A new technique for correcting synchronization errors in the transmission of discrete-symbol information is developed. The technique can be applied to any t-additive-error-correcting Bose-Chaudhuri-Hocquenghem code, to provide protection against synchronization errors. The synchronization error is corrected at the first complete received word after the word containing the synchronization error,...

In conventional coding for error control, all the information symbols of a message are regarcred equally significant, and hence codes are devised to provide equal protection for each information symbol against channel errors. are more significant than the other symbols. However, in some occasions, some information symbols in a message As a result, it is desired to devise codes with multi-level ...

Transmission of information takes place over “noisy” signals. This is the case in satellite transmissions and storing data. For this reason, it is useful to encode information so that errors can be detected and corrected. For our purposes, we will assume all information to be encoded constists of words of fixed length k using symbols from a fixed alphabet, and all encoded messages are divided i...

Error correcting codes make possible much of digital technology, from modems to cell phones to compact disk players. The problem is to send a message across a noisy channel with perfect fidelity, or at least with as much fidelity as possible. Below we will describe the theory of these codes. It is based on some ideas from “modern algebra,” including finite number systems called rings and fields...

This thesis deals with quantum error correcting codes. In first two chapters necessary introduction to quantum computation and classical error correction is presented. Previous results on construction of quantum error correcting codes are presented in the third and fourth chapter. Mainly Calderbank-Steane-Shor (CSS) codes and stabilizer codes are discussed together with the introduction to codi...

These notes are a record of proceedings in the QMW Combinat-orics Study Group in November and December 1998. Since we are discrete mathematicians and know little quantum theory, the notes are not strong on the physics background (but we give references to several sources for this). We have tried to compare quantum with classical error correction where possible, and to provide enough information...

Markus GRASSL received his diploma degree in Computer Science in 1994 and his doctoral degree in 2001, both from the Fakultät für Informatik, Universität Karlsruhe (TH), Germany. From 1994 to 2007 he was a member of the Institut für Algorithmen und Kognitive Systeme, Fakultät für Informatik, Universität Karlsruhe (TH), Germany. From 2007 to 2008 he was with the Institute for Quantum Optics and ...

is an encoder, that is, regarding Fq as the set of words in a natural language , the function V tells how to encode the words. The matrix V = (vij) that describes the linear map V is called a generating matrix of the code. We say that V is in standard form if V = (IdP ) for a matrix P , that is vij = δij , for i, j = 1, . . . , d (where δij = 0, i 6= j, δii = 1). In this case we say that the fi...

We propose a novel automatic target recognition (ATR) system for classification of three types of ground vehicles in the MSTAR public release database. First, each image chip is pre-processed by extracting fine and raw feature sets, where raw features compensate for the target pose estimation error that corrupts fine image features. Then, the chips are classified by using the adaptive boosting ...