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This module provides a brief extension of Viterbi convolutional decoders to turbo decoding.

Turbo encoding and decoding

Introduction

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

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
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
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
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.
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
Brian Reply
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?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
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 ?
Bob Reply
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?
Damian Reply
what king of growth are you checking .?
Renato
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
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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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
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