National University of Sciences & Technology, Islamabad
Information Coding homeworks
EE 801

Fall 2015
Name :
Spring 2014
MATH 220
Homework 4
1. Let C be the binary code word generator matrix
1
0
Due on Thursday 2/13/14
0
1
1
0
0
1
.
(a) Set up a standard array for C.
(b) Write down the coset leaders of each coset.
(c) Use your standard array to decode the
National University of Sciences & Technology, Islamabad
Information Coding homeworks
EE 801

Fall 2015
EE 605: Error Correcting Codes
Instructor: Saravanan Vijayakumaran
Indian Institute of Technology Bombay
Autumn 2011
Assignment 4 : 20 points
Due date: November 11, 2011
Each of the following exercises is worth 5 points. Every nontrivial step in a proof s
National University of Sciences & Technology, Islamabad
Information Coding homeworks
EE 801

Fall 2015
EE376A: Homeworks #7 Solutions
1. Exact number of types.
Let xn denote the sequence x1 , x2 , . . . , xn whose components take values in the finite
alphabet X . Letting Pn denote the collection of all types Pxn of sequences of length n,
find the exact num
National University of Sciences & Technology, Islamabad
Information Coding homeworks
EE 801

Fall 2015
EE376A: Homeworks #6
Due on Thursday, February 27, 2014
You can hand in the homework either after class or deposit it, before 5 PM, in the EE376A
drawer of the class file cabinet on the second floor of the Packard Building.
1. Channel capacity with cost c
National University of Sciences & Technology, Islamabad
Information Coding homeworks
EE 801

Fall 2015
ERALE
ECOLE
POLYTECHNIQUE FED
DE LAUSANNE
School of Computer and Communication Sciences
Handout 24
Solutions to homework 10
Information Theory and Coding
December 10, 2013
Problem 1.
(a)
I(X; Y ) = I(Xk , K; Yk , K) = I(K; Yk , K) + I(Xk ; YK , KK) = H
National University of Sciences & Technology, Islamabad
Information Coding homeworks
EE 801

Fall 2015
ERALE
ECOLE
POLYTECHNIQUE FED
DE LAUSANNE
School of Computer and Communication Sciences
Handout 12
Homework 6
Information Theory and Coding
October 22, 2013
Problem 1. Let the alphabet be X = cfw_a, b. Consider the infinite sequence X1 =
abababababababa
National University of Sciences & Technology, Islamabad
Information Coding homeworks
EE 801

Fall 2015
Math 342
Homework Assignment #1 (Due Thursday, January 16, at
beginning of class)
1. Exercise 2.5 in text.
2. Exercise 2.6 in text.
3. How many errors can each of the following codes detect/correct? Briefly
explain why.
a. cfw_001, 111, 010, 100, q = 2
b.
National University of Sciences & Technology, Islamabad
Information Coding homeworks
EE 801

Fall 2015
Math 342
Homework Assignment #4 (Due by Friday, February 14, 5 PM, my oce)
1. Find the multiplicative inverse of a in Z727 .
(a) a = 726
(b) a = 372
2. Recall the denition of the eld F4 , given in class:
(F4 , +)
0
1
a
b
0
0
1
a
b
1
1
0
b
a
a
a
b
0
1
b
b
National University of Sciences & Technology, Islamabad
Information Coding homeworks
EE 801

Fall 2015
ERALE
ECOLE
POLYTECHNIQUE FED
DE LAUSANNE
School of Computer and Communication Sciences
Handout 8
Homework 4 (Graded  Due on Oct. 16, 2013  6 PM)
Information Theory and Coding
Oct. 08, 2013
Problem 1. (25 pts) In this problem, we investigate what happ
National University of Sciences & Technology, Islamabad
Information Coding homeworks
EE 801

