Engineering topics
Publications and source records attributed to Yao, K..
In this paper, the performance of the repeat-accumulate codes with (ML) decoding are analyzed and compared to random codes by very tight bounds. Some simple codes are shown that perform very close to Shannon limit with maximum likelihood decoding.
In this paper we propose an innovative channel coding scheme called Accumulate Repeat Accumulate codes. This class of codes can be viewed as trubo-like codes, namely a double serial concatenation of a rate-1 accumulator as an outer code, a regular or irregular repetition as a middle code, and a punctured accumulator as an inner code.
In practical applications of importance sampling (IS) simulation, two basic problems are encountered, that of determining the estimation variance and that of evaluating the proper IS parameters needed in the simulations. The authors derive new upper and lower bounds on the estimation variance which are applicable to IS techniques. The upper bound is simple to evaluate and may be minimized by the proper selection of the IS parameter. Thus, lower and upper bounds on the improvement ratio of various IS techniques relative to the direct Monte Carlo simulation are also available. These bounds are shown to be useful and computationally simple to obtain. Based on the proposed technique, one can readily find practical suboptimum IS parameters. Numerical results indicate that these bounding techniques are useful for IS simulations of linear and nonlinear communication systems with intersymbol interference in which bit error rate and IS estimation variances cannot be obtained readily using prior techniques.
The problem of modeling and equalization of a nonlinear satellite channel is considered. The channel is assumed to be bandlimited and exhibits both amplitude and phase nonlinearities. In traditional models, computations are usually performed in the frequency domain and solutions are based on complex numerical techniques. A discrete time model is used to represent the satellite link with both uplink and downlink white Gaussian noise. Under conditions of practical interest, a simple and computationally efficient time-domain design technique for the minimum mean square error linear equalizer is presented. The efficiency of this technique is enhanced by the use of a fast and simple iterative algorithm for the computation of the autocorrelation coefficients of the output of the nonlinear channel. Numerical results on the evaluations of bit error probability and other relevant parameters needed in the design and analysis of a nonlinear bandlimited QPSK system demonstrate the simplicity and computational efficiency of the proposed approach.
Three truncated QR methods are proposed for sinusoidal frequency estimation: (1) truncated QR without column pivoting (TQR), (2) truncated QR with preordered columns, and (3) truncated QR with column pivoting. It is demonstrated that the benefit of truncated SVD for high frequency resolution is achievable under the truncated QR approach with much lower computational cost. Other attractive features of the proposed methods include the ease of updating, which is difficult for the SVD method, and numerical stability. TQR methods thus offer efficient ways to identify sinusoidals closely clustered in frequencies under stationary and nonstationary conditions.
A systolic array processing technique is applied to implementing the stack algorithm form of the sequential decoding algorithm. It is shown that sorting, a key function in the stack algorithm, can be efficiently realized by a special type of systolic arrays known as systolic priority queues. Compared to the stack-bucket algorithm, this approach is shown to have the advantages that the decoding always moves along the optimal path, that it has a fast and constant decoding speed and that its simple and regular hardware architecture is suitable for VLSI implementation. Three types of systolic priority queues are discussed: random access scheme, shift register scheme and ripple register scheme. The property of the entries stored in the systolic priority queue is also investigated. The results are applicable to many other basic sorting type problems.
One of the most promising new directions for high-throughput-rate problems is that based on systolic arrays. In this paper, using the matrix-decomposition approach, a systolic Kalman filter is formulated as a modified square-root information filter consisting of a whitening filter followed by a simple least-squares operation based on the systolic QR algorithm. By proper skewing of the input data, a fully pipelined time and measurement update systolic Kalman filter can be achieved with O(n squared) processing cells, resulting in a system throughput rate of O (n).
The paper considers a methodology on the analysis and design of a minimum mean-square error criterion linear system incorporating a tapped delay line (TDL) where all the full-precision multiplications in the TDL are constrained to be powers of two. A linear equalizer based on the dispersive and additive noise channel is presented. This microprocessor implementation with optimized power of two TDL coefficients achieves a system performance comparable to the optimum linear equalization with full-precision multiplications for an input data rate of 300 baud.
In this paper a modified importance sampling technique for improving the convergence of Importance Sampling is given. By using this approach to estimate low false alarm rates in radar simulations, the number of Monte Carlo runs can be reduced significantly. For one-dimensional exponential, Weibull, and Rayleigh distributions, a uniformly minimum variance unbiased estimator is obtained. For Gaussian distribution the estimator in this approach is uniformly better than that of previously known Importance Sampling approach. For a cell averaging system, by combining this technique and group sampling, the reduction of Monte Carlo runs for a reference cell of 20 and false alarm rate of lE-6 is on the order of 170 as compared to the previously known Importance Sampling approach.
