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Turbo Codes Promise Better Wireless Transmission
captain igor writes "IEEE is running a story about two French professors that have created a new class of encoding, called 'Turbo Codes,' that will allow engineers to pass almost twice as much data through a given communications channel, or equivalently, the same amount of data at half the power. The new codes allow the Shannon Limit (the theoretical maximum capacity of a channel) to be approached to, currently, within .5 dB. Scientists hope that this breakthrough will revolutionize wireless communications, especially with the coming reclamation of large swaths of the EM spectrum." As the article points out, such codes are in use now, but seem poised for much wider implementation.
Oh wait...
It also seems to be making a natural progression into new areas, beginning at satellite transmissions 11 years ago and making it's way into other digital wireless applications along the way.
Thanks to timothy for almost clearing this up
Eve Fairbanks says I drive a hybrid!LOL
Sounds a lot like this story...
Double your hard drive space, your bandwidth, data transfer, penis size...
Clever AND good looking !
I'll do it for cheesy poofs.
Whilst turbo codes are cool, as the article points out they were developed in 1993. I graduated last year and we covered them on my course.
Now they are a fairly obvious choice in any digital communications system and it's hardly groundbreaking that someone has chosen to use them.
Like the article says, these codes were introduced in 1993. This would have made a good story - back then.
The problem is that turbo codes are so computationally intensive that using them in consumer electronics is only new becoming feasible.
Finally, by forcing more air into the cylinders than ordinary air pressure would allow, we will be able to achieve more efficient combustion, which will in turn allow us to transmit more data using radio frequencies. ...Don't you just hate it when terminology gets mis-applied to stuff it has nothing to do with?
Dang it, this software isn't made out of platinum, either.
You see? You see? Your stupid minds! Stupid! Stupid!
Can this be applied to wired transmissions too?
----
I live in a rural area, where we are sometimes lucky that we have a signal, let alone a good one. This could improve the reception for us a lot. Either that, or it doubles the battery life of the cell phones. Either way, I am happy. Although I wonder if this coding could be used in wireless devices as well. Hopefully this could somehow be used to help limit the battery drain of WiFi on a laptop/PDA.
That's the Nyquist limit actually. ;-)
Could turbo codes be used with a 56K modem giving somewhere around 80kbps of bandwidth?
Turbo codes aren't really new. As the article states, they were invented in 1993. I have a big stack of papers on them at home.
Turbo codes have a few problems, though. One, they are a pain to implement and consume a lot of resources. Two, turbo codes are SNR dependent, which makes them harder to use in varried channels.
The article also makes it seem like there were no coding advances since Shannon published his orginal paper on channel capacity. Ungerbock's papers on trellis coded modulation (TCM) from 1987 or so radically altered digital communications, and he should have been mentioned. Some of the current turbo code research is trying to unify TCM and Turbo Coding (TTCM), which has great promise once it is practical.
(S(SKK)(SKK))(S(SKK)(SKK))
Error correction again seems like one of the bottom less pits... like trying to achieve zero kelvin... perfect vacuum and of course this landmark talk by feynman.
Another thing that worries me is why all prepostrous claims are met with so much resistance.... relativity, quantum mechanics, secure-crashfree-windows(oops)...
strange world we live in.
[all generalizations are untrue except this one]
Ehm, what have you been smoking recently?
Is there a similar Law to Moores law (or a combination of such) that could be applied to this compression of data and the effective use of the spectrum? As time goes I feel we are going to see the need for the available ammount of wireless transmission medium to increase. How long before we hit the theoretical limit of data transmission and the planet is saturated?
Just interested...
Does it go on forever?
From a theoretical standpoint, there is no difference between wired and wireless communications. The difference lies in how you model the channel. So, turbo codes can be applied to wired communications.
(S(SKK)(SKK))(S(SKK)(SKK))
Nyquist is the sample-rate guy (the Nyquist theorem).