Fall 2015
ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE
School of Computer and Communication Sciences
Handout 23
Homework 10 (Graded  Due on Dec. 09, 2013  3 PM)
Information Theory and Coding
Nov. 26, 2013
Problem 1. Let P1 and P2 be two channels of input alphabet X1
National University of Sciences & Technology, Islamabad
Information Coding homeworks
EE 801

Fall 2015
Math 342
Homework Assignment #4 (Due by Friday, February 14, 5 PM, my office,
SOLUTIONS)
1. Find the multiplicative inverse of a in Z727 .
(a) a = 726
(b) a = 372
Solution:
a. 726 = 1 mod 727, and so 7261 = (1)1 = 1 = 726 mod 727.
b. We apply the Euclidea
National University of Sciences & Technology, Islamabad
Information Coding homeworks
EE 801

Fall 2015
EE376A: Homeworks #8 Solutions
1. Size of strong typical set.
For all > 0, show that
2n(H(X)() T (X) 2n(H(X)+() ,
for n sufficiently large and for some () > 0 where lim0 () = 0.
Solution: Size of strong typical set.
It is clear that if xn T (X), then 2n
National University of Sciences & Technology, Islamabad
Information Coding homeworks
EE 801

Fall 2015
EE 605: Error Correcting Codes
Instructor: Saravanan Vijayakumaran
Indian Institute of Technology Bombay
Autumn 2011
Solution to Assignment 3
1. Let g(X) be the generator polynomial of a binary cyclic code of length n.
(a) Show that if g(X) has X + 1 as a
National University of Sciences & Technology, Islamabad
Information Coding homeworks
EE 801

Fall 2015
ECE 5311: Information Theory & Coding
Homework 9: Due at the start of class on 17Apr.
Spring 2014
1. 9.6
2. 9.8 (Follow the example in the class and use KKT conditions to find the optimal power
allocation scheme)
3. 9.15
4. 9.22
5. 10.1 (Ignore the last
National University of Sciences & Technology, Islamabad
Information Coding homeworks
EE 801

Fall 2015
Math 342
Homework Assignment #8 (Due Thursday, April 3, in class)
Justify all of your answers.
1. Which of the following polynomials in F [x] are irreducible?
(a) f (x) = x2 + x + 1, F = F2
(b) f (x) = x2 + x + 1, F = F4
(c) f (x) = x4 + x + 1, F = F2
(d)
National University of Sciences & Technology, Islamabad
Information Coding homeworks
EE 801

Fall 2015
Name :
MATH 220
Spring 2014
Homework 6
Due on Thursday 3/6/14
1. It is given that f (x) = x4 + x + 1 is irreducible and primitive over GF (2). Define by f () = 0.
(a) Set up a table for GF (16) containing the binary, exponential and polynomial representat
National University of Sciences & Technology, Islamabad
Information Coding homeworks
EE 801

Fall 2015
EE376A: Homeworks #7
Due on Thursday, March 6, 2014
You can hand in the homework either after class or deposit it, before 5 PM, in the EE376A
drawer of the class file cabinet on the second floor of the Packard Building.
1. Exact number of types.
Let xn de
National University of Sciences & Technology, Islamabad
Information Coding homeworks
EE 801

Fall 2015
Math 342
Homework Assignment #6 (Due Thursday, March 6, in class)
Justify all of your answers.
1. (a) Let p be prime. Show that a subset of the vector space Fpn is a subspace of Fpn
if and only if it is a subgroup of Fpn , considered as a group with coord
National University of Sciences & Technology, Islamabad
Information Coding homeworks
EE 801

Fall 2015
Math 342
Homework Assignment #5 (Due Thursday, Feb. 27, in class)
Justify all of your answers.
1. Which of the following subsets are subspaces of Fqn ?
(a) cfw_0000, 1111, 1010, 0101, q = 2, n = 4
(b) cfw_0000, 1111, 1010, 0101, q = 3, n = 4
(c) cfw_000,
National University of Sciences & Technology, Islamabad
Information Coding homeworks
EE 801

