This article is an extension of a recent paper by McEliece and Swanson dealing with the decoder error probability for Reed-Solomon codes (more generally, linear MDS codes). McEliece and Swanson offered an upper bound on Weight Distribution Formula forDecodable Words in a Linear MDS Code A. IntroductionWe begin with the following definitions. Let C be a linear code of length n , dimension k, and minimum distance d. Let In Section I, we rederive the weight distribution formula for a linear MDS code by using the principle of inclusion and 21 3 https://ntrs.nasa.gov/search.jsp?R=19880003317 2018-05-11T02:55:21+00:00Z

Expert elicitation is increasingly applied to different research areas. Multiple approaches have been implemented, but the development of methods to quantify experts' biases and calibration represents a challenge. As a result, the integration of multiple and often conflicting opinions can be demanding, owing to the complexity of properly weighting experts' contributions. We propose an approach to address this problem when probability densities for seed calibration variables are not available. The methodology generates an expert score that is employed to aggregate multiple-expert assessments. The approach has been experimentally applied to engineering design risk analysis. Results indicate that the approach improves the quality of the estimations. The weighted aggregations of experts' estimates based on the experts' scores achieve better results than the corresponding aggregations based on experts' opinions equally weighted.

A large array of small antennas can be used to enhance signals with very low signal-to-noise ratio and can also be used to replace large apertures. In this paper, a fast combining algorithm is proposed and analyzed to maximize the combined output signal-to-noise ratio. Our approach does not assume any sequence of trained symbols and is a blind combining technique, which does not require a priori knowledge of spacecraft's or the array's spatial information. Our method for computing the optimal weight is based on the generalized Eigen theory and the algorithms are built upon the Power method. Unique advantages of our proposed algorithm include (i) no formation of covariance matrices and hence less storage is required (ii) the optimal weight is obtained with significant less efforts and thus the optimal weight can be attained more quickly (iii) our proposed algorithm is capable of handling the case when the symbol signal-to-noise-ratios at the receivers are very weak. Mathematical framework for large antenna arrays using the Eigen-based signal combining techniques along with detailed performance analysis, numerical algorithms and computer simulations are presented.

We study the loss in quantizing coded symbols from the AWGN channel with BPSK or QPSK modulation. A new quantization scheme and branch metric calculation method are presented. For the uniformly quantized AWGN channel, cutoff rate is used to determine the stepsize and the smallest number of quantization bits needed for a given bit signal-to-noise ratio (& / N O) loss. A 9-level quantizer is presented, along with 3bit branch metrics for a rate 1/2 code, which causes anEb/.'Vo loss of only 0.14 dB. These results also apply to soft-decision decoding of block codes. A tight upper bound is derived for the range of path metrics in a Viterbi decoder. The calculations are verified by simulations of several convolutional codes, including the new memory 14, rate 1/4 or 1/6 codes used by the big Viterbi decoders at JPL.

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