Shannon capacity is the theoretical bit-rate you can stuff through a channel of a given physical bandwidth with a given signal to noise ratio:
C = W * Log2(1+S/N)
where C is capacity (bits per second), W is bandwidth (Hz), S is signal power, and N is noise power.
As far as Turbo Codes go, without getting too technical, its an extension of the principle that you can increase the efficiency of a channel while transmitting at a given power by attaching some redundant bits (redundant signal dimensions is probably a better way to look at it, though) to the signal. I'm not too familiar with the particulars of Turbo Coding, but it is a lot like Viterbi coding where these redundant bits are dependent on the data bits and when you detect an error (the redundant bit doesn't match the proper sequence), you back-trace through your data and find the most likely non-errored sequence and adjust your data bits accordingly.
Tim
There are a lot of high data rate links where it's either prohibitively complex to implement turbo codes, or the nature of the channel actually makes trellis codes concatenated with some other code a better choice.
--- Ban humanity.
As other posters have commented, turbo codes have been around along time. Any Digital Modulation Course will cover it.
Turbo Codes do have one major drawback
After partially reading the FA It seems that this scheme is particularly well suited for what it is currently doing, Sat Comm and deep space probes where you have alot of computational and analysis power at the recieving end but not a good way to ask for a re-transmission, when you have a multiple second (or multiple hour) latency in your communication system but really, this is not going to be in a cell phone for quite a while, cell phones are built to make lots of connections from one tower, not to make your phone get insane coverage or to make your battery last longer. especially the stuff abour predicting bit value based on analog value, so now we turn every digital reciever into a digital reciever + Analog to Digital reciever in x bits.... honestly i think most consumer applications are not worth the added cost. keep in mind it has been 11 years since this tech came out... communications companies aren't stupid... it WOULD be on the market if it was feasable/affordable.
Snowden and Manning are heroes.
Sort-of. You may be thinking of the Nyquist criterion, but this is related in a way. Shannon was the first to quantify the concept of information via "entropy", which leads to the concept of "mutual" or shared information (i.e. between inputs and outputs of a channel). Distortion (additive noise or some other form) limits the amount of mutual information shared between the input an output of a channel, and is independent of the nature of the data source. Thus, he proved that communication channels have a theoretical limit to the amount of data that can be reliably (error free) transmitted through them. He also suggested coding as a method to achieve this theoretical limit, which turbo codes approach for certain classes of channels (additive gaussian noise channel, for instance).
People have been working on them for ages and yes there are significant advantages.
However, the latest word on source and channel coding though, is Space-Time Coding. Especially convolutionsal S-T codes are very very promising and quite naturally perform even better than block S-T codes...
What I don't understand is why this now? It's like running a feature on GSM, instead of writing about TDD or FDD in 3G, or even the discussion going on about how 4G will shape out to be...
/. Where the truth
What is this Nobel price you speak of?
Lasers Controlled Games!
Yesterday, Nextel finalized a deal to add a pretty big chunk of spectrum to their business (in exchange for some sort of administration requirements for police and other channels which currently fit in that band.
Are there any of you who could comment on whether this will reduce the value of such a chunk of the spectrum?
Read jack phelps dot net
Briefly, the big problem in data communication is achieving the Shannon limit, which is the maximum theoretical data rate at which information can be transmitted with arbitrarily low probability of error. Shannon proved his result in 1948, but until the Turbo guys, nobody knew how to achieve it.
The main problem is that optimal decoding of any non-trivial code is NP-hard, which has been known for about 30 years now (i.e., the only known algorithm has exponential complexity in the code length). The Turbo breakthrough was to show that a suboptimal decoder with O(n) complexity for code length n could nonetheless achieve excellent results. This is the so-called "Turbo principle".
There is an even "newer" class of codes called Low-Density Parity-Check Codes that can beat turbo codes. Turbo codes have a small gap to the Shannon limit, and these new codes can potentially eliminate the gap. Small gains are a big deal; the rule of thumb is that 1 dB of gain is equal to a million dollars of annual revenue for a wireless provider.
