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| In [[digital communications]], a '''turbo equalizer''' is a type of [[Receiver (information theory)|receiver]] used to receive a message corrupted by a [[Channel (communications)|communication channel]] with [[intersymbol interference]] (ISI). It approaches the performance of a [[maximum a posteriori]] (MAP) receiver via iterative [[message passing]] between a [[soft-in soft-out]] (SISO) [[Equalizer (communications)|equalizer]] and a SISO [[decoder]].<ref>R. Koetter, A.C. Singer, and M. Tüchler [http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=1267050 ''Turbo Equalization''] IEEE Signal Processing Mag., vol. 21, no. 1, pp. 67–80, Jan. 2004.</ref> It is closely related to [[turbo codes]], as a turbo equalizer may be considered a turbo decoder if the channel is viewed as a [[convolutional code]].
| | If you're seeking to obtain nice kitchen knives—and are determined to acquire a set—you will not beat the Wüsthof Classic 8-Piece Deluxe Knife Set ($350) for value, efficiency and all round presentation. In between the ordinary knifes in the kitchen Best Kitchen Knives Set Review drawer, you [https://www.google.com/search?hl=en&gl=us&tbm=nws&q=swiftly&btnI=lucky swiftly] discover your favourite knife. The funky colors of the kitchen knives becomes handy when your not that [http://Www.Dailymail.Co.uk/home/search.html?sel=site&searchPhrase=organized organized] as I am. Should you loved this information and you want to receive more info about [http://www.thebestkitchenknivesreviews.com/best-knife-set-reviews-top-kitchen-sets/ Best Kitchen Knives Debenhams] generously visit our own web-page. You can uncover your favourite red knife in a blink of an eye. The rainbow colored kitchen six-piece utensil set consists of a spaghetti server, slotted spoon, ladle, slotted turner, solid spoon, and versatile turner. Most Japanese chefs use a Santoku knife.<br><br>When you get the steel with each other with the set, you can be confident that they are from 1 and the same manufacturer and that the firmness of the honing steel conforms to the firmness of the blades of the knives from the set. If you are an knowledgeable cook, you will in all probability have a incredibly great idea of what knives and accessories your set ought to include. It is the preferred way to mark high quality in knife generating.<br><br>It is the most solid part of the knife exactly where the strain of pressing on the deal with travels through into the blade. Low density or soft woods or other low density materials are not advised for knife handles. The steel maintains a good cutting edge, but will not give the knife one particular if it has gone blunt with no a lot of perform. The Rapala Lithium Ion is also a superior cordless fillet knife and it is handy because you can just plug it into your cigarette lighter and it will get via practically anything.<br><br>Their excellent set, which includes a knife block, would place you out $335, although their price range set only charges $190. To achieve some insight into which knives the typical residence cook basically requires, I called up chef Brendan McDermott, who teaches 20 knife expertise classes a month for household cooks through the Institute of Culinary Education (ICE) in New York City. While America's Test Kitchen does not recommend getting knife sets, their editors do have opinions on what to appear for in a set.<br><br>I have noticed this set in several retail stores all over the net with a value around $130 to $180. The only point that can be enhanced is the length of the steak knives, a little bigger steak knives with a slightly longer handle and the set could be perfect. And if the set had incorporated a utility knife with a plain blade, that would have been good. Initially of all, you Consumer Reports Best Kitchen Knife Set require a fantastic set of pots and pans.<br><br>You can usually get a single kitchen knife block or holder if you want a unified appearance for them. Now that I really use a paring knife for paring, preparing meals appears a whole lot much easier. Good hub, It seriously is worth spending money and finding a very good set of knifes. I got a set of Sabatier and have under no circumstances looked back. Hi PegCole17, for me, I feel the most important tool is a sharp knife. Chefs typically speak about a "superior" sharp knife as getting critical. Obtaining a set will be more economical. |
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| ==History== | |
