# 0.13 Coding  (Page 9/22)

 Page 9 / 22

is not Spanish (the input file was Cervante's Don Quijote , also with m=3 ), and

Seule sontagne trait homarcher de la t au onze le quance matices Maississait passepart penaientla ples les au cherche de je Chamain peut accide bien avaien rie se vent puis il nez pande

is not French (the source was Le Tour du Monde en Quatre Vingts Jours , a translation of Jules Verne's Around the World in Eighty Days. )

The input file to the program textsim.m is a M atlab .mat file that is preprocessed to remove excessive line breaks, spaces, and capitalization using textman.m , which is why there is no punctuation in these examples. A large assortment oftext files is available for downloading at the website of Project Gutenberg (at http://promo.net/pg/).

Text, in a variety of languages, retains some of the character of its language with correlationsof 3 to 5 letters (21–35 bits, when coded in ASCII). Thus, messages written in those languagesare not independent, except possibly at lengths greater than this. A result from probability theory suggests that ifthe letters are clustered into blocks that are longer than the correlation, then the blocksmay be (nearly) independent. This is one strategy to pursue when designing codes that seek to optimize performance. "Source Coding" will explore some practical ways to attack this problem, but the next two sections establish a measure ofperformance such that it is possible to know how close to the optimal any given code lies.

## Entropy

This section extends the concept of information from a single symbol to a sequence of symbols.As defined by Shannon, Actually, Hartley was the first to use this as a measure of information in his1928 paper in the Bell Systems Technical Journal called “Transmission of Information.” the information in a symbol is inversely proportional to its probability of occurring.Since messages are composed of sequences of symbols, it is important to be able to talk concretelyabout the average flow of information. This is called the entropy and is formally defined as

$\begin{array}{ccc}\hfill H\left(x\right)& =& \sum _{i=1}^{N}p\left({x}_{i}\right)I\left({x}_{i}\right)\hfill \\ & =& \sum _{i=1}^{N}p\left({x}_{i}\right)log\left(\frac{1}{p\left({x}_{i}\right)}\right)\hfill \\ & =& -\sum _{i=1}^{N}p\left({x}_{i}\right)log\left(p\left({x}_{i}\right)\right),\hfill \end{array}$

where the symbols are drawn from an alphabet ${x}_{i}$ , each with probability $p\left({x}_{i}\right)$ . $H\left(x\right)$ sums the information in each symbol, weighted by the probability of that symbol.Those familiar with probability and random variables will recognize this as an expectation. Entropy Warning: though the word is the same, this is not the sameas the notion of entropy that is familiar from physics since the units here are in bits per symbol whilethe units in physics are energy per degree kelvin. is measured in bits per symbol, and so gives a measure of the average amount of informationtransmitted by the symbols of the source. Sources with different symbol sets and different probabilitieshave different entropies. When the probabilities are known, the definition is easy to apply.

Consider the $N=3$ symbol set defined in Example [link] . The entropy is

$H\left(x\right)=\frac{1}{2}·1+\frac{1}{4}·2+\frac{1}{4}·2=1.5\phantom{\rule{4.pt}{0ex}}\text{bits/symbol}.$

Reconsider the fair die of [link] . What is its entropy?

Suppose that the message $\left\{{x}_{1},{x}_{3},{x}_{2},{x}_{1}\right\}$ is received from a source characterized by

#### Questions & Answers

are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!