The twist is that these LDPC codes were actually proposed in a 1963 PhD thesis, but were disregarded as beyond the computational abilities of the time. They were only "rediscovered" in 1996, after the Turbo code furore.
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Lots of /.ers have been quick to point out that turbo codes have been around since 1993. However, the IEEE article points out that LDPC ( low density parity check) codes were invented in the early 1960s. Researchers have gotten the LDPC codes to outperform the turbo codes, and to top it off, the LDPC patents have all expired, meaning no royalty fees like turbo codes.
My first slashdot post ... be gentle!!!
I hope they get cracking on
Up, Up, Down, Down, Left, Right, Left, Right... etc.
"much as when, in a crowded pub, you have to shout for a beer several times"
I was wondering when they would get to the practical applications.
They were discussed in classes at both universities I attended, too...
I've had this sig for three days.
Turbo coding basically does block interleaving of the output of two different convolution encoders of the input.
(S(SKK)(SKK))(S(SKK)(SKK))
I just heard about Turbo Codes recently, but from a different perspective. I think at the time, they developed these codes with rates so close to the Shannon limit, and no one believed it. Even then, I don't think they were aware of the theoretical basis for why they worked.
Theory finally caught up with them more recently, from the framework of probabilistic networks. It turned out that if you have a Bayesian network with cycles, inference is difficult. But there is a method of belief propagation through message passing that can be used, and it turned out that this is exactly what these guys were doing. (The network itself would include a probabilistic model of noise and its effect on the messages from the sender to receiver.)
Didn't the word "turbo" go out several years ago, along with the useless PC case button of the same name?
--- "When I think back on all the crap I learned in high school, it's a wonder I can think at all..."
Just assign every possible file a name, let's call it... hmmm... a "universal resource locator". Now, instead of exchanging huge files, you just exchange these universal resource locators, or "URLs". Imagine the savings! The only slight problem is that you can't actually read the file without downloading / transferring it.
Hint: transmitting the names of things is not the same as transmitting the things themselves.
Ceci n'est pas une signature
I was looking up an article the other day for my Analysis class....I needed an article that involved "proof" meathods and such, I put in google "numerical analysis and cyphers"
I got a reseach paper about turbo codes....and now today, I see this....I swear coincidences like this don't happen by chance.
I am the Alpha and the Omega-3
Since turbo codes cause a delay at the decoder: You would be waiting a long time for you beer. You'd better stick to good old parity bits: Keep on shouting...
I've seen that some people are curious about Shannon's limit, so I though I would give a little insight to it. It starts, with Nyquist's theorem which states:
max data rate = 2H log V bits/sec
Here, H is the bandwith available, usually through a low-pass filter, and V is the number of discrete signal levels (V = 2 in a straight binary system).
This equation however is for a noiseless channel, which doesn't exist. So Shannon updated the formula for a channel which contains a signal-to-noise ratio. This turns out to be:
max bits/sec = H log (1 + S/N)
Here the log is again base 2, H is still the bandwith (in Hertz) and S/N is the signal-to-noise ratio in dB. Notice that the parameter V is missing. This is because no matter how many discrete symbols you have, or how often you sample them, this is still the maximum number of bits/sec that you will be able to attain.
Most coding schemes, or modulation techniques as they are also called, rely on shifting signal amplitude, frequency, and phase to transmit more than one bit per symbol. The problem is that the more symbols there are, the harder it is to detect them correctly with the addition of noise. Basically, when you fire up your modem, and you hear all that weird buzzing and beeping, a lot of that is time being spent for your modem trying to determine just how noisy the channel is, and what the best modulation scheme it can use is while still being able to detect symbols correctly.
Microsoft should hire me. I can write code that doesn't work faster than the guys they have doing it now.
I always enjoy the moment in history when theory becomes practice.
1904 Einstein predicts the energy released from nuclear fission (E=MC^2). ~1938 first atom split, the equation was correct.
FM radio was therorized for many years, but until Amstrong came up with his Phase Lock Loop none could make an FM radio capable of broadcasting more than about a hundred feet.