| In 1993, [[turbo codes]] were introduced by [[Claude Berrou|Berrou]], [[Alain Glavieux|Glavieux]], and [[Punya Thitimajshima|Thitimajshima]].<ref>{{Citation|url=http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=397441 |first=Claude|first2=Alain|first3=Punya|last=Berrou|last2=Glavieux|last3=Thitimajshima|title=Near Shannon Limit Error – Correcting}} International Conference on Communications, 1993.</ref> In 1995, the turbo principle, which was developed for turbo codes, was applied to an equalizer by [[Catherine Douillard|Douillard]], [[Michel Jézéquel|Jézéquel]], and [[Claude Berrou|Berrou]].<ref>{{Citation| url=http://www3.interscience.wiley.com/journal/121408109/abstract |first=Catherine|first2=Michel|first3=Claude|last=Douillard|last2=Jézéquel|last3= Berrou|title=Iterative Correction of Intersymbol-Interference: Turbo-Equalization}} European Transactions on Telecommunications, vol. 6, no. 5, pp. 507-511, September–October 1995.</ref> They formulated the ISI receiver problem as a turbo code decoding problem, where the channel is thought of as a rate 1 convolutional code and the error correction coding is the second code. In 1997, [[Alain Glavieux|Glavieux]], [[Christophe Laot|Laot]], and [[Joël Labat|Labat]] demonstrated that a linear equalizer could be used in a turbo equalizer framework.<ref>A. Glavieux, C. Laot, and J. Labat, [http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.143.6389 “Turbo equalization over a frequency selective channel,”] in Proc. Int. Symp. Turbo Codes, Brest, France, Sept. 1997, pp. 96–102.</ref> This discovery made turbo equalization computationally efficient enough to be applied to a wide range of applications.<ref>M. Tüchler, R. Koetter, and A.C. Singer, “[http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.16.8619 Turbo Equalization: Principles and New Results],” IEEE Transactions on Communications, vol. 50, no. 5, pp. 754-767, May 2002.</ref>
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| == Overview ==
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| === Standard Communication System Overview ===
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| Before discussing turbo equalizers, it is necessary to understand the basic receiver in the context of a communication system. This is the topic of this section.
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| At the [[transmitter]], information [[bit]]s are [[code|encoded]]. Encoding adds redundancy by mapping the information bits <math>a</math> to a longer bit vector – the code bit vector <math>b</math>. The encoded bits <math>b</math> are then [[forward error correction#Interleaving|interleaved]]. Interleaving permutes the order of the code bits <math>b</math> resulting in bits <math>c</math>. The main reason for doing this is to insulate the information bits from bursty noise. Next, the symbol mapper maps the bits <math>c</math> into [[Modulation|complex symbols]] <math>x</math>. These digital symbols are then converted into analog symbols with an [[Digital-to-analog converter|D/A converter]]. Typically the signal is then [[Radio frequency upconverter|up-converted]] to pass band frequencies by mixing it with a [[Carrier wave|carrier]] signal. This is a necessary step for complex symbols. The signal is then ready to be transmitted through the [[Channel (communications)|channel]].
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| At the [[Receiver (information theory)|receiver]], the operations performed by the transmitter are reversed to recover <math>\hat{a}</math>, an estimate of the information bits. The [[Digital down converter|down-converter]] mixes the signal back down to baseband. The [[Analog-to-digital converter|A/D converter]] then samples the analog signal, making it digital. At this point, <math>y</math> is recovered. The signal <math>y</math> is what would be received if <math>x</math> were transmitted through the digital [[baseband]] equivalent of the channel plus [[Noise (electronics)|noise]]. The signal is then [[Equalizer (communications)|equalized]]. The equalizer attempts to unravel the [[Intersymbol interference|ISI]] in the received signal to recover the transmitted symbols. It then outputs the bits <math>\hat{c}</math> associated with those symbols. The vector <math>\hat{c}</math> may represent hard decisions on the bits or soft decisions. If the equalizer makes soft decisions, it outputs information relating to the probability of the bit being a 0 or a 1. If the equalizer makes hard decisions on the bits, it quantizes the soft bit decisions and outputs either a 0 or a 1. Next, the signal is deinterleaved which is a simple permutation transformation that undoes the transformation the interleaver executed. Finally, the bits are decoded by the decoder. The [[decoder]] estimates <math>\hat{a}</math> from <math>\hat{b}</math>.
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| A diagram of the communication system is shown below. In this diagram, the channel is the equivalent baseband channel, meaning that it encompasses the D/A, the up converter, the channel, the down converter, and the A/D.
