ECE 635 Error Detecting and Correcting Systems Design and Hardware Implementation
By
Nagi M. El Naga
Department of Electrical and Computer Engineering California State University
September, 2009
C Nag
1.Introduction:
Cyclic codes form an important subclass of linear codes. These codes are attractive for two
reasons: first, encoding and decoding can be implemented easily by employing shift-registers
ECE 635
Error Detecting and Correcting Systems Design
and Hardware Implementation
Cyclic Codes
Is a linear code that has the following characteristics:
1. Encoding and syndrome calculation of a cyclic
By
Nagi M. El Naga
Department of Electrical and Computer Engineering
California State University
September,2003
Nagi El Naga
ECE 635
Error Detecting and Correcting Systems Design
and Hardware Impleme
ECE 635
Error detecting and Correcting Systems Design
Professor: Dr. N. El Naga
Office: EN 3521
Telephone: 677-3204
"Work expands so as to fill the time available for its completion."
COURSE POLICY AN
ECE 635
DR. N. EL NAGA
MIDTERM EXAM Guide
For the midterm Exam, you need to be familiar with the definition of the following:
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The Rules of Exams
1. All Exams are closed book and closed notes. None of them should be on your desk during the
exam time.
2. No calculator, cell phone or any electronic device including watches and
ECE 635
Error Detecting and Correcting Systems Design
and Hardware Implementation
Dr. N. M. El Naga
Course Syllabus
Office: JD3521
Telephone: (818) 677-3204
Office Hours: Tuesday 1:00 2:00 PM & Thursd
YASAMAN DIANATPEY
ECE 635
Dr. N. El Naga
Homework #1
1.
Solve the following simultaneous equations of X,Y,Z, and W with modulo-2 arithmetic:
1
2
3
4
X + Y + W = 1,
X + Z + W = 0,
X + Y + Z + W = 1,
Y
By
Nagi M. El Naga
Department of Electrical and Computer Engineering
California State University
September,2003
Nagi El Naga
ECE 635
Error Detecting and Correcting Systems Design
and Hardware Impleme
By
Nagi M. El Naga
Department of Electrical and Computer Engineering
California State University
Nagi El Naga
ECE 635
Error Detecting and Correcting Systems Design
and Hardware Implementation
Course
ECE 635
Dr. N. El Naga
Homework # 2
2.1 Let be a primitive element in GF(24). Use the table given in class to solve the following
simultaneous equations for X, Y, and Z:
X + 5Y + Z = 7,
X + Y + 7Z = 9
EE 229B Solutions for Homework 2
ERROR CONTROL CODING
Spring 2005
1. (Weights of codewords in a cyclic code) Let g (X ) be the generator polynomial of a binary cyclic code of length n. (a) Show that i
An overview on error correcting codes
Linear codes
Cyclic codes
Encoding and decoding with cyclic codes
An introduction to cyclic codes
Emanuele Betti1 , Emmanuela Orsini2
1 [email protected] D
TCOM 370
NOTES 99-9
CYCLIC CODES, AND THE CRC (CYCLIC REDUNDANCY CHECK) CODE
1. CYCLIC CODES Cyclic codes are a special type of linear block code that are popular because they are very effective for e
ECE 635 Homework #1 1.
Dr. N. El Naga
Solve the following simultaneous equations of X,Y,Z, and W with modulo-2 arithmetic: X+ Y + X +Z+ X+ Y+ Z + Y+ Z + W= W= W= W= 1, 0, 1, 0.
2. 3. 4. (a) (b) (c) (d
ECE 635 Homework # 2
2.1
Dr. N. El Naga
Let be a primitive element in GF(24). Use the table given in class to solve the following simultaneous equations for X, Y, and Z: X X 2X + 5Y + Y +Y +Z + 7Z + 6
ECE 635 Homework # 4
4.1
Dr. N. El Naga
Let g(X) = 1 + X + X2 + X4 + X5 + X8 + X10 be the generator polynomial of a (15,5) cyclic code. (a) (b) Find the parity polynomial h(X) of this code. Find the c
ECE 635 Homework # 5
5.1 5.2
Dr. N. El Naga
List the code words of the (7,3) code with g(X) = X4 + X3 + X2 +1. Find dmin. X15 + 1 = (X + 1)(X4 + X + 1)(X4 + X3 +1)(X4 +X3 + X2 + X + 1).(x2 + X +1) Det
Chapter 4 Linear Cyclic Codes
4.1 Definition of Cyclic Code
An (n, k) linear code C is called a cyclic code if any cyclic shift of a codeword is another codeword. That is, if c = ( c 0 , c 1 ,L , c n-
Chapter 8
Cyclic Codes
Among the rst codes used practically were the cyclic codes which were generated using shift registers. It was quickly noticed by Prange that the class of cyclic codes has a rich
IV054 CHAPTER 3: Cyclic and convolution codes
Cyclic codes are of interest and importance because
They posses rich algebraic structure that can be utilized in a variety
of ways. They have extremely c
EE 387, John Gill, Stanford University
Notes #5, October 31, Handout #21
Cyclic codes: overview
A linear block code is called cyclic if every cyclic shift of a codeword is a codeword. Cyclic codes hav
Assignment on Cyclic Codes
EE512: Error Control Coding Questions marked (Q) or (F) are questions from previous quizzes or nal exams, respectively.
1. What is the ideal describing the cyclic code cfw_0