# 0.13 Coding  (Page 9/22)

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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

anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
how did you get the value of 2000N.What calculations are needed to arrive at it
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