<< Chapter < Page Chapter >> Page >
This module provides a brief extension of Viterbi convolutional decoders to turbo decoding.

Turbo encoding and decoding


A paper was published by Claude Berrou and coauthors at the ICC conference in 1993 that rocked or shook the field of forward error correction coding (FECC). This described a method of creating much more powerful block error correcting coding with only the minimum amount of effort. Its main features were two recursive convolutional encoders (RCE) interconnected via an interleaver. The data is fed into the first encoder directly and into the second encoder after interleaving or reordereing of the input data.

Turbo encoding

The important features are the use of two recursive convolutional encoders and the design of the interleaver which gives a block code with the block size equal to the interleaver size, [link] . Random interleavers tend to work better than row and column interleavers. Note that recursive convolutional encoders were known about well before their use in turbo codes, but the difficulties in driving them into a known state made them less popular than the non-recursive convolutional encoders described in the previous module.

The name turbo decoder came from the turbo charger in an automobile where the exhaust gasses are used to drive a compressor in a feedback loop to increase the input of fuel and hence the vehicles ultimate performance.

Turbo encoder with recursive encoding loops

The desired output rate was initially achieved by puncturing (ignoring every second output) from each of the encoders.

Turbo decoding

Turbo decoding is iterative. The decoding is also soft, the values that flow around the whole decoder are real values and not binary representations (with the exception of the hard decisions taken at the end of the number of iterations you are prepared to perform). They are usually log likelihood ratios (LLRs), the log of the probability that a particular bit was a logic 1 divided by the probability the same bit was a logic 0.

Decoding is accomplished by first demultiplexing the incoming data stream into d, y 1 , y 2 . d and y 1 go into the decoder for the first code, [link] . This gives an estimate of the extrinsic information from the first decoder which is interleaved and past on to the second decoder. The second decoder thus has three inputs, the extrinsic information from the first decoder, the interleaved data d, and the received values for y 2 . It produces its extrinsic information and this is deinterleaved and passed back to the first encoder. This process is then repeated or iterated as required until the final solution is obtained from the second decoder interleaver.

Turbo decoder

The decoders themselves generally use soft output Viterbi algorithm (SOVA) to decode the received data. However the preferred turbo decoding method is to use the maximum a-priori (MAP) algorithm but this is too mathematical to discuss here!

Probability of error for turbo decoders with variable number of iterations

Coder performance

[link] shows these ½ rate decoders operating at much lower E b N 0 or SNR values than the convolutional Viterbi decoders of the previous section and, further, as the number of iterations increases to beyond 15, then the performance comes very very close to the theoretical Shannon bound.

This is the attraction that has excited the FECC community, who were unable to achieve this low error rate before 1993! Now that iterative decoding has been introduced for turbo decoders it is also being re-applied in low delay parity check (LDPC) decoders with equal enthusiasm and success.

[link] includes a turbo decoding example (which as an animated power point slide) will show the black dot noise induced errors being corrected on each subsequent iteration with the black dots being progressively reduced in the upper cartoon.

This module has been created from lecture notes originated by P M Grant and D G M Cruickshank which are published in I A Glover and P M Grant, "Digital Communications", Pearson Education, 2009, ISBN 978-0-273-71830-7. Powerpoint slides plus end of chapter problem examples/solutions are available for instructor use via password access at http://www.see.ed.ac.uk/~pmg/DIGICOMMS/

Questions & Answers

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 ?
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
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.
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
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Got questions? Join the online conversation and get instant answers!
QuizOver.com Reply

Get the best Algebra and trigonometry course in your pocket!

Source:  OpenStax, Communications source and channel coding with examples. OpenStax CNX. May 07, 2009 Download for free at http://cnx.org/content/col10601/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Communications source and channel coding with examples' conversation and receive update notifications?