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A description of the Huffman source encoding algorithm.

One particular source coding algorithm is the Huffman encoding algorithm. It is a source coding algorithm which approaches, and sometimes achieves, Shannon's bound forsource compression. A brief discussion of the algorithm is also given in another module .

Huffman encoding algorithm

  • Sort source outputs in decreasing order of their probabilities
  • Merge the two least-probable outputs into a single output whose probability is the sum of the corresponding probabilities.
  • If the number of remaining outputs is more than 2, then go to step 1.
  • Arbitrarily assign 0 and 1 as codewords for the two remaining outputs.
  • If an output is the result of the merger of two outputs in a preceding step, append the current codeword with a 0 and a 1 toobtain the codeword the the preceding outputs and repeat step 5. If no output is preceded by another output in a preceding step, thenstop.

X A B C D with probabilities { 1 2 , 1 4 , 1 8 , 1 8 }

Average length 1 2 1 1 4 2 1 8 3 1 8 3 14 8 . As you may recall, the entropy of the source was also H X 14 8 . In this case, the Huffman code achieves the lower bound of 14 8 bits output .

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In general, we can define average code length as

x x X p X x x
where X is the set of possible values of x .

It is not very hard to show that

H X H X 1
For compressing single source output at a time, Huffman codes provide nearly optimum code lengths.

The drawbacks of Huffman coding

  • Codes are variable length.
  • The algorithm requires the knowledge of the probabilities, p X x for all x X .
Another powerful source coder that does not have the aboveshortcomings is Lempel and Ziv.

Questions & Answers

how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
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.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
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
anybody can imagine what will be happen after 100 years from now in nano tech world
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
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
can nanotechnology change the direction of the face of the world
Prasenjit Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Information and signal theory. OpenStax CNX. Aug 03, 2006 Download for free at http://legacy.cnx.org/content/col10211/1.19
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