University of Illinois
Fall 2005
ECE 556: Second MidSemester Exam
Thursday November 17, 2005, 8:30 a.m. 9:50 a.m. This is a open-text open-handwritten-notes examination. No printed materials other than the textbook and Problem Sets and Solutions distribut
University of Illinois
Fall 2005
ECE 556: Solutions to the First MidSemester Exam
1. (a) Applying the result wt(x y) = wt(x) + wt(y) - 2 wt(x y) to codewords x and y, we use the fact that wt(x), wt(y), and wt(x y) are multiples of 4 to deduce that wt(x y)
University of Illinois
Fall 2005
ECE 556/CS 577/MATH 579: Solutions to the Final Examination
1. An (n, k) Hamming code over GF(q) of redundancy r has block length (q r 1)/(q 1). (a) Hence, n = (33 1)/(3 1) = 13 and k = n r = 10. (b) Suppose that the predi
University of Illinois, Urbana-Champaign ECEN 556 Fall 2009 Homework 1 Issued: September 8th; Due: September 15th A- Grade Problems 1. Binary error-correcting codes are usually designed for communication system modeled by the binary symmetric channel. How
ECE 556: Coding Theory, 2009 Issued: September 15th, 2009
September 17, 2009
1) Prove the following bound on the size of the code: For a code with n < 2d, it holds that M 2 2) Show that the only two families of binary codes that meet the Singleton bound
ECE 556: Coding Theory, 2009 HW 3 Issued: September 24th, 2009 Due: September 29th, 2009
September 23, 2009
1) Problem 4.6 of text (Roth). 2) Problem 4.9 of text (Roth) 3) Find the length, dimension, and minimum distance of the product of a [n1 , k1 , d1
ECE 556: Coding Theory, 2009 HW 4 Issued: October 5th, 2009 Due: October 15th, 2009
October 5, 2009
A- range Problems 1) Show that over any nite eld of order q and characteristic p, one has ( x + y ) p = xp + y p . 2) Roth text, problem 4.29. 3) Consider
ECE 556: Coding Theory, 2009 HW 5 Issued: October 21st, 2009 Due: November 3rd, 2009
October 21, 2009
A- range Problems 1) A Hadamard matrix Hn of order n is a an n n amtrix of +1s and 1s T such that Hn Hn = nI , where I denotes the identity matrix. If Hn
ECE 556: Coding Theory, 2009 HW 6 Issued: November 8th, 2009 Due: November 17th, 2009
November 8, 2009
A range Problems 1) Find the best binary linear code you can that has length 1000 and can correct 100 errors. 2) You saw in the exam that a binary cycli
ECE 556: Coding Theory, 2009 HW 7 Issued: November 19th, 2009 Due: December 9th, 2009
November 19, 2009
1) a) Show that the minimum distance of an R(r, m) code is 2mr . Can you nd a simple characterization of R(1, m) codes? b) Show that the Plotkin const
Midterm I: Issued October 22nd, 2009 1. Suppose that instead of using f(v)=v3 as the second row of the parity-check matrix of a double-error correcting BCH code, we use f(v)=v-1. For the case m=4, does this structure work as a double-error correcting code
ECE 556 Midterm II F all 2009
Problem 1 Consider the subcode of the Golay code obtained by taking only those codewords that project onto the all-zero hexacodeword. Find the dimension and weight enumerator of this code. What is the covering radius of the c
Suggested class project topics recommended reading:
1) LDPC Codes: Low-density parity-check codes, Gallager http:/www.inference.phy.cam.ac.uk/mackay/gallager/papers/ H YPE RL I NK " h ttp :/ / www. i n feren ce. p h y . ca m. a c. u k / ma ck a y / a b s