CDMA has been around for a while too, Qualcomm doesn't own the pattent on it, just some techniques for practically implementing it which wasn't possible until microprocessor and DSP technology got sufficientlt small and powerful to fit in a cell phone.
This is the difference between science and engineering and I think it's very fitting that an engineering journal (that's the last E in IEEE) is pointing out that a bit of science has finally become interesting to a rather large group of engineers.
Actually, both, Nyquist and Shannon, discovered the sample-rate formula at the same time, hence you can call it Nyquist theorem or Shannon's critical sample-rate theorem.
It happened quite often that people - geographically separated by thousands of miles - invented/discovered the same thing at the same time, +/- a few weeks.
Studying EE, comm. electronics / systems.
You must remember that LDPC codes rely upon block (Codeword) lengths of many bits, e.g. over 10,000 bits long in order to achieve performance better than turbo codes. So your parity check matrix is enormous.
I'm sure there are some efficient implementations, but for certain applications having packets that long can be prohibitive.
I have been dying for an article in my field to post on! Actually new classes of LDPC codes based on finite geometries have shown that you can construct them at almost any size (say 1000 bits, much more practical). These 'algebraic' LDPC codes perform much better than both Turbo codes and other LDPC codes mostly because they have more structure and are not generated by random computer searches.
;-)
Also they don't require the more time consuming decoding algorithm needed for Turbo Codes (although they can be used). Check 'em out, you can search for papers on IEEE Xplore. Also someone is working on research to show Turbo Codes are LDPC codes! Crazy.
I almost crapped my pants when I saw that statement that Turbo codes were new.
-Take that Lisa's beliefs!
"Take that Lisa's beliefs!" - Homer Simpson
.... was the fate of Shannon. He is the father/creator of information theory which he shared with the world in a brilliant paper. He was afflicted by Alzheimer's disease, and he spent his last few years in a Massachusetts nursing home.
"Consensus" in science is _always_ a political construct.
If you use high-speed "1x" data (e.g. 153 kbps) on the CDMA networks from Verizon, Sprint, others, there is a reasonable chance that you are already using turbo codes (the high-speed data channels also support convolutional codes).
Check here for all the gory detail (WARNING: 2.3 MB PDF).
I believe the most important aspect of turbo codes is that it uses signal strength in it's error-correction algorithm. It's a rather important chunk of data which allows them to refine their signal bits through parity checking to correct errors by determining which bits went wrong.
---If you can't trust a nerd, who can you trust?
The neat thing about Turbo codes is that they're being used in the 3G cell phone standards (along with various other codes.) Turbo codes are powerful because they are iterative: they make several approximations at the information sent across the wire (or lack of wire, heh).
This allows the system to do a good job of guessing what the original message is quickly. If you're interested in Turbo Codes, one of my former professors has done a lot of work with them, and has links to other turbo code sites on his website:
http://www.csee.wvu.edu/~mvalenti
Click on the turbo code link.
Did I forget to mark this on my calendar? At first it's hard drives and now bandwidth. What's next, how to overclock your pc/microwave/toaster/car?
Gee- thats funny. I work a a satellite internet company, and we use Turbo-codes in our FPGA's. The delay from TPC is in the low milisecond range- trust me.
Anything close to one second would have been unacceptable.
I dont know where you got your numbers from.
Hey, I just finished my PhD on LDPC codes. Where do you work?
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Actually, as someone above pointed out, it is slightly similar to a turbo exhaust. You take the output of the decoder (its guesses basically) and feed it back into the decoder for another pass. As you iterate over the data block in different dimensions, thus after correcting one section in one axis, you might be able to correct a different section in another axis that previously had too many errors to correct.
Back to the point, it is somewhat similar to a turbo, more so than most things that use the name.
Bit synchronizers with soft decision outputs have been available for decades. Error correction decoding algorithms that take advantage of soft decision inputs have also been around for a very long time, even if they haven't been widely implemented.
