Solutions to Homework Set #3
(Prepared by Yu Xiang)
1. Time until the n-th arrival. Let the random variable N (t) be the number of packets arriving
during time (0, t]. Suppose N (t) is Poisson with pmf
(t)n t
e
for n = 0, 1, 2, . . . .
n!
Let the random v
Solutions to Homework Set #7
(Prepared by TA Yu Xiang)
1. Symmetric random walk. Let Xn be a random walk defined by
X0 = 0,
n
X
Zi ,
Xn =
i=1
where Z1 , Z2 , . . . are i.i.d. with Pcfw_Z1 = 1 = Pcfw_Z1 = 1 = 21 .
(a) Find Pcfw_X10 = 10.
(b) Approximate Pc
Solutions to Homework Set #5
(Prepared by Lele Wang)
1. Neural net. Let Y = X + Z, where the signal X U[1, 1] and noise Z N (0, 1) are
independent.
(a) Find the function g(y) that minimizes
MSE = E (sgn(X) g(Y )2 ,
where
sgn(x) =
(
1 x 0
+1 x > 0.
(b) Plo
UCSD ECE 153
Prof. Young-Han Kim
Handout #11
Thursday, April 14, 2011
Solutions to Homework Set #2
(Prepared by Lele Wang)
1. Polyas urn. Suppose we have an urn containing one red ball and one blue ball. We draw a
ball at random from the urn. If it is red
Midterm Examination
(Total: 70 points)
There are 3 problems, each problem with multiple parts. Your answer should be as clear
and readable as possible.
1. (20 pts).There are two independent random variables, denoted by X and Y and with
pdfs fX and fY . Co
UCSD ECE153
Prof. Tara Javidi
Tuesday, April 14, 2015
Homework Set #3
Due: Thursday, April 23, 2015
1. Time until the n-th arrival. Let the random variable N(t) be the number of packets
arriving during time (0, t]. Suppose N(t) is Poisson with pmf
pN (n)
UCSD ECE153
Prof. Tara Javidi
Tuesday, May 21, 2015
Homework Set #6
Due: Thursday, May 28, 2015
1. Gaussian random vector. Given a Gaussian random vector X N (, ), where
= (1 5 2)T and
1 1 0
= 1 4 0 .
0 0 9
(a) Find the pdfs of
i.
ii.
iii.
iv.
v.
X1 ,
X
Midterm Examination
(Total: 70 points)
There are 3 problems, each problem with multiple parts. Your answer should be as clear
and readable as possible.
1. (20 pts).There are two independent random variables, denoted by X and Y and with
pdfs fX and fY . Co
UCSD ECE153
Prof. Tara Javidi
Tuesday, April 7, 2015
Homework Set #2
Due: Thursday, April 16, 2015
1. Polyas urn. Suppose we have an urn containing one red ball and one blue ball. We
draw a ball at random from the urn. If it is red, we put the drawn ball
UCSD ECE153
Prof. Tara Javidi
Tuesday, May 25, 2015
Homework Set #7
Due: Thursday, June 4, 2015
1. Symmetric random walk. Let Xn be a random walk defined by
X0 = 0,
n
X
Xn =
Zi ,
i=1
where Z1 , Z2 , . . . are i.i.d. with Pcfw_Z1 = 1 = Pcfw_Z1 = 1 = 12 .
(
UCSD ECE153
Prof. Tara Javidi
Tuesday, May 12, 2015
Homework Set #5
Due: Thursday, May 21, 2015
1. Neural net. Let Y = X + Z, where the signal X U[1, 1] and noise Z N (0, 1) are
independent.
(a) Find the function g(y) that minimizes
MSE = E (sgn(X) g(Y )2
UCSD ECE153
Prof. Tara Javidi
Sunday, May 2, 2015
Homework Set #4
Due: Tuesday, May 12, 2015
1. Two envelopes. An amount A is placed in one envelope and the amount 2A is placed
in another envelope. The amount A is fixed but unknown to you. The envelopes a
UCSD ECE153
Prof. Tara Javidi
Tuesday, March 31, 2015
Homework Set #1
Due: Thursday, April 9, 2015
1. World Series. The World Series is a seven-game series that terminates as soon as
either team wins four games and is won mostly by the United States. Supp
Midterm Examination
(Total: 100 points)
There are 3 problems, each problem with multiple parts, each part worth 10 points. Your
answer should be as clear and readable as possible.