Fall 2015
Math 342
Homework Assignment #5 (Due Thursday, Feb. 27, in class) SOLUTIONS
Justify all of your answers.
1. Which of the following subsets are subspaces of Fqn ?
(a) cfw_0000, 1111, 1010, 0101, q = 2, n = 4
(b) cfw_0000, 1111, 1010, 0101, q = 3, n = 4
(c)
National University of Sciences & Technology, Islamabad
Information Coding homeworks
EE 801

Fall 2015
Math 342
Homework Assignment #2 (Due Thursday, January 23, at beginning of class)
1. Let C = cfw_0000, 1110. Suppose that C is used for transmission across the binary
symmetric channel, with crossover probability p, and incomplete nearest neighbour
decodi
National University of Sciences & Technology, Islamabad
Information Coding homeworks
EE 801

Fall 2015
ERALE
ECOLE
POLYTECHNIQUE FED
DE LAUSANNE
School of Computer and Communication Sciences
Handout 13
Solutions to homework 6
Information Theory and Coding
October 29, 2013
Problem 1.
(a) We have (X1 ) = 0. We show this by showing that (X1 ) for any > 0. T
National University of Sciences & Technology, Islamabad
Information Coding homeworks
EE 801

Fall 2015
Math 342
Homework Assignment #2 (Due Thursday, January 23, at beginning of class)
SOLUTIONS
1. Let C = cfw_0000, 1110. Suppose that C is used for transmission across the binary
symmetric channel, with crossover probability p, and incomplete nearest neighb
National University of Sciences & Technology, Islamabad
Information Coding homeworks
EE 801

Fall 2015
Name :
MATH 220
Spring 2014
Homework 3
Due on Thursday 2/6/14
0 0 1 0 1
1. Let C be the binary code with generator matrix 1 1 0 1 1 .
1 0 1 1 0
(a) Write down all the codewords in C.
(b) Find a generator matrix in standard form for C.
(c) Find a parity ch
National University of Sciences & Technology, Islamabad
Information Coding homeworks
EE 801

Fall 2015
ERALE
ECOLE
POLYTECHNIQUE FED
DE LAUSANNE
School of Computer and Communication Sciences
Handout 3
Solutions to homework 1
Information Theory and Coding
Sep. 24, 2013
Problem 1. Note that E0 = E1 E2 E3 .
(a) (1) For disjoint events, P (E0 ) = P (E1 ) + P
National University of Sciences & Technology, Islamabad
Information Coding homeworks
EE 801

Fall 2015
COLLEGE OF COMPUTER STUDIES
Basic Web Design with Client Side Scripting [ITWEBDES]
CASE STUDY #1
Your manager at Jenflex has asked you to create a fivepage prototype of the web pages
in the new entertainment section for the online magazine, Citystuf. The
National University of Sciences & Technology, Islamabad
Information Coding homeworks
EE 801

Fall 2015
AMPERE'S CIRCUIT LAWMAGNETIC FLUX
DENSITY
Applications of Amperes Law
INFINITELY LONG COAXIAL TRANSMISSION LINE
Consider an infinitely long transmission line consisting of two
concentric cylinders having their axes along the zaxis. The cross
section of t
National University of Sciences & Technology, Islamabad
Information Coding homeworks
EE 801

Fall 2015
FORCES DUE TO
MAGNETIC FIELDS
Forces Due To Magnetic Fields
We considered the basic laws and techniques commonly used
in calculating magnetic field B due to currentcarrying
elements.
Now we will study the force a magnetic field exerts on
charged partic
National University of Sciences & Technology, Islamabad
Information Coding homeworks
EE 801

Fall 2015
AMPERE'S CIRCUIT LAWMAXWELL'S EQUATION
Amperes Circuit Law
Ampere's circuit law states that the line integral of the
tangential component of H around a dosed path is the same
as the net current Ienc enclosed by the path.
.
=
The closed integral in the a