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List Estimation

Shahrivari, Farzad | 2017

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 50530 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Amini, Arash; Aminzadeh Gohari, Amin
  7. Abstract:
  8. Let X be an unknown vector of size n which is to be estimated from a known m 1 vector Y. According to the MMSE criterion, the best estimator (denoted bX(Y)) is an estimator which minimizes the mean squared error. Now, consider a List Decodingproblem in which the sender delivers a list of codes instead of a single decoder. Assume that it is allowed to use multiple parallel estimators (bX1 (Y); ^X2(Y); : : : ; bX k(Y)) instead of delivering a single estimation of samples. The goal is to find the best possible list of estimators, in a way that the mean squared error is optimized between the multiple bX i(Y); (i = 1; 2; : : : ; k). As a medical example, imagine a MRI device which produces three different images instead of one after taking samples from a patient that only one of them has substantially higher quality than a single image device (the number of the optimum image is different for each person).The purpose of this paper is to describe a new method of estimation called ”List Estimation”. This problem is obtained from ideas related to two main problems named ”List Decoding” and ”Vector Quantization”. First, we will give a method to produce a list of estimators using k-means clustering algorithm. Then, we intoduce and solve some problems to compare our method with 2 classical estimation methods based on MMSE,reusing components from the preceding ideas where possible
  9. Keywords:
  10. List Decoding ; Mean Square Error (MSE) ; K-means Clustering ; Estimators

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