# 0.13 Coding  (Page 17/22)

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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).

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?
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
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.
what is nano technology
what is system testing?
preparation of nanomaterial
how did you get the value of 2000N.What calculations are needed to arrive at it
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