# 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).

find the 15th term of the geometric sequince whose first is 18 and last term of 387
I know this work
salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
hmm
Abhi
is it a question of log
Abhi
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Abhi
I rally confuse this number And equations too I need exactly help
salma
But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends
salma
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
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Tamia
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Uday
hi
salma
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
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algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
how do you translate this in Algebraic Expressions
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
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
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Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
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preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
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
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
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
Azam
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Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
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