Let C be a block code of block length 10 over an alphabet of size 7....
Let C be a block code of block length 10 over an alphabet of size 7. What is the upper bound on the number of code words in C that the sphere packing bound (also known as the Hamming bound) gives?
Homework Answers
Add Answer to:
Let C be a block code of block length 10 over an alphabet of
size 7....
Let C be a Huffman binary code for source with alphabet S = {s1, · ·...
Let C be a Huffman binary code
for source with alphabet S = {s1, · · · , sq}. The code words are
w1, w2, · · · , wq. Prove that the equality holds in Kraft’s
inequality, i.e., X q k=1 1 2 lk = 1, where lk is the length of
wk.
Let be a Huffman binary code for source with alphabet S = {sı, . . . , sq). The code words are wi, w2,'.. ,wq. Prove...
Consider BPSK transmission that are encoded using (7,4) hamming block code. Let Pe be the BPSK...
Consider BPSK transmission that are encoded using (7,4) hamming block code. Let Pe be the BPSK bit error probability and given as De = 10 to the power -7 • Calculate the block error rate. Note: By hamming code, system can correct one bit.
What is the maximum number of different encryption functions of a block cipher over the alphabet...
What is the maximum number of different encryption functions of a block cipher over the alphabet {0,1} with block length n?
This is for any supplemental information needed: (2.1.4) PROBLEM. Prove that in A with A, a...
This is for any supplemental information needed:
(2.1.4) PROBLEM. Prove that in A with A, a sphere of radius e contains m1) words. For example, a sphere of radius 2 in (0,1has volume 1+ ' ) + )=1+90 + 4005-4096-212 possibilities for a double error. A sphere of radius 2 in {0, 1, 2)" has volume 8 (8-3-1)2-1+16+112-129 Let A be any finite set. A block code or code, for short, will be any nonempty subset of the set A"...
Problem 3 a) How many strings are there of length 10 over the alphabet (a, b)...
Problem 3 a) How many strings are there of length 10 over the alphabet (a, b) with exactly five a's? b) How many strings are there of length 10 over the alphabet (a, b, c) with exactly five a's?
Let n be an even number. How many ternary strings (i.e. strings over the alphabet 10,...
Let n be an even number. How many ternary strings (i.e. strings over the alphabet 10, 1,2]) of length n are there in which the only places that zeroes can appear are in the odd-numbered positions?
Consider the set of words of length n over the 3-letter alphabet {0，1，2} a) Prove that...
Consider the set of words of length n over the 3-letter alphabet {0，1，2} a) Prove that the number of such words with an even number of 0’s is (3^n+1)/2 and the number of such words with an odd number of 0’s is (3^n-1)/2. (Hint: Try a proof by induction.) b) Prove that C(n,0)*2^n+C(n,1)2^(n-2)+C(n,4)2^(n-4)+....+C(n,q)2^(n-q)=(3^n+1)/2.
Let C be the code generated by the matrix [1 0 0 11 G= 0 1...
Let C be the code generated by the matrix [1 0 0 11 G= 0 1 0 2 over Fz. Lo 0 1 1] (i) How many codewords will have, and why? (ii) Give three distinct codewords of C and find their Hamming weights. (iii) List all the steps required for finding the minimum distance of any code. 7
discrete math '-(oe : length(a) 29, be the alphabet {a,b,c,d,e,f,g) and let 7. Let a) How many elements are in the following set? {ωΣ: no letter in ω is used more than once) b) Find the proba...
discrete math
'-(oe : length(a) 29, be the alphabet {a,b,c,d,e,f,g) and let 7. Let a) How many elements are in the following set? {ωΣ: no letter in ω is used more than once) b) Find the probability that a random word we has al distinct letters. e) Find the probability that a random word oe has the letter g used exactly once. d) Find the probability that a random word e does not contain the letter g.
'-(oe : length(a)...
(4) [20 pts] Let L be the language defined by a regular expression (O | 1)0+(01 1)). over t alphabet f(o,1, +) (a) (4pt) Write down 5 different words from L (b) (8pt) Describe L using words. (c) (8pt...
(4) [20 pts] Let L be the language defined by a regular expression (O | 1)0+(01 1)). over t alphabet f(o,1, +) (a) (4pt) Write down 5 different words from L (b) (8pt) Describe L using words. (c) (8pt) Draw an automaton accepting L (ideally, deterministic).