Mea navis aericumbens anguillis abundat
If turbo codes get used in cell phones, does that mean that new cell phones will have a Turbo button? Great, now I have to use advanced duct-tape technology so that the turbo button is always activated.
Well, there's spam egg sausage and spam, that's not got much spam in it.
This is not some dumb use of turbo to mean fast, it's based on the fact that the decoders are using feedback to improve the error correction. This quote is taken from the article:
It was France Telecom that asked Berrou to come up with a commercial name for the invention. He found the name when one day, watching a car race on TV, he noticed that the newly invented code used the output of the decoders to improve the decoding process, much as a turbocharger uses its exhaust to force air into the engine and boost combustion. Voila: "turbo codes"!
Of course, the fact that I graduated from the school where they're teaching/doing research may be the reason I feel that I need to defend their name choice...
The button was right there next to the power button, "Turbo". Must've used turbo codes when you pressed it. ;)
Could turbo codes be used with a 56K modem giving somewhere around 80kbps of bandwidth?
Nope. (They'd actually reduce the data rate if used.)
Turbo codes are members of the class "Forward Error Correction" codes, which are used to correct errors that creap in during signal propagation from a sender to a receiver over a noisy channel. They work by sending EXTRA bits (typically 3 times as many with turbo), then processing what you get to correct the errors.
Turbo codes are typically used on noisy analog channels - such as radio links. Because they make the data bits less susceptable to noise you can reduce the amount of power you use to transmit them. It's like saying the same sentence three times in a noisy room, rather than scraeming over the noise level just once, so the guy at the next table can hear exactly what you said.
Turbo code (and other FEC codes) send more bits. But because the underlying data is so much less likely to be received incorrectly the sender can can reduce the amount of power used for each bit by MORE than enough to make up for the extra bits. You can trade this "coding gain" either for more BPS at a given power level or a lower power consumption at a given BPS.
But adding bits also increases the amount of information you're sending - either by broadening the bandwidth or more finely dividing the signaling symbol (for instance: more tightly specifying and measuring the voltage on a signal). So if your bitrate is limited by the channel capacity rather than the noise level you're stuck. The coding scheme will "hit the wall" and after that the extra bits come right out of your data rate. Not a problem with Ultra Wideband, or with encoding more bits-per-baud to get closer to a noise floor. But a big problem with telephone connections.
If you had a pure analog telephone connection they would be useful for increasing your bandwidth utilization. And in the old days you did. And analog modems struggled to push first 110 BPS, then 300, then 1200 through it despite the distortion and noise. Then they got fancy and cranked it up to 9.6k and beyond by using DSPs.
But these days you don't have an analog connection all the way. Your analog call is digitized into 8,000 8-bit samples per second and transmitted at 64,000 BPS to the far end. No matter WHAT you do to your signal you can't get more than that number of bits through it.
(This is actually very good, by the way, if the connection is more than a couple miles long. The digital signal is propagated pretty much without error, while an analog signal would accumulate noise, crosstalk, and distortion. So for calls outside your neighborhood you usually get a better signal-to-noise ratio with the digital system for the long hops than with an analog system. That's why cross-continent calls these days sound better than cross-town calls in the '50s.)
In practice it's worse than 64,000 BPS - because the system sometimes steals one of the bits from one sample in six for signaling about dialing, off-hook, ringing, etc. And you don't know WHICH sample. So you can only trust 7 of the bits. 56,000 BPS max. (It's a tad worse yet, because some combinations of signals are forbidden due to regulatory restrictions on how much energy you can put on a phone line - a particular signal could slightly exceed the limit. This makes the actual bit rate a little lower. And you have to sacrifice a little bandwidth to keep the receiver synchronized, too.)
And you only get the approximately 56k in the downlink direction, because to use it you have to have a digital connection at the head end to make full use of the digital transmission. At your uplink you can't be sure enough of the sampling moment to create a waveform that would force exactly the right bit pattern out of the A-to-D converter. So you have to fall back to a modulation scheme that allows some slop when you're transmitting at the POTS end of the link. (If you had a digital connection at both ends - i.e. ISDN - yo
Bantam Dominique roosters crow a four-note song. Once you've heard it as "Happy BIRTHday" you can't NOT hear it that way
The article simply says that turbo coding is about to go mainstream.
