Trieu Truong - Academia.edu (original) (raw)

Papers by Trieu Truong

Cornell University - arXiv, Aug 25, 2014

In this paper, the performance of quadratic residue (QR) codes of lengths within 100 is given and... more In this paper, the performance of quadratic residue (QR) codes of lengths within 100 is given and analyzed when the hard decoding, soft decoding, and linear programming decoding algorithms are utilized. We develop a simple method to estimate the soft decoding performance, which avoids extensive simulations. Also, a simulation-based algorithm is proposed to obtain the maximum likelihood decoding performance of QR codes of lengths within 100. Moreover, four important theorems are proposed to predict the performance of the hard decoding and the maximum-likelihood decoding in which they can explore some internal properties of QR codes. It is shown that such four theorems can be applied to the QR codes with lengths less than 100 for predicting the decoding performance. In contrast, they can be straightforwardly generalized to longer QR codes. The result is never seen in the literature, to our knowledge. Simulation results show that the estimated hard decoding performance is very accurate in the whole signal-to-noise ratio (SNR) regimes, whereas the derived upper bounds of the maximum likelihood decoding are only tight for moderate to high SNR regions. For each of the considered QR codes, the soft decoding is approximately 1.5 dB better than the hard decoding. By using powerful redundant paritycheck cuts, the linear programming-based decoding algorithm, i.e., the ACG-ALP decoding algorithm performs very well for any QR code. Sometimes, it is even superior to the Chase-based soft decoding algorithm significantly, and hence is only a few tenths of dB away from the maximum likelihood decoding.

2018 IEEE 23rd International Conference on Digital Signal Processing (DSP), 2018

This work aims to recovery the signal that is corrupted by impulsive disturbance. To that end, th... more This work aims to recovery the signal that is corrupted by impulsive disturbance. To that end, the ellp\ell_{p}ellp-norm (0ltpleq1)(0 \lt p \leq 1)(0ltpleq1) is employed to promote sparsity of the signal of interest and the impulsive disturbance. By doing so, the signal recovery and disturbance suppression are simultaneously achieved. Two improved solvers based on block coordinate descent (BCD) and alternative direction method of multipliers (ADMM) frameworks are developed by utilizing the principle of the reweighted recursive least squares. Numerical experiments demonstrate that the superior performance of the proposed algorithms is obtained compared with the state-of-the-art proximal BCD and ADMM algorithms.

J. Inf. Sci. Eng., 2007

In this paper, an algebraic decoding method is proposed for the quadratic residue codes that util... more In this paper, an algebraic decoding method is proposed for the quadratic residue codes that utilize the Berlekamp-Massey algorithm. By a modification of the technique developed by He et al., one can express the unknown syndromes as functions of the known syndromes. The unknown syndromes are determined by an efficient algorithm also developed in this paper. With the appearance of unknown syndromes, one obtains the consecutive syndromes that are needed for the application of the Berlekamp-Massey algorithm. The decoding scheme, developed here, is easier to implement than the previous decoding algorithm developed for the Golay code and the (47, 24, 11) QR code. Moreover, it can be extended to decode all codes of the family of binary quadratic residue codes with irreducible generating polynomials.

A decoding method for a (23,12) Golay code is extended to the important 1/2-rate (24,12) Golay co... more A decoding method for a (23,12) Golay code is extended to the important 1/2-rate (24,12) Golay code so that three errors can be corrected and four errors can be detected. It is shown that the method can be extended to any decoding method which can correct three errors in the (23,12) Golay code.

The advantages of a very large scalee integration (VLSI) architecture for implementing a digital ... more The advantages of a very large scalee integration (VLSI) architecture for implementing a digital filter using fermat number transforms (FNT) are the following: It requires no multiplication. Only additions and bit rotations are needed. It alleviates the usual dynamic range limitation for long sequence FNT's. It utilizes the FNT and inverse FNT circuits 100% of the time. The lengths of the input data and filter sequences can be arbitraty and different. It is regular, simple, and expandable, and as a consequence suitable for VLSI implementation.

A quick method is described for finding the primitive (2 to power p + 1)p-th root of unity in the... more A quick method is described for finding the primitive (2 to power p + 1)p-th root of unity in the Galois field GF(q squared), where q = (2 to power p) - 1 and is known as a Mersenne prime. Determination of this root is necessary to implement complex integer transforms of length (2 to power k) times p over the Galois field, with k varying between 3 and p + 1.

