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A Gray code has the property that the binaryrepresentation for each symbol differs from its neighbors by exactly one bit.A Gray code for the translation of binary into 4-PAM is

01 + 3 11 + 1 10 - 1 00 - 3

Mimic the code in naivecode.m to implement this alternative and plot the number of errors as a function ofthe noise variance v . Compare your answer with [link] . Which code is better?

Symbols to signals

Even though the original message is translated into the desired alphabet, it is not yet ready for transmission:it must be turned into an analog waveform. In the binary case, a simple method is to use a rectangular pulseof duration T seconds to represent + 1 , and the same rectangular pulse inverted (i.e., multiplied by - 1 ) to represent the element - 1 . This is called a polar non-return-to-zero line code.The problem with such simple codes is that they use bandwidth inefficiently.Recall that the Fourier transform of the rectangular pulse in time is the sinc ( f ) function in frequency [link] , which dies away slowly as f increases. Thus, simple codes like the non-return-to-zeroare compact in time, but wide in frequency, limiting the number of simultaneous nonoverlapping users ina given spectral band.

More generally, consider the four-level signal of [link] . This can be turned into an analog signal for transmission by choosinga pulse shape p ( t ) (that is not necessarily rectangular and not necessarily of duration T ) and then transmitting

p ( t - k T ) if the k th symbol is 1 - p ( t - k T ) if the k th symbol is - 1 3 p ( t - k T ) if the k th symbol is 3 - 3 p ( t - k T ) if the k th symbol is - 3

Thus, the sequence is translated into an analog waveform by initiating a scaled pulse at the symbol time k T , where the amplitude scaling is proportional to the associated symbolvalue. Ideally, the pulse would be chosen so that

  • the value of the message at time k does not interfere with the value of the message at other sample times(the pulse shape causes no intersymbol interference ),
  • the transmission makes efficient use of bandwidth, and
  • the system is resilient to noise.

Unfortunately, these three requirements cannot all be optimized simultaneously, and so the design of thepulse shape must consider carefully the tradeoffs that are needed. The focus in Chapter [link] is on how to design the pulse shape p ( t ) , and the consequences of that choice in terms of possible interference betweenadjacent symbols and in terms of the signal-to-noise properties of the transmission.

For now, to see concretely how pulse shaping works, let's pick a simple nonrectangular shape and proceedwithout worrying about optimality. Let p ( t ) be the symmetrical blip shape shown in the top part of [link] , and defined in pulseshape.m by the hamming command. The text string in str is changed into a 4-level signal as in Example [link] , and then the complete transmitted waveform is assembled by assigning an appropriatelyscaled pulse shape to each data value. The output appears in the bottom of [link] . Looking at this closely, observe that the first letter T is represented by the four values - 1 - 1 - 1 - 3 , which corresponds exactly to the first four negative blips, three small and one large.

Questions & Answers

what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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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