If you read the article (Not sure if that's possible to do without paying $$$ unless you're an IEEE member, in which case you have it in dead-tree format and can access it for free online), the reason they were called "turbo" codes was because one of the creators of turbo codes was apparently a big automotive racing fan.
Part of the turbo coding system involves a feedback loop between two seperate decoders at the receiver. The feedback from each decoder helps the other decoder make a better decision about the data.
Similarly, a turbocharger relies on feedback to operate. Exhaust pressure spins the turbo, which is used to compress intake air to the engine, increasing the amount of fuel that can be burned. More fuel/air being burned in the cylinders means more exhaust gases being pushed out, which results in a positive feedback loop that increases power until something is done to interrupt the loop. (Usually a wastegate that dumps the exhaust gas in a path that bypasses the turbine once the pressure reaches a certain threshold.)
Thus while the naming of "turbo" codes isn't completely appropriate (no turbine...), it is far more appropriate than the old inappropriate association of the word "turbo" with anything fast.
retrorocket.o not found, launch anyway?
Why are they not all migrating to VMSK, the magical modulation that promises to exceed the Shannon limit by orders of magnitude? Approaching it by .5dB seems to be not very much of an accomplishment, compared to that.
Checkout http://www.vmsk.org/ where all the claims are made. Supposedly you could compress all communication to 1Hz bandwidth, or so.
[of course I do not believe this]
Doubling power does not double available channel capacity.
Note the log(1 + SNR) in Shannon's theorem...
retrorocket.o not found, launch anyway?
FYI, this applies not to compression of data, but to error correction. It's assumed with turbo codes that there is no redundancy in the information being encoded. (In reality there may be, but that's a completely different problem.)
i.e. a communications system is always optimized to maximize performance with a bitstream that is assumed to be non-redundant.
Turbo codes are a method for error correction, not compression. In fact, they do the exact opposite of compression - they ADD redundant data.
As to a limit - Turbo codes have performance within 0.5 dB of SNR of Shannon's limit for a given channel. Can't do much better. (Although it may be possible to come up with a coding scheme that is less computationally intensive/has less latency)
retrorocket.o not found, launch anyway?
Actually, that's incorrect. A "Turbocharger" also commonly referred to as a "Turbo" on an automobile uses a turbine that sits in the exhaust stream to push another turbine connected to the intake stream to pressurize the intake stream. EGR is a separate thing used for emissions, where exhasut gas is introduced back into the intake manifold. It is supposed to help the engine reach operating temperature quickly, and reduce the amount of hydrocarbons, but all it really does is make the inside of your intake manifold turn black.
Nothing says "unprofessional job" like wrinkles in your duct tape.
Maybe we should also stop using the words "FAST" and "SLOW" to describe how "quickly" a computer can process things. It's a word commonly associated with "fast", why get all aggravated about it? "Cool" is commonly associated with "good", but do you get all upset about that? I mean really.
Nothing says "unprofessional job" like wrinkles in your duct tape.
nosphalot is correct: The Turbo breakthrough was that they determined that by using feedback, just as in an engine turbo, you could get arbitrarily close to Shannons limit.
;.)
The key idea is that this feedback gives you an infinite impulse response, i.e. in theory all bits ever transmitted through such a channel will continue to affect it for ever after.
Even if you do limit the feedback time to more reasonable levels, you can still get a very useful increase in channel capacity.
It is also important to notice that such a channel must have significant delay, i.e. here's another reason to complain about being lagged.
Terje
"almost all programming can be viewed as an exercise in caching"
And it won't.
-- Repeat with me: "There is no right to profits".
I don't even have the slightest idea what "linear" or "nonlinear" means in the context of information entropy. Thus I can only assume you're talking about the channel theorem.
