TRAVEL NOTES.IX. A WINTER SEMESTER.

Mathematics 309 a : Abstract Algebra Winter Semester 2010

Information Theory and Coding EPFL Winter Semester 2008 / 2009

Our experience with data compression so far has been of the following type: We are given the statistical description of an information source, we then try to design a system which will represent the data produced by this source efficiently. In this note we depart from this model, and consider a method which will represent a sequence efficiently without knowing by which means the sequence was pr...

Theory and Coding EPFL Winter Semester 2009 / 2010

Problem 2 (Parallel Channels and Choice of channels) (a) Find the capacity C of the union of two channels (X1, p1(y1|x1),Y1) and (X2, p2(y2|x2),Y2), where at each time, one can send a symbol over channel 1 or channel 2 but not both. Assume that the output alphabets are distinct and do not intersect. Show that 2 = 21 + 22 . Thus 2 is the effective alphabet size of a channel with capacity C. (b) ...

Signal Processing for Communications EPFL Winter Semester 2007 / 2008

which are simply four points in the second quadrant on the unit circle. 2. Each couple of complex-conjugate zeros contributes a factor of the form (1−2z−1 cos θ+ z−2) to the transfer function, where θ is the angle of the complex zero. We have in the end: H(z) = (1 + z)(1 + z)(1− 2 cos( 3 4 π) z + z) 3. H(z) is a 5th degree polynomial in z−1 and therefore it has at most 6 nonzero coefficients. T...

Information Theory and Coding EPFL Winter Semester 2009 / 2010

• You are allowed to use 1 sheet of paper for reference. No mobile phones or calculators are allowed in the exam. • You can attempt the problems in any order as long as it is clear which problem is being attempted and which solution to the problem you want us to grade. • If you are stuck in any part of a problem do not dwell on it, try to move on and attempt it later. • Please solve every probl...