IEEE Transactions on Vehicular Technology, 2020

Global navigation satellite system multipath channel modeling is important for signal simulation ... more Global navigation satellite system multipath channel modeling is important for signal simulation and error mitigation in urban scenarios. However, there have not been sufficient studies on channel statistical models for dynamic land vehicles in eastern Asian cities. This paper presents both MULTIPATH and non-line-of-sight (NLOS) channel models for GPS L1CA and BDS B1I signals. They are based on an extensive field dataset collected in the Shanghai-Lujiazui area. In addition, a method is developed to estimate multipath components and NLOS signal parameters in a dynamic channel environment. It is found that the Gamma function best fits the distribution of MULTIPATH channel delays while the exponential function is better suited for the distribution of NLOS channel delays. Both MULTIPATH and NLOS channel signals follow a linear decline average power-delay trend and a zero-mean Gaussian distribution power scattering model. The Doppler fading frequency distribution for MULTIPATH and NLOS channels can be modeled by the Gaussian function except for the MULTIPATH channel signal at the low velocity range (0∼3 km/h), where an absolute exponential distribution is a better fit. The lifetime distribution for MULTIPATH and NLOS channels is represented by the generalized Pareto distribution function. These findings offer insights into the GNSS signal models in urban propagation channels and are essential to the development of accurate urban navigation systems.

Neural Processing Letters, 2020

Human listeners often have difficulties understanding speech in the presence of background noise ... more Human listeners often have difficulties understanding speech in the presence of background noise in daily speech communication environments. Recently, deep neural network (DNN)-based techniques have been successfully applied to speech enhancement and achieved significant improvements over the conventional approaches. However, existing DNN-based methods usually minimize the log-power spectral-based or the masking-based mean squared error (MSE) between the enhanced output and the training target (e.g., the ideal ratio mask (IRM) of the clean speech), which is not closely related to human auditory perception. In this letter, a modified bark spectral distortion loss function, which can be considered as an auditory perception-based MSE, is proposed to replace the conventional MSE in DNN-based speech enhancement approaches to further improve the objective perceptual quality. Experimental results reveal that the proposed method can obtain improved speech enhancement performance, especially in terms of objective perceptual quality in all experimental settings when compared with the DNN-based methods using the conventional MSE criterion.

IEEE Transactions on Signal Processing, 2020

In order for an orthogonal frequency division multiplexing (OFDM)-based radar and communication (... more In order for an orthogonal frequency division multiplexing (OFDM)-based radar and communication (RadCom) system to perform well, accurate range and velocity estimation needs to be realized. To achieve this goal, the intrapulse and intersubcarrier Doppler effects that are both typically ignored in conventional methods must be considered and properly utilized. In this paper, we first conceive of a complete receiving model considering the intrapulse and intersubcarrier Doppler effects. Then, an alternating projection-maximum likelihood (AP-ML) method is developed based on this complete model. Considering the heavy computational burden of the AP-ML method, the use of the expectation maximization (EM) algorithm is introduced to reduce the computational complexity. Simultaneously, the computational cost of the EM algorithm can be further reduced by using the reduced-rank technique. Consequently, better estimation results can be obtained with this reduced-rank EM algorithm when there are no approximation errors. Moreover, an analytical expression of the Cramer-Rao bound (CRB) is provided for the complete receiving model. The mutual impacts between the radar and communication functions are analyzed in detail. Finally, excellent experimental results illustrate the superiority of our proposed methods. Index Terms-Orthogonal frequency division multiplexing (OFDM), intrapulse Doppler effect, intersubcarrier Doppler effect, alternating projection-maximum likelihood (AP-ML) method, expectation maximization (EM) algorithm, Cramer-Rao bound (CRB).

Biomedical Signal Processing and Control, 2018

This work addresses the electrocardiogram (ECG) recovery problem in the presence of power line in... more This work addresses the electrocardiogram (ECG) recovery problem in the presence of power line interference (PLI) that corrupts the signal quality if it is not effectively suppressed. In this paper, the PLI is modeled as a linear superposition of sinusoidal signals, which has a sparse representation in the frequency domain. To accurately reconstruct the ECG, the time, second-order difference, and wavelet domains are exploited to sparsely represent the ECG. From the reformulations conducted, a novel joint optimization estimation is devised to simultaneously perform the ECG recovery and PLI suppression in the transform domains. Moreover, in order to solve the optimization problem, two efficient schemes based on the greedy algorithm together with the basis pursuit (BP) are developed. Finally, numerical studies demonstrate that the performance of the joint estimation algorithm is superior to the state-of-the-art approaches.

IEEE Transactions on Geoscience and Remote Sensing, 2018

This paper addresses the problem of recovering a synthetic aperture radar (SAR) signal that is co... more This paper addresses the problem of recovering a synthetic aperture radar (SAR) signal that is corrupted by both radio frequency interference (RFI) and wideband interference (WBI). The time-frequency domain is utilized for both the SAR signal and interference in the form of sparse representations. By doing so, a unified framework that allows one to suppress both the RFI and WBI while recovering the SAR signal can be developed. The resulting framework is an optimization problem that is efficiently solved using a customized alternating direction method of multipliers approach. Finally, simulation results are provided to demonstrate that the performance of the joint estimation algorithm is superior to the performances of other methods in terms of both subjective and objective evaluation standards.