Right, Gallager worked out LDPC codes in 1963. Then they were forgotton for 20 years until people realized that Digital Fountain's "Tornado" codes were LDPC codes.
LDPC codes will be behind DVB-S2, the new transmission system for digital satellite video distribution. Since they approach the Shannon limit so closely, there will be no DVB-S3.
I should say that the IEEE article is a little over-hyped, in that these codes really only buy about 2-4 dB additional gain, concatenated RS and convolutional coding were pretty close to the Shannon limit in AWGN, but those last couple of dBs were nice, but the remaining 0.5-1 dB beyond LDPC & Turbo Codes isn't worth much.
Much more important now are ways to handle "fast fading" channels found in mobile environments, this is what is driving OFDM.
Also, both Turbo Codes and LDPC codes are really computationally intensive to decode. They are currently only decoded at speeds below 20 Mbps, generally implemented as (expensive) FPGAs. We won't see real cheap ASICs for another year or two.
I RTFLA and the attached pdf . First, let me say that the PDF sums it up, you can avoid the article. Second, I would like to know, according to this pdf, how did the system rate a +8 on a scale of -7 to +7?
I don't know if they are being used right now (I think not), but what you're describing happens for a different reason. Digitized speech in a cell phone is passed through a lossy compression algorithm which is optimized for voice as opposed to general sounds (they're called "vocoders"). As such they can achieve huge gains in compression over general lossy compression, though music will always sound like crap.
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Can you explain how they are relating dB to datarates?
dB what? dBf (decible fempto-watts, used for receiver signal strength often)?
The original paper is here
E 127/EE127B/handout/berrou.pdf
.. not "new", but currently still a hot topic in telecomm.)
Claude Berrou, Alain Glavieux, and Punya Thitimajshima, "Near Shannon Limit Error-Correcting Coding and Decoding:Turbo-Codes", in Proceedings of IEEE International Conference on Communications, (Geneva, Switzerland), pp. 1064--1070, May 1993.
http://gladstone.systems.caltech.edu/EE/Courses/E
(with 400 citations, as counted by CiteSeer ResearchIndex
http://citeseer.ist.psu.edu/context/31968/0
-- yeah, it is since 1993
about the authors, the first two are French professors who had already mentioned in the article, the last one is Thai, at that time a PhD student at Ecole.
Yes, I hear that Space-Time coding is the 'new deal' for Rayleigh type fading channels. A few people in my dept. have been doing research into these codes. I should probably read the work whenever I don't have other projects, assignments, TA duties, marking, etc. to do. ;-).
What amazes me is how far behind these companies are in actually implementing this technology. 10-years old is actually new.
A friend of mine was saying that even when new research developments are implemented in new hardware the IT people (read: customers) don't understand how to use it anyways or just don't configure it at all (his comments applied specifically to high-end network hardware and new routing schemes). Reminds me of people who setup the company wireless network with 'default'.
"Take that Lisa's beliefs!" - Homer Simpson
AOL jokes are so 1999.
evil adrian
So I don't understand how sending the same data three times over is efficient? The example illustration is sending 15 bits to code 5 bits.
Please explain.
-- PC architecture - what a mess.
Usually the dB refers to the signal power to noise power ratio (SNR) -- noise power is usually proportional to the noise variance. Thus, an SNR of 0 dB means that the signal power and the noise power is the same.
Ability to accurately distinguish bits in a communication system decreases with data rate (crudely speaking, this is because you get less time to "look" at each bit and distinguish it from noise.) For a given communication system, we have an acceptable probability of bit error, say 10^-6. Given this probability, usually we try to find the minimum SNR for a given data rate so that the criterion is achieved. To say that one system has 3 dB gain over another is to say that 3dB is the difference in SNR required to achieve the required probability of error. Since noise power is usually normalized, this means the difference in signal power is 3 dB.
Of course, you can look at the problem from the other direction and say, for fixed SNR, what is the difference in data rate? In this sense, SNR and data rate are interchangeable.
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