ECE 1502 Information Theory Problem Set 3 solutions November 2, 2007 5.3 Slackness in the Kraft inequality. Instantaneous codes are prex free codes, i.e., no codeword is a prex of any other codeword. Let lmax = maxcfw_l1 , l2 , ., lm . There are Dlmax seq
Lecture 5 - EE 359: Wireless Communications - Fall 2011
Narrowband Model. In-Phase/Quad RX Signals.
Uniform AoA. Signal Envelope Distribution
Lecture Outline
Narrowband Fading Approximation.
In-Phase and Quad Signal Components under CLT.
Correlation of
EE359 Lecture 5 Outline
Announcements:
No lecture Mon 10/17
Lecture Wed. 10/19 moved to 6pm (w/pizza)
Makeup lecture 10/21 9:30-10:45am (w/donuts)
n
Correction: CLT (not LLN) means: lim xi Gaussian for xi iid
n
i 1
Review of Last Lecture
Narrowband Fadi
EE359 Lecture 5 Outline
Announcements:
No lecture Mon 10/17
Lecture Wed. 10/19 moved to 6pm (w/pizza)
Makeup lecture 10/21 9:30-10:45am (w/donuts)
n
Correction: CLT (not LLN) means: lim xi Gaussian for xi iid
n
Review of Last Lecture
N
c ( , t ) n (t )e
Lecture 6 - EE 359: Wireless Communications - Fall 2011
Fading Distributions and Duration. Markov Model.
Wideband Fading. Doppler and Delay Spread
Lecture Outline
Signal Envelope (Fading) Distributions
Level Crossing Rate and Average Fade Duration
Mark
EE359 Lecture 6 Outline
Announcements:
No lecture Mon, lectures 10/19 6pm, 10/21 9:30am
HW this week deadline extended to Friday 5pm
Next HW posted today, due Friday 10/21@5pm
Review of Last Lecture
Signal Envelope Distributions
Average Fade Duration
EE359 Lecture 6 Outline
Review of Last Lecture
Announcements:
No lecture Mon, lectures 10/19 6pm, 10/21 9:30am
HW this week deadline extended to Friday 5pm
Next HW posted today, due Friday 10/21@5pm
For fn~U[0,2p], rI(t),rQ(t) zero mean, WSS, with
Ar (t )
Error Correcting Codes: Combinatorics, Algorithms and Applications
(Fall 2007)
Lecture 11: Shannon vs. Hamming
September 21,2007
Lecturer: Atri Rudra
Scribe: Kanke Gao & Atri Rudra
In the last lecture, we proved the positive part of Shannons capacity theo
Error Correcting Codes: Combinatorics, Algorithms and Applications
(Fall 2007)
Lecture 15: Gilbert-Varshamov Bound
October 2, 2007
Lecturer: Atri Rudra
Scribe: Thanh-Nhan Nguyen
In the previous lectures, we have only seen upper bounds on the rate of a cod
Error Correcting Codes: Combinatorics, Algorithms and Applications
(Fall 2007)
Lecture 17: Proof of a Geometric Lemma
October 5, 2007
Lecturer: Atri Rudra
Scribe: Sandipan Kundu & Atri Rudra
In the last lecture, we proved the Plotkin bound, except for a c
Lecture 2 - EE 359: Wireless Communications - Fall 2011
Signal Propagation and Path Loss Models
Lecture Outline
Overview of Signal Propagation
Free Space Path Loss Model
Ray Tracing Path Loss Models
Simplied Path Loss Model
Empirical Path Loss Models
EE359 Lecture 2 Outline
Announcements
1st HW posted today, due next Thursday
Discussion section starts next week.
Review of Last Lecture
Signal Propagation Overview
TX and RX Signal Models
Complex
baseband models
Path Loss Models
Free-space Path Loss
EE359 Lecture 2 Outline
Announcements
Complex baseband
Path Loss Models
Free-space Path Loss
Ray Tracing Models
Simplified Path Loss Model
Empirical Models
Multimedia Requirements
Current Wireless Systems
models
Technical Challenges
Review of Last Lectur
Lecture 3 - EE 359: Wireless Communications - Fall 2011
Shadowing, Combined Path Loss/Shadowing,
Coverage Area, Model Parameters.
Lecture Outline
Log Normal Shadowing
Combined Path Loss and Shadowing
Outage Probability
Cell Coverage Area
Model Parame
University of Toronto November 6, 2007
Department of Electrical & Computer Engineering
ECE1502F Information Theory
Midterm Test
Instructions
You have one hour and fty minutes of in-class time, followed by three days of take-home time to complete this tes
University of Toronto November 9, 2007
Department of Electrical & Computer Engineering
ECE1502F - Information Theory
Midterm Test Solution
1. (Noisy Gates) (a) The noisy XOR gate induces a binary symmetric channel (BSC) with crossover probability p. As sh
P = NP
Vinay Deolalikar
HP Research Labs, Palo Alto
vinay.deolalikar@hp.com
August 6, 2010
Abstract
We demonstrate the separation of the complexity class NP from its subclass
P. Throughout our proof, we observe that the ability to compute a property
on st
ECE 1502 - Information Theory Problem Set 1 solutions1 October 5, 2007 2.1 (a) The number X of tosses till the first head appears has the geometric distribution with parameter p = 1/2, where P (X = n) = pq n-1 , n cfw_1, 2, . . .. Hence the entropy of X i
ECE 1502 - Information Theory Problem Set 3 solutions October 17, 2007 2.14 Entropy of a sum. (a) Z = X + Y . Hence p(Z = z|X = x) = p(Y = z - x|X = x). H(Z|X) = = -
x
p(x)H(Z|X = x) p(x)
z
p(Z = z|X = x) log p(Z = z|X = x) p(Y = z - x|X = x) log p(Y = z
University of Toronto February 28, 2006
Department of Electrical & Computer Engineering
ECE1502S Information Theory
Midterm Test
Instructions
You have one hour and fty minutes of in-class time, followed by two days of take-home time to complete this test