# 0.13 Coding

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Before Shannon it was commonly believed that the only way of achieving arbitrarily small probability of error on a communicationschannel was to reduce the transmission rate to zero. Today we are wiser. Informationtheory characterizes a channel by a single parameter; the channel capacity. Shannon demonstrated that it is possible to transmit information at any ratebelow capacity with an arbitrarily small probability of error.

—from A. R. Calderbank, “The Art of Signaling: Fifty Years of Coding Theory,” IEEE Transactions on Information Theory, p. 2561, October 1998.

The underlying purpose of any communication system is to transmit information. But what exactly is information? How is it measured?Are there limits to the amount of data that can be sent over a channel, even when all the parts of the system are operatingat their best? This chapter addresses these fundamental questions usingthe ideas of Claude Shannon (1916–2001), who defined a measure of information in terms of bits.The number of bits per second that can be transmitted over the channel (taking into account its bandwidth,the power of the signal, and the noise) is called the bit rate , and can be used to define the capacity of the channel.

Unfortunately, Shannon's results do not give a recipe for how to construct a system that achieves the optimal bit rate.Earlier chapters have highlighted several problems that can arise in communication systems (including synchronization errors suchintersymbol interference). This chapter assumes that all of these are perfectly mitigated. Thus, in [link] , the inner parts of the communication system are assumed to be ideal, except for the presenceof channel noise. Even so, most systems still fall far short of the optimal performance promised by Shannon.

There are two problems. First, most messages that people want to send are redundant, and the redundancy squandersthe capacity of the channel. A solution is to preprocess the messageso as to remove the redundancies. This is called source coding , and is discussed in "Source Coding" . For instance, as demonstrated in "Redundancy" , any natural language (such as English),whether spoken or written, is repetitive. Information theory (as Shannon's approach is called)quantifies the repetitiveness, and gives a way to judge the efficiency of a source codeby comparing the information content of the message to the number of bits required by the code.

The second problem is that messages must be resistant to noise. If a message arrives at the receiver in garbledform, then the system has failed. A solution is to preprocess the message by addingextra bits, which can be used to determine if an error has occurred, and to correct errors when they do occur.For example, one simple system would transmit each bit three times.Whenever a single bit error occurs in transmission, then the decoder at the receiver can figure out by a simplevoting rule that the error has occurred and what the bit should have been.Schemes for finding and removing errors are called error-correcting codes or channel codes , and are discussed in "Channel Coding" .

where we get a research paper on Nano chemistry....?
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
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
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
how did you get the value of 2000N.What calculations are needed to arrive at it
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