# 0.13 Coding  (Page 17/22)

 Page 17 / 22

Using the routine writetext.m (this file, which can be found on the website, uses the M atlab command fwrite ), write the Wizard of Oz text to a file OZ.doc . Use a compression routine ( uuencode on a Unix or Linux machine, zip on a Windows machine, or stuffit on a Mac) to compress OZ.doc . Note the file size when the file is in its compressed form,and the file size after decompressing. How does this compare with the compression ratio achieved in [link] ?

## Channel coding

some redundancy to a signal before it is transmitted so that it becomes possible to detect when errors have occurredand to correct them, when possible.

Perhaps the simplest technique is to send each bit three times. Thus, in order to transmit a 0, the sequence 000is sent. In order to transmit 1, 111 is sent.This is the encoder . At the receiver, there must be a decoder . There are eight possible sequences that can be received,and a “majority rules” decoder assigns

$\begin{array}{cccc}000↔0& 001↔0& 010↔0& 100↔0\\ 101↔1& 110↔1& 011↔1& 111↔1.\end{array}$

This encoder/decoder can identify and correct any isolated single error and so the transmissionhas smaller probability of error. For instance, assuming no more than one error per block, if101 was received, then the error must have occurred in the middle bit, while if 110 was received,then the error must have been in the third bit. But the majority rules coding scheme is costly:three times the number of symbols must be transmitted, which reduces the bit rate by a factor of three.Over the years, many alternative schemes have been designed to reduce the probability of error in thetransmission, without incurring such a heavy penalty.

Linear block codes are popular because they are easy to design, easy to implement, and because they havea number of useful properties. With $n>k$ , an $\left(n,k\right)$ linear code operates on sets of $k$ symbols, and transmits a length $n$ code word for each set. Each code is defined by two matrices:the $k$ by $n$ generator matrix $G$ , and the $n-k$ by $n$ parity check matrix $H$ . In outline, the operation of the code is as follows:

1. Collect $k$ symbols into a vector $\mathbf{x}=\left\{{x}_{1},{x}_{2},...,{x}_{k}\right\}$ .
2. Transmit the length $n$ code word $\mathbf{c}=\mathbf{x}G$ .
3. At the receiver, the vector $\mathbf{y}$ is received. Calculate $\mathbf{y}{H}^{T}$ .
4. If $\mathbf{y}{H}^{T}=0$ , then no errors have occurred.
5. When $\mathbf{y}{H}^{T}\ne 0$ , errors have occurred. Look up $\mathbf{y}{H}^{T}$ in a table of “syndromes,” which contains a list of all possible received valuesand the most likely code word to have been transmitted, given the error that occurred.
6. Translate the corrected code word back in to the vector $\mathbf{x}$ .

The simplest way to understand this is to work through an example in detail.

## A $\left(\mathbf{5},\mathbf{2}\right)$ Binary linear block code

To be explicit, consider the case of a $\left(5,2\right)$ binary code with generator matrix

$G=\left[\begin{array}{ccccc}1& 0& 1& 0& 1\\ 0& 1& 0& 1& 1\end{array}\right]$

and parity check matrix

${H}^{T}=\left[\begin{array}{ccc}1& 0& 1\\ 0& 1& 1\\ 1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right].$

This code bundles the bits into pairs, and the four corresponding code words are

$\begin{array}{ccc}\hfill {x}_{1}& =& 00↔{c}_{1}={x}_{1}G=00000,\hfill \\ \hfill {x}_{2}& =& 01↔{c}_{2}={x}_{2}G=01011,\hfill \\ \hfill {x}_{3}& =& 10↔{c}_{3}={x}_{3}G=10101,\hfill \\ \hfill and{x}_{4}& =& 11↔{c}_{4}={x}_{4}G=11110.\hfill \end{array}$

There is one subtlety. The arithmetic used in the calculation of the code words (and indeed throughout the linear block codemethod) is not standard. Because the input source is binary, the arithmetic is also binary.Binary addition and multiplication are shown in [link] . The operations of binary arithmetic may be more familiar as exclusive OR (binary addition), and logical AND (binary multiplication).

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
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
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
Got questions? Join the online conversation and get instant answers!