# 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).

#### Questions & Answers

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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.
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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.
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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?
s. Reply
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.
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s.
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s. Reply
of graphene you mean?
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or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
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Cied
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AMJAD
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In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
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after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
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I'm interested in Nanotube
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Source:  OpenStax, Software receiver design. OpenStax CNX. Aug 13, 2013 Download for free at http://cnx.org/content/col11510/1.3
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