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Selective error correction

We have found that digital transmission errors occur with a probability that remains constant no matter how "important"the bit may be. For example, in transmitting digitized signals, errors occur as frequently for the most significantbit as they do for the least significant bit. Yet, the former errors have a much larger impact on the overallsignal-to-noise ratio than the latter. Rather than applying error correction to each sample value, why not concentratethe error correction on the most important bits? Assume that we sample an 8 kHz signal with an 8-bit A/D converter.We use single-bit error correction on the most significant four bits and none on the least significant four. Bits aretransmitted using a modulated BPSK signal set over an additive white noise channel.

  1. How many error correction bits must be added to provide single-bit error correction on the mostsignificant bits?
  2. How large must the signal-to-noise ratio of the received signal be to insure reliablecommunication?
  3. Assume that once error correction is applied, only the least significant 4 bits can be received in error.How much would the output signal-to-noise ratio improve using this error correction scheme?

Compact disk

Errors occur in reading audio compact disks. Very few errors are due to noise in the compact disk player; mostoccur because of dust and scratches on the disk surface. Because scratches span several bits, a single-bit error israre; several consecutive bits in error are much more common. Assume that scratch and dust-inducederrors are four or fewer consecutive bits long. The audio CD standard requires 16-bit, 44.1 kHz analog-to-digitalconversion of each channel of the stereo analog signal.

  1. How many error-correction bits are required to correct scratch-induced errors for each 16-bitsample?
  2. Rather than use a code that can correct several errors in a codeword, a clever 241 engineer proposes interleaving consecutive coded samples. As the cartoon shows, the bits representing coded samples are interpersed before they are written onthe CD. The CD player de-interleaves the coded data, then performs error-correction. Now, evaluate thisproposed scheme with respect to the non-interleaved one.

Communication system design

RU Communication Systems has been asked to design a communication system that meets the following requirements.

  • The baseband message signal has a bandwidth of 10 kHz.
  • The RUCS engineers find that the entropy H of the sampled message signal depends on how many bits b are used in the A/D converter (see table below).
  • The signal is to be sent through a noisy channel having a bandwidth of 25 kHz channel centered at 2 MHzand a signal-to-noise ration within that band of 10 dB.
  • Once received, the message signal must have a signal-to-noise ratio of at least 20 dB.

b H
3 2.19
4 3.25
5 4.28
6 5.35

Can these specifications be met? Justify your answer.

Questions & Answers

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
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
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
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Answers please
Nikki Reply

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Source:  OpenStax, Fundamentals of electrical engineering i. OpenStax CNX. Aug 06, 2008 Download for free at http://legacy.cnx.org/content/col10040/1.9
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