EE 421 Fall 2010 - Midterm B Answer as many questions as you can out of the following: 1) Consider the binary code composed of the 4 codewords: C1=cfw_(0000000),(0110011),(1001100), (1111111) Is this code linear? Which are its n1 and k1 values? What is it
EE 421 Fall 2010 - Midterm A Answer as many questions as you can out of the following: 1) Consider the binary code composed of the 4 codewords: C1=cfw_(0000000),( 1100110),( 0011001), (1111111) Is this code linear? Which are its n1 and k1 values? What is
EE 421 Fall 2010 Solution to Homework 3 Problem 1 Consider the encoder shown in the figure below. Determine the encoder rate Rc, the parameters n and k, the encoder memory m and constraint length K Determine the effective rate if L=1000 bits are transmitt
EE 421 Fall 2010 Homework 3, due Thursday December 2nd Problem 1 Consider the encoder shown in the figure below. Determine the encoder rate Rc, the parameters n and k, the encoder memory m and constraint length K Determine the effective rate if L=1000 bit
EE 421 Fall 2010 Homework 2 Problem 1 Consider the binary code composed by the 4 codewords: C=cfw_(000000),(100100),(010010), (001001) What is its minimum distance? Is this code linear?
Problem 2 Find the lower bound on required minimum distance for the f
EE 421 Fall 2010 Homework 1 Due Thursday October 14th Chapter 1 Given a (9,5) systematic code with equations: ci=mi i=0,1,2,3,4 c5=m0+m1+m4 c6=m1+m3+m4 c7=m2+m3 c8=m3+m4 encode the following messages: (00010), (00100),(11111),(10101) Chapter 2 1) Construc
Coding for Communications
Lecture 5
Convolutional codes
1
Convolutional Codes
Another class of linear codes We study the structure of the encoder. We study different ways for representing the encoder.
Questions on convolutional codes
How the decoding is p
Coding for Communications
Lecture 4
Linear block codes
The information bit stream is chopped into blocks of k bits. Each block is encoded to a larger block of n bits. The coded bits are modulated and sent over the channel. The reverse procedure is done a
Coding for Communications
Lecture 3 Introduction to linear block codes
Linear block codes
1
Channel coding
(r0,rn-1) (u0,uk-1)
(m0,mk-1)
(c0,cn-1)
Theorem
What are linear block codes?
Theorem
2
Linear block codes
Let us review some basic definitions first
Coding for Communications
Lecture 2 Finite Groups and Fields
Galois fields and finite fields algebra
1
Sets and operations over sets
Groups
Theorem: identity is unique Theorem: inverse is unique
2
Example: modulo-2 addition
Theorem: identity is unique The
Coding for Communications
Lecture 1 Introduction Channel models
Motivation
Digital communications: Computer networks, wireless telephony, data and media storage, RF communication (terrestrial, space) Transmission over communication channels is prone to e
Summary of schemes with and without retransmission No retransmission
d 1 Given a code with correction capability t = min we have correct reception when 2 there are up to t errors, and incorrect reception when there are more than t errors. P(C)=P(correct
Suggested poblems Problem 1 1. 2. 3. 4. Generate the G and H matrix for the dual code of the Hamming code with n=15. Determine a code basis for the dual code Evaluate the minimum distance Evaluate the error correction capability t and the error detection
Suggested poblems Problem 1 1. 2. 3. 4. Generate the G and H matrix for the dual code of the Hamming code with n=15. Determine a code basis for the dual code Evaluate the minimum distance Evaluate the error correction capability t and the error detection
EE 421 Fall 2010 Homework 2 - Solutions Problem 1 Consider the binary code composed by the 4 codewords: C=cfw_c1=000000, c2=100100, c3=010010, c4=001001 Is this code linear?
No, the code is not linear. For instance, c2+c3= 100100+010010=110110 does not be
Sample problem 1. 2. 3. 4. 5. Generate the G and H matrix for a Hamming code with r=n-k=3. Determine a code basis Evaluate the minimum distance Evaluate the error correction capability t and the error detection capability e Evaluate the block error probab
Sample problem 1. 2. 3. 4. 5. Generate the G and H matrix for a Hamming code with r=n-k=3. Determine a code basis Evaluate the minimum distance Evaluate the error correction capability t and the error detection capability e Evaluate the block error probab
Sample problem 1. 2. 3. 4. 5. Generate the G and H matrix for a Hamming code with r=n-k=3. Determine a code basis Evaluate the minimum distance Evaluate the error correction capability t and the error detection capability e Evaluate the block error probab
EE 421 Fall 2010 Note about midterm
During the midterm the students can use: book, notes distributed on the web, 4 one-sided cheat sheets, but NOT SOLVED PROBLEMS.