over EEP respectively in Rayleigh fadi ng channel. Modified MAP in UEP class 1 and class 2 gained 0.8 dB and 0.6 dB respectively in AW GN channel where as in fading channel class 1 and 2 gained 0.4 dB and 0.6 dB respectively. Conclusion/Recommendations: The modified MAP algorithm improves the Bit Error Rate (BER) performance in EEP as well as UEP both in AWGN and fading channels. We propose modified MAP error correction algorithm with UEP for broad band communication.

Improved BDFE Using A Priori Information for Turbo Equalization

Turbo equalization improves communication system performance by iteratively exchanging information between soft-input soft-output (SISO) equalizer and SISO channel decoder. The trellis-based maximum a posteriori probability (MAP) algorithm serves as the optimum SISO equalizer for turbo equalization. However, MAP algorithm is unsuitable for systems with large modulation constellation size and severe inter-symbol interference (ISI) due to its prohibitively high computational complexity. In this paper, an improved SISO block decision feedback equalizer (BDFE) is proposed for low complexity turbo equalization. Unlike other sub-optimum equalizers which perform symbol by symbol detection, the proposed equalizer generates the soft output for each data bit by collecting information from a sequence of samples as in MAP algorithm. The sequence-based equalization is enabled by using not only soft a priori input from channel decoder, but also hard a priori information obtained from BDFE in previous iteration. The combination of soft a priori information and hard a priori information renders better performance with less iterations compared to other sub-optimum algorithms. In addition, the computational complexity of the proposed algorithm is on the same order as conventional SISO BDFE algorithm, and is much lower compared to the trellis-based MAP algorithm.

画像処理技術 予測誤差に基づいたＭＡＰ受信機に関する検討

A MAP (Maximum A posteriori Probability) receiver is described that is designed for Markovian sources in a wireless environment. A MAP receiver, a well-known efficient receiver, uses the stochastic characteristics of the source in the decision procedure. However, it is very difficult to implement a MAP algorithm at the front of the receiver because of its calculation costs. To reduce these costs we introduce a source predictor in the receiver. With the aid of the predictor, the MAP detector can be operated with a small calculation cost. Experimental PCM (Pulse Coded Modulation) image transmission demonstrated the feasibility of the proposed receiver. Simulation of the receiver's performance showed it had better MSE (Mean Squared Error) performance in spite of its implementation simplicity.

MAP algorithms for decoding linear block codes based on sectionalized trellis diagrams

The maximum a posterioriprobability (MAP) algorithm is a trellis-based MAP decoding algorithm. It is the heart of turbo (or iterative) decoding that achieves an error performance near the Shannon limit. Unfortunately, the implementation of this algorithm requires large computation and storage. Furthermore, its forward and backward recursions result in a long decoding delay. For practical applications, this decoding algorithm must be simplifled and its decoding complexity and delay must be reduced. In this paper, the MAP algorithm and its variation's, such as log-MAP and max-log-MAP algorithms, are first applied to sectionalized trellises for linear block codes and carried out as two-stage decodings. Using the structural properties of properly sectionalized trellises, the decoding complexity and delay of the MAP algorithms can be reduced. Computation-wise optimum sectionalizations of a trellis for MAP algorithms are investigated. Also presented in this paper are bidirectional and parallel MAP decodings.

Reduced-state variant of optimum MAP equaliser

Although the reduced-state technique has been widely used in Viterbi equalisers, its application to maximum a posteriori probability (MAP) equalisers is not satisfactory because it cannot operate due to the backward recursion of the conventional MAP algorithm. A new kind of MAP algorithm is proposed in which the forward and backward recursions are exactly symmetric. The reduced-state technique can thus be applied to both forward and backward recursions and a gain in performance is achieved over that of conventional reduced-state MAP equalisers at the cost of double the computational overhead.

Soft-output equalization and TCM for wireless personal communication systems

This paper investigates the use of a maximum a posteriori probability (MAP) algorithm to realize soft-output equalization in a concatenated equalization and trellis-coded modulation (TCM) decoding-based wireless communication system. Specifically, we first begin with a general MAP algorithm and then focus on studying Bahl's (1974) MAP and Lee's (1974) MAP algorithms. We then propose a modified version of Lee's MAP algorithm which is much simpler than the original, in terms of complexity, and is more practical. In particular, a very simple channel estimation method which employs orthogonal training sequences is proposed. In order to improve the system performance, equal-gain combining and selection diversity are also considered. Finally, we compare the performance of the MAP algorithm-based equalization with our previously proposed equalization scheme, which combines decision feedback equalization and TCM.

Symbol-by-symbol MAP demodulation of CPM and PSK signals on Rayleigh flat-fading channels

Demodulation using the symbol-by-symbol maximum a posteriori probability (MAP) algorithm is presented. The algorithm is derived for the case of continuous phase modulation (CPM) signals transmitted over Rayleigh flat-fading channels, and a corresponding receiver structure is specified. It is shown that the MAP algorithm requires computing, for each trellis branch, the sum of the products of the weights of all paths through the trellis which pass through that branch, and that this generic computational problem can be solved efficiently by an approach that uses a forward and backward recursion through the trellis. Simulation results are presented which show both the hard and soft decision performance of the MAP receiver to be robust, even in the presence of fade rates of up to 30% of the symbol rate. The application of the receiver concept to phase-shift keying (PSK) signals is also discussed, and then evaluated via simulation. The concept of joint demodulation and decoding using iterative processing techniques is introduced. It is shown that the MAP receiver is well suited for iterative processing applications due to its use of a priori symbol probabilities and its production of optimal soft decisions. Simulation results for the reception of quaternary PSK (QPSK) show that the bit error rate (BER) performance of the iterative MAP receiver can approach that of a receiver operating with perfect knowledge of the fading process.

A soft-output decoding algorithm for concatenated systems

The reliability measure for a decoded symbol is the probability P/sub c/ that the symbol is correct or the probability of error P/sub e/=1-P/sub c/. Such quantities can be obtained by the symbol-by-symbol MAP (maximum a posteriori probability) algorithm. Unfortunately this algorithm is computationally inefficient. A soft output Viterbi algorithm (SOVA) can provide an estimate of P/sub e/ which is accurate only for large SNR. This paper proposes an efficient modified MAP algorithm for obtaining P/sub c/ for the outputs of convolutional inner decoders. The outer decoder uses P/sub c/ to perform soft decision decoding by choosing a codeword which maximizes the maximum likelihood (ML) metric. Decoding based on this ML metric is referred to as generalised soft decision decoding since it includes the Euclidean metric on AWGN channels and binary memoryless channels as special cases.

Performance evaluation of an iterative image reconstruction algorithm for positron emission tomography

An image reconstruction method motivated by positron emission tomography (PET) is discussed. The measurements tend to be noisy and so the reconstruction method should incorporate the statistical nature of the noise. The authors set up a discrete model to represent the physical situation and arrive at a nonlinear maximum a posteriori probability (MAP) formulation of the problem. An iterative approach which requires the solution of simple quadratic equations is proposed. The authors also present a methodology which allows them to experimentally optimize an image reconstruction method for a specific medical task and to evaluate the relative efficacy of two reconstruction methods for a particular task in a manner which meets the high standards set by the methodology of statistical hypothesis testing. The new MAP algorithm is compared to a method which maximizes likelihood and with two variants of the filtered backprojection method.