1. Lottery (20 pts).
There are two types of lottery tickets. A regular tick
Page1
ECE 35 Lab 1
Introduction to Analog Circuits
This lab will illustrate some of the differences between analog and digital circuits. There are
assignments for this first lab, A & B. In part A we design a circuit to produce an arbitrary
voltage, rather
ECE 25 Lab 4 Sequential Circuits, Sequence Recognizer
Introduction
The goal of this lab is to design a circuit to recognize the start bit and data bits from a
Sony IR remote. Information on the IR SONY can be found on Lab Web site datasheet. This
should b
Huikai Wang: A13596089
Raghav Kansal: A92121242
Matthew Rice: A12686471
ECE 35
Section: A52, Tuesday, 7-10pm
Lab 03: Analog Optical Data Link
Introduction:
The purpose of this lab is to design and build an analog optical data link which is a light emissio
Huikai Wang: A13596089
Raghav Kansal: A92121242
ECE 35
Section: A52, Tuesday, 7-10pm
Lab 02: Digital to Analog Converter (DAC)
Introduction:
The purpose of this lab is to test a Digital to Analog Converter (DAC) that consists of an
R/R2 ladder network. A
Huikai Wang: A13596089
Raghav Kansal: A92121242
Matthew Rice: A12686471
ECE 35
Section: A52, Tuesday, 7-10pm
Lab 04:Project 4 Rc Circuits
Introduction:
The objective of this lab is to measure the time characteristics of RC circuits and demonstrate
how RC
Huikai Wang: A13596089
Raghav Kansal: A92121242
ECE 35
Section: A52, Tuesday, 7-10pm
Lab 1: Introduction to Analog Circuits
Introduction:
The purpose of this lab is to test elementary circuit and electric laws, and analyze the
discrepancies between ideal/
SPECIAL ISSUE ON NETWORK CODING
1
On the Capacity of Information Networks
Nicholas J. A. Harvey, Robert Kleinberg and April Rasala Lehman
Abstract An outer bound on the rate region of noise-free
information networks is given. This outer bound combines pro
Fifty-second Annual Allerton Conference
Allerton House, UIUC, Illinois, USA
October 1 - 3, 2014
Chop and Roll: Improving the Cutset Bound
Sudeep Kamath
Young-Han Kim
Department of Electrical Engineering
Princeton University
Email:[email protected]
De
Applications of Lattice Codes in
Communication Systems
by
Amin Mobasher
A thesis
presented to the University of Waterloo
in fulfillment of the
thesis requirement for the degree of
Doctor of Philosophy
in
Electrical and Computer Engineering
Waterloo, Ontar
IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 52, NO. 6, JUNE 2006
2825
Coding On Demand by an Informed Source (ISCOD) for
Efcient Broadcast of Different Supplemental Data to
Caching Clients
Yitzhak Birk, Senior Member, IEEE, and Tomer Kol, Member, IEEE
A
ITW 2009, Volos, Greece, June 10 - 12, 2009
Distributed Computation of Symmetric Functions
with Binary Inputs
Nikhil Karamchandani
Rathinakumar Appuswamy
Massimo Franceschetti
California Institute for Telecommunications and Information Technology
Departme
MILAN KUNDERA "LAUGHABLE LOVES"
"Light, wry, and wise." John Skow, Time
Milan Kundera is a master of graceful illusion and illuminating surprise. In one of these stories a
young man and his girlfriend pretend that she is a stranger he picked up on the roa
1
On the Index Coding Problem and its Relation to
Network Coding and Matroid Theory
Salim El Rouayheb, Alex Sprintson, and Costas Georghiades
Department of Electrical and Computer Engineering
Texas A&M University, College Station, TX 77843
cfw_rouayheb, s
3544
IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 55, NO. 8, AUGUST 2009
Nonlinear Index Coding Outperforming the
Linear Optimum
Eyal Lubetzky and Uri Stav
AbstractThe following source coding problem was introduced
by Birk and Kol: a sender holds a word
1440
IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 44, NO. 4, JULY 1998
On Characterization of Entropy
Function via Information Inequalities
Zhen Zhang, Senior Member, IEEE, and Raymond W. Yeung, Senior Member, IEEE
Abstract Given n discrete random variab
EE 520: Topics Compressed Sensing
Linear Algebra Review
Notes scribed by Kevin Palmowski, Spring 2013
Notes on matrix spark courtesy of Brian Lois
Notes based primarily on Horn and Johnson, Matrix Analysis, 1e and 2e, as well as Dr.
Namrata Vaswanis in-cl