(4) [20 pts] Let L be the language defined by a regular expression (O | 1)0+(01 1)). over t alphabet f(o,1, +) (a) (4pt) Write down 5 different words from L (b) (8pt) Describe...
Let C be a Huffman binary code
for source with alphabet S = {s1, · · · , sq}. The code words are
w1, w2, · · · , wq. Prove that the equality holds in Kraft’s
inequality, i.e., X q k=1 1 2 lk = 1, where lk is the length of
wk.
Let be a Huffman binary code for source with alphabet S = {sı, . . . , sq). The code words are wi, w2,'.. ,wq. Prove...
Consider BPSK transmission that are encoded using (7,4) hamming block code. Let Pe be the BPSK bit error probability and given as De = 10 to the power -7 • Calculate the block error rate. Note: By hamming code, system can correct one bit.
This is for any supplemental information needed:
(2.1.4) PROBLEM. Prove that in A with A, a sphere of radius e contains m1) words. For example, a sphere of radius 2 in (0,1has volume 1+ ' ) + )=1+90 + 4005-4096-212 possibilities for a double error. A sphere of radius 2 in {0, 1, 2)" has volume 8 (8-3-1)2-1+16+112-129 Let A be any finite set. A block code or code, for short, will be any nonempty subset of the set A"...
Problem 3 a) How many strings are there of length 10 over the alphabet (a, b) with exactly five a's? b) How many strings are there of length 10 over the alphabet (a, b, c) with exactly five a's?
Let n be an even number. How many ternary strings (i.e. strings over the alphabet 10, 1,2]) of length n are there in which the only places that zeroes can appear are in the odd-numbered positions?
Let C be the code generated by the matrix [1 0 0 11 G= 0 1 0 2 over Fz. Lo 0 1 1] (i) How many codewords will have, and why? (ii) Give three distinct codewords of C and find their Hamming weights. (iii) List all the steps required for finding the minimum distance of any code. 7
discrete math
'-(oe : length(a) 29, be the alphabet {a,b,c,d,e,f,g) and let 7. Let a) How many elements are in the following set? {ωΣ: no letter in ω is used more than once) b) Find the probability that a random word we has al distinct letters. e) Find the probability that a random word oe has the letter g used exactly once. d) Find the probability that a random word e does not contain the letter g.
'-(oe : length(a)...
(4) [20 pts] Let L be the language defined by a regular expression (O | 1)0+(01 1)). over t alphabet f(o,1, +) (a) (4pt) Write down 5 different words from L (b) (8pt) Describe L using words. (c) (8pt) Draw an automaton accepting L (ideally, deterministic).
(4) [20 pts] Let L be the language defined by a regular expression (O | 1)0+(01 1)). over t alphabet f(o,1, +) (a) (4pt) Write down 5 different words from L (b) (8pt) Describe...
Most questions answered within 3 hours.
-
What is the methodology that should be used when developing a
risk management plan for an...
asked 25 minutes ago -
The factory method and the abstract factory pattern use
different object oriented
mechanisms are used to...
asked 4 hours ago -
Given the data below for the monthly sales data at each branch in
your region for...
asked 4 hours ago -
Blossom Company owns 10000 of the 50000 outstanding shares of
Taylor, Inc. common stock. During 2018,...
asked 6 hours ago -
Calculate the following: ***SHOW ALL WORK!!!! Or
NO CREDIT*** Circle your answers. 8pts
each
In the...
asked 8 hours ago -
Bank Z is currently advertising interest rates on its checking
account. They claim to pay an...
asked 7 hours ago -
List two ways of transformation on the response variable that
can be used to deal with...
asked 8 hours ago -
If a 2000 ohm resistor has a -3.90 mA current going through it.
What is the...
asked 8 hours ago -
Please comment on the sentences.
Some types of jobs require more training than others. Some
companies...
asked 9 hours ago -
The )G01 for the hydrolysis of phosphorarginine
reaction depicted below is –32 kJ mol-1.
Phosphoarginine ...
asked 10 hours ago -
Cross a heterozygous blue-eyed goat with a homozygous brown-eyed
goat. Be sure to indicate which kids...
asked 10 hours ago -
Use the following information to answer the next two
questions.
Please refer to question 9-90. A...
asked 10 hours ago