Let q = 2, 0 ≤ k ≤ n− 1 and k 6= n/2. In this paper we determine the value distribution of following exponential sums

– The Welch-Berlekamp (WB) key equation arises in the decoding of Reed-Solomon (RS) codes over finite fields where the decoding problem is viewed as a rational interpolation problem. The significance of this decoding approach lies in the fact that it does not require the prior evaluation of power sum symmetric functions, i.e. the so-called syndrome vector corresponding to a received word. It ha...

P. Xia was with the the Department of Electrical and Computer Engineering, University of Minnesota, and is now with Samsung Information System America, 75 West Plumeria Drive, San Jose, CA 95134 (email: [email protected]). S. Zhou is with the Department of Electrical and Computer Engineering, University of Connecticut, 371 Fairfield Road U-2157, Storrs, Connecticut 06269, USA (email: shen...

This paper reports the results of a system that performs network anomaly detection through the use of Hidden Markov Models (HMMs). The HMMs used to detect anomalies are designed and trained using Genetic Algorithms (GAs). The use of GAs helps automating the use of HMMs, by liberating users from the need of statistical knowledge, assumed by software that trains HMMs from data. The number of stat...

We present a learning algorithm for hidden Markov models with continuous state and observation spaces. All necessary probability density functions are approximated using samples, along with density trees generated from such samples. A Monte Carlo version of Baum-Welch (EM) is employed to learn models from data, just as in regular HMM learning. Regularization during learning is obtained using an...

In this paper, drills wear monitoring method that based on the mahalanobis distance (MD) of spectrum energy features form cutting torque is proposed. The method consists of three steps. First, using the wavelet transform carried out separating cutting torque components from the original signals. Second, signals feature is adopted to Welch spectrum method extracted on wavelet coefficients of dif...