Contract generated publications are compiled which describe the research activities for the reporting period. Study topics include: equivalent configurations of systolic arrays; least squares estimation algorithms with systolic array architectures; modeling and equilization of nonlinear bandlimited satellite channels; and least squares estimation and Kalman filtering by systolic arrays.
A systematic approach is presented for designing systolic arrays and their equivalent configurations for certain general classes of recursively formulated algorithms. A new method is also introduced to reduce the input bandwidth and storage requirements of the systolic arrays through the study of dependence among the input data. Many well known systolic arrays can be rederived and also many new systolic arrays can be discovered by this approach.
The problem of modeling and equalization of a nonlinear satellite channel is considered. The channel is assumed to be bandlimited and exhibits both amplitude and phase nonlinearities. A discrete time satellite link is modeled under both uplink and downlink white Gaussian noise. Under conditions of practical interest, a simple and computationally efficient design technique for the minimum mean square error linear equalizer is presented. The bit error probability and some numerical results for a binary phase shift keyed (BPSK) system demonstrate that the proposed equalization technique outperforms standard linear receiver structures.
Least-squares (LS) estimation is a basic operation in many signal processing problems. Given y = Ax + v, where A is a m x n coefficient matrix, y is a m x 1 observation vector, and v is a m x 1 zero mean white noise vector, a simple least-squares solution is finding the estimated vector x which minimizes the norm of /Ax-y/. It is well known that for an ill-conditioned matrix A, solving least-squares problems by orthogonal triangular (QR) decomposition and back substitution has robust numerical properties under finite word length effect since 2-norm is preserved. Many fast algorithms have been proposed and applied to systolic arrays. Gentleman-Kung (1981) first presented the trianglular systolic array for a basic Givens reduction. McWhirter (1983) used this array structure to find the least-squares estimation errors. Then by geometric approach, several different systolic array realizations of the recursive least-squares estimation algorithms of Lee et al (1981) were derived by Kalson-Yao (1985). Basic QR decomposition algorithms are considered in this paper and it is found that under a one-row time updating situation, the Householder transformation degenerates to a simple Givens reduction. Next, an improved least-squares estimation algorithm is derived by considering a modified version of fast Givens reduction. From this approach, the basic relationship between Givens reduction and Modified-Gram-Schmidt transformation can easily be understood. This improved algorithm also has simpler computational and inter-cell connection complexities while compared with other known least-squares algorithms and is more realistic for systolic array implementation.
Many communication, control, and information processing subsystems are modeled by linear systems incorporating tapped delay lines (TDL). Such optimized subsystems result in full precision multiplications in the TDL. In order to reduce complexity and cost in a microprocessor implementation, these multiplications can be replaced by single-shift instructions which are equivalent to powers of two multiplications. Since, in general, the obvious operation of rounding the infinite precision TDL coefficients to the nearest powers of two usually yield quite poor system performance, the optimum powers of two coefficient solution was considered. Detailed explanations on the use of branch-and-bound algorithms for finding the optimum powers of two solutions are given. Specific demonstration of this methodology to the design of a linear data equalizer and its implementation in assembly language on a 8080 microprocessor with a 12 bit A/D converter are reported. This simple microprocessor implementation with optimized TDL coefficients achieves a system performance comparable to the optimum linear equalization with full precision multiplications for an input data rate of 300 baud. The philosophy demonstrated in this implementation is dully applicable to many other microprocessor controlled information processing systems.
It is proposed that the derivation of least-square algorithms for systolic array processing is best accomplished via a geometrical approach. This approach generates a set of vector equations from which a large number of new and previously known systolic arrays can be obtained in a unified manner. The paper presents and qualitatively describes these vector equations and shows how one such systolic array follows.
The floating-point roundoff error effect under finite word length limitations is analyzed for the time updates of reflection coefficients in the spatial lattice algorithm. It is shown that recursive computation is superior to direct computation under finite word length limitations. Moreover, the forgetting factor, which is conventionally used to smooth the time variations of the inputs, is also a crucial parameter in the consideration of the system stability and adaptability under finite word length constraints.
Lattice algorithm has been employed in numerous adaptive filtering applications such as speech analysis/synthesis, noise canceling, spectral analysis, and channel equalization. In this paper the application to adaptive-array processing is discussed. The advantages are fast convergence rate as well as computational accuracy independent of the noise and interference conditions. The results produced by this technique are compared to those obtained by the direct matrix inverse method.
The theory and implementation of a multiplication-free linear mean-square error criterion equalizer for data transmission are considered. For many real-time signal processing situations, a large number of multiplications is objectionable. The linear estimation problem on a binary computer is considered where the estimation parameters are constrained to be powers of two and thus all multiplications are replaced by shifts. The optimal solution is obtained from an integer-programming-like problem except that the allowable discrete points are non-integers. The branch-and-bound algorithm is used to obtain the coefficients of the equalization TDL. Specific experimental performance results are given for an equalizer implemented with a 12 bit A/D device and a 8080 microprocessor.