%Homework Assignment 2
%Jay Joshi.
%CWID - A20339855
%
clc;
clear all;
close all;
p = 3; m = 5; % chosing numbers
pol = gfprimfd(m,'max',p); % Find primitive polynomials for a Galois field
fprintf('\n First Primitive Polynmial of GF(3^5):\n');
gfpretty(po
Chapter 2
1. Let m be a positive number. If m is not a prime, prove that the setcfw_1,2, , 1 is not a group
under modulo- multiplication.
2. Construct a table for (23 ) based on the primitive polynomial () = 1 + + 3 . Display
the power, polynomial and vec
An Introduction to Low-Density Parity Check Codes
Daniel J. Costello, Jr.
Department of Electrical Engineering
University of Notre Dame
August 10, 2009
The author gratefully acknowledges the help of Tom Fuja
in the preparation of this presentation.
D. J.
ECE 519
Coding for Reliable Communications Course Syllabus
Spring 2016
Instructor: Guillermo Atkin
Office:
SH 335, 312-567-6810
Office Hours: T and R: 10:30 to noon
e-mail:
[email protected]
Class Hours: T & R: 8:35 to 9:50 AM, SB 106
TA:
function turbo_dec(varargin)
%Input in the following order: SNR (dB), number of decoder
iterations, number of
imulations required
%codeword length
K = 128;
param.K = K;
if ~nargin
SNR = 6;
iter_len = 5;
sim_len = 1e4;
else
SNR = varargincfw_1;
iter_len =
5:.6Part a: If X | l is a factor of g[X], then an arbitrary codeword v(X] can be written as
v(X] = (X + 1]a(X] = Xa(X] + af]
where apt") is a polynomial of degree n l or less. Thus, v(X] is the sum of two
polynomials, both having the same number of nonzer
Homework
1. Use matlab to find all the primitive polynomials for
A. (2% )
B. (2' )
2. Given the polynomial = 1 + - + . + % + / in the
GF(2). Check if p(X) is irreducible with reference to (2) or
primitive by using the routine
3. State a list
Project#1
Project Report: (Submit to the Blackboard no hardcopies)
Section A. LDCP Code
The project report must include:
1) Give a brief description of the LDPC encoder and Decoder;
Requirement:
a) Refer to the LDPC presentation slides provided, and use t
5.3
We need to show that g(X) divides X21 + 1. Note
that
g(X) = (X + 1)(X3 + X2 + 1)(X6 + X4 + X2 + X + 1) .
As can be seen from any table enumerating the minimal polynomials of the elements of ttF (2m)
for small values of m, each of the factors is the mi
Solution :
Let C denote the binary cyclic code (n, k) with generator polynomial g(X). We know
that g(X) divides X n + 1. Since C contains both even and odd weight codewords,
X + 1 does not divide g(X). Thus (X + 1)g(X) divides X n + 1. Hence it is the
gen
SECRET KEY:
STREAM CIPHERS
CIPHERS
& BLOCK
Sicurezza nelle reti e nei sistemi informatici
SECRET KEY CRYPTOGRAPHY
March 2011
SiReSI slide set 2 (Secret key)
Alice and Bob share
A crypto protocol E
A secret key K
They communicate using E with
4.20
Euclids algorithm is most commonly encountered in nding lowest common
multiples of numbers. in the process of so doing it identies common factors so
that these can be taken into account in computing the lowest common multiple.
Many authors preface a
5
4
3. Program with Matlab to: find out at least two primitive polynomials for each of GF (3 ) , GF (5 ) , and
GF (73 ) ; construct
GF (73 ) using the primitive polynomial
polynomial and vector representations of the elements
minimal polynomial of
3
70
,
TAKE HOME EXAM 1
DHRUV RAJAN SAXENA
A20348805
3. Program with Matlab to find at least two primitive polynomials in (35), (54) and
(73) .
Construct (73) using the primitive polynomial () = 3 + 6 2 + 5 + 4. Obtain the power ,
polynomial and vector represent
Q1. Berlekamps Method:
clc;
R=[1 zeros(1,16), 1 zeros(1,10) 1 0 0];
Rgf=gf(R);
[m, num]=bchdec(Rgf,31,21);
% For the BCH code decoding
display(Rgf);
display(m);
display(num);
%Variable num shows the errors of polynomial. The no. of errors are greater
than
HOMEWORK 1
1. Consider the (15,11) cyclic Hamming code generated by () = 1 + + 4 .
a. Determine the parity polynomial () of this code.
b. Determine the generator polynomial of its dual code.
c. Find the generator and parity check matrices in systematic fo
3. Program with Matlab to: find out at least two primitive polynomials for each of (35 ), (54 ), and (73 );
construct (73 ) using the primitive polynomial () = 3 + 6 2 + 5 + 4, obtain the power, polynomial and
vector representations of the elements 70 , 7
Q1. Berlekamps Method:
clc;
R=[1 zeros(1,16), 1 zeros(1,10) 1 0 0];
Rgf=gf(R);
[m, num]=bchdec(Rgf,31,21); % For the BCH code decoding
display(Rgf);
display(m);
display(num);
%Variable num shows the errors of polynomial. The no. of errors are greater than
%Assignment #2
%Primitive Polynomials For GF(3^5)
clc
clear all;
close all;
p = 7;
m = 3;
% We use the primitive polynomial X^3+6X^2+5^X+4 for GF(7^3).
prim_poly = [4 5 6 1]; % for primitive polynomial
field = gftuple([70:80]',prim_poly,p)% to create fiel
Homework #7
1. Construct (73 ) using the primitive polynomial
() = 3 + 6 2 + 5 + 4. Obtain the power,
polynomial and vector representations of the
elements 70 , 71 80 (using MATLAB).
2. Solve 7.4 from the textbook using MATLAB
3. Solve 7.5 using Euclid an
a) Prove that a (11,1) binary code (repetition code) with n odd is a perfect code.
Hint: The following facts may be useful:
ill-l
CHEJ :52.
(f: 2 q
A
'1
2
' g Y\! ("Ru G cob
2. b) Show that the singleton bound holds true for this code.
gwgrlw low 6
02
a)
Project#2 Turbo Code
Project Report: (Submit to the Blackboard no hardcopies)
The project report must include:
1) a brief description of the turbo code.
2) Presenting your data in tables as in the paper.
3) What are the decoded bits.
4) Source code of you