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A description of channel coding, in particular linear block codes.

Channel coding is a viable method to reduce information rate through the channel and increase reliability. This goal isachieved by adding redundancy to the information symbol vector resulting in a longer coded vector of symbols that aredistinguishable at the output of the channel. Another brief explanation of channel coding is offered in Channel Coding and the Repetition Code . We consider only two classes of codes, block codes and convolutional codes .

Block codes

The information sequence is divided into blocks of length k . Each block is mapped into channel inputs of length n . The mapping is independent from previous blocks, that is,there is no memory from one block to another.

k 2 and n 5

00 00000
01 10100
10 01111
11 11011
information sequencecodeword (channel input)

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A binary block code is completely defined by 2 k binary sequences of length n called codewords.

C c 1 c 2 c 2 k
c i 0 1 n
There are three key questions,
  • How can one find "good" codewords?
  • How can one systematically map information sequences into codewords?
  • How can one systematically find the corresponding information sequences from a codeword, i.e. , how can we decode?
These can be done if we concentrate on linear codes and utilize finite field algebra.

A block code is linear if c i C and c j C implies c i c j C where is an elementwise modulo 2 addition.

Hamming distance is a useful measure of codeword properties

d H c i c j # of places that they are different
Denote the codeword for information sequence e 1 1 0 0 0 0 0 by g 1 and e 2 0 1 0 0 0 0 by g 2 ,, and e k 0 0 0 0 0 1 by g k . Then any information sequence can be expressed as
u u 1 u k i 1 k u i e i
and the corresponding codeword could be
c i 1 k u i g i
c u G
with c 0 1 n and u 0 1 k where G g 1 g 2 g k , a k x n matrix and all operations are modulo 2.

In with

00 00000
01 10100
10 01111
11 11011
g 1 0 1 1 1 1 and g 2 1 0 1 0 0 and G 0 1 1 1 1 1 0 1 0 0

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Additional information about coding efficiency and error are provided in Block Channel Coding .

Examples of good linear codes include Hamming codes, BCH codes, Reed-Solomon codes, and many more. The rate of these codes is defined as k n and these codes have different error correction and error detection properties.

Questions & Answers

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
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
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Akash Reply
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Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
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?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
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
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what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
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Source:  OpenStax, Digital communication systems. OpenStax CNX. Jan 22, 2004 Download for free at http://cnx.org/content/col10134/1.3
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