IEEE Sensors Journal, 2016

This work aims at achieving a joint estimation of direction-of-arrival (DOA) and array perturbati... more This work aims at achieving a joint estimation of direction-of-arrival (DOA) and array perturbations such as gain and phase uncertainty, mutual coupling, and sensor location error, which deteriorate the performance of the DOA estimation if not carefully handled. To that end, in this work, the array perturbations represented by a perturbation matrix as multiplicative noise to the array manifold are then reformulated to facilitate the perturbation compensations. One great finding on the perturbation matrix is that it is a sparse matrix, which contains a lot of zero elements and only few nonzero elements. With this reformulation, the perturbation compensation problems turn into sparse matrix completion problems. Then, by utilizing the sparsity of both the DOAs and perturbation matrix, a joint estimation of DOAs and array perturbations is proposed under a unified optimization framework. Additionally, numerical studies are presented to demonstrate the effectiveness of the joint estimation.

IEE Proceedings E Computers and Digital Techniques, 1990

... 206 Fig. 4 Flowchart for decoding ( n + 1, k, d + 1) code 7 Conclusion The two-error BCH algo... more ... 206 Fig. 4 Flowchart for decoding ( n + 1, k, d + 1) code 7 Conclusion The two-error BCH algorithm of Berlekamp is extended to correct three errors in a (23,12,7) Golay code. This procedure isbased on the fact that if one bit is reversed in a codeword that has three errors, this ...

Central Auditory Processing and Neural Modeling, 1998

Medical image data compression is significant to medical image data processing, since the amount ... more Medical image data compression is significant to medical image data processing, since the amount of medical image data is increasing. The image data compression can be used to reduce the storage requirement of a fixed memory and decrease the time needed to transfer medical image data between different communication lines or networks (Wang and Huang, 1996).

IEEE Transactions on Communications, 2015

In this paper, a new algebraic method to decode the (71, 36, 11) QR code up to five errors is pro... more In this paper, a new algebraic method to decode the (71, 36, 11) QR code up to five errors is proposed. It completely avoids computing the unknown syndromes, and uses the previous scheme of decoding this QR code up to three errors, but corrects four and five errors with a new different method. In the four-error case, the new algorithm directly determines the coefficients of the error-locator polynomial by eliminating unknown syndromes in Newton identities. Subsequently, the shift-search algorithm can be utilized to decode the fifth error and the concept of bit reliability is also introduced to accelerate the decoding process. In other words, a weight-five-error pattern can be decoded in terms of the four-error case by inverting an incorrect bit of the received word in ascending order of reliability. Particularly, a threshold parameter γ can be preset to limit the number of inverting bits one by one, and a corresponding upper bound of the probability that decoding fails is derived. Finally, simulation and analysis show that the proposed new decoding algorithm for the abovementioned QR code not only significantly reduces the decoding complexity in terms of CPU time but also saves a lot of memory while maintaining the same error-rate performance. Additionally, the introduction of γ achieves a better tradeoff between the decoding performance and the computational complexity.

2015 IEEE China Summit and International Conference on Signal and Information Processing (ChinaSIP), 2015

In this work, a sparse Kalman filter (SKF) exploring the signal sparse property is developed to t... more In this work, a sparse Kalman filter (SKF) exploring the signal sparse property is developed to track unknown time-varying signals. To derive SKF, the measurement update in KF is reformulated into a convex optimization problem first, and then a regularization term ℓ1-norm on parameters of interest is introduced to yield sparse estimates. Coupled the reformulated measurement update with prediction step in KF, the SKF is achieved. The SKF method can be straightforwardly implemented in the standard KF framework, in which it does not require pseudo measurements. Numerical studies demonstrate the superior performance of SKF compared to other reconstruction schemes.

IEEE Communications Letters, 2015

In this paper, a hard-decision (HD) scheme is presented to facilitate faster decoding of the (47,... more In this paper, a hard-decision (HD) scheme is presented to facilitate faster decoding of the (47, 24, 11) quadratic residue (QR) code. The new HD algorithm uses the previous scheme of decoding the (47, 24, 11) QR code up to three errors, but corrects four and five errors with new different methods. In the four-error case, the new algorithm directly determines the coefficients of the error-locator polynomial by eliminating unknown syndromes in Newton identities and simplifies the condition that exactly indicates the occurrence of four errors. Subsequently, the reliability-based shift-search algorithm can be utilized to decode weight-5 error patterns. In other words, a five-error case can be decoded in terms of a four-error case after inverting an incorrect bit of the received word. Simulation results show that the new HD algorithm not only significantly reduces the decoding complexity in terms of CPU time but also saves a lot of memory while maintaining the same error-rate performance.

IEEE Pacific Rim Conference on Communications, Computers and Signal Processing, 2003

In this paper, an efficient Euclidean decoding algorithm is presented to solve the Berlekamp'... more In this paper, an efficient Euclidean decoding algorithm is presented to solve the Berlekamp's key equation of Reed-Solomon (RS) code for correcting erasures as well as errors by replacing the initial condition of the Euclidean algorithm with the erasure locator polynomial and the Forney syndrome polynomial. By this proposed algorithm, the errata locator polynomial and errata evaluator polynomial can be