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| [[Image:COMMblockdiagram.png|none]]
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| ===Turbo Equalizer Overview===
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| The block diagram of a communication system employing a turbo equalizer is shown below. The turbo equalizer encompasses the equalizer, the decoder, and the blocks in between. | |
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| [[Image:TEQUdiagram.png|none]]
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| The difference between a turbo equalizer and a standard equalizer is the feedback loop from the decoder to the equalizer. Due to the structure of the code, the decoder not only estimates the information bits <math>a</math>, but it also discovers new information about the coded bits <math>b</math>. The decoder is therefore able to output extrinsic information, <math>\tilde{b}</math> about the likelihood that a certain code bit stream was transmitted. Extrinsic information is new information that is not derived from information input to the block. This extrinsic information is then mapped back into information about the transmitted symbols <math>x</math> for use in the equalizer. These extrinsic symbol likelihoods, <math>\tilde{x}</math>, are fed into the equalizer as ''a priori'' symbol probabilities. The equalizer uses this ''a priori'' information as well as the input signal <math>y</math> to estimate extrinsic probability information about the transmitted symbols. The ''a priori'' information fed to the equalizer is initialized to 0, meaning that the initial estimate <math>\hat{a}</math> made by the turbo equalizer is identical to the estimate made by the standard receiver. The information <math>\hat{x}</math> is then mapped back into information about <math>b</math> for use by the decoder. The turbo equalizer repeats this iterative process until a stopping criterion is reached.
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| ===Turbo Equalization in Practical Systems===
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| In practical turbo equalization implementations, an additional issue need to be considered. The ''[[channel state information]] (CSI)'' that the equalizer operates on comes from some channel estimation technique, and hence un-reliable. Firstly, in order to improve the reliability of the CSI, it is desirable to include the channel estimation block also into the turbo equalization loop, and parse soft or hard decision directed channel estimation within each turbo equalization iteration.<ref>M. Sandell, C. Luschi, P. Strauch, and R.Yan, “Iterative Data Detection
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| and Channel Estimation for Advanced TDMA Systems,” IEEE GLOBECOM, Australia, pp. 3728–3733, Nov 1998.</ref><ref>S. Y. Park and C. G. Kang, “Complexity-Reduced Iterative MAP Receiver for Interference Suppression in OFDM-Based Spatial Multiplexing Systems,” IEEE Transactions on Vehicular Technology, vol. 53, pp. 1316–1326, Sep 2004.</ref> Secondly, incorporating the presence of CSI uncertainty into the turbo equalizer design leads to a more robust approach with significant performance gains in practical scenarios.<ref>M. Danish Nisar and Wolfgang Utschick. [http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=5672616 "Minimax Robust A-priori Information Aware Channel Equalization"], in IEEE Transactions on Signal Processing, Volume 59, pp 1734 - 1745, April 2011.</ref><ref>N. Kalantarova, S. S. Kozat, and A. T. Erdogan, “Robust Turbo Equalization Under Channel Uncertainties,” IEEE
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| Transactions on Signal Processing, 2012.</ref>
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| == References ==
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| <references />
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| == External links ==
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| * [http://www.turboequalization.net/ Turbo Equalization Resources] includes an annotated bibliography, interactive block diagram, and turbo equalization simulation code.
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| * [http://www.ifp.illinois.edu/~singer/journalpapers/koetter_2004.pdf Turbo Equalization] a Signal Processing Magazine primer on turbo equalization. Since it was written for the signal processing community in general, it is relatively accessible.
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| * [http://www.ifp.illinois.edu/~singer/journalpapers/tuchler_2002a.pdf Turbo Equalization: Principles and New Results] an IEEE Transactions on Communications journal article that offers a detailed, clear explanation of turbo equalization.
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| ==See also==
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| *[[Equalizer (communications)]]
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| {{DEFAULTSORT:Turbo Equalizer}}
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| [[Category:Telecommunication theory]]
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| [[Category:Signal processing]]
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If you're seeking to obtain nice kitchen knives—and are determined to acquire a set—you will not beat the Wüsthof Classic 8-Piece Deluxe Knife Set ($350) for value, efficiency and all round presentation. In between the ordinary knifes in the kitchen Best Kitchen Knives Set Review drawer, you swiftly discover your favourite knife. The funky colors of the kitchen knives becomes handy when your not that organized as I am. Should you loved this information and you want to receive more info about Best Kitchen Knives Debenhams generously visit our own web-page. You can uncover your favourite red knife in a blink of an eye. The rainbow colored kitchen six-piece utensil set consists of a spaghetti server, slotted spoon, ladle, slotted turner, solid spoon, and versatile turner. Most Japanese chefs use a Santoku knife.
When you get the steel with each other with the set, you can be confident that they are from 1 and the same manufacturer and that the firmness of the honing steel conforms to the firmness of the blades of the knives from the set. If you are an knowledgeable cook, you will in all probability have a incredibly great idea of what knives and accessories your set ought to include. It is the preferred way to mark high quality in knife generating.
It is the most solid part of the knife exactly where the strain of pressing on the deal with travels through into the blade. Low density or soft woods or other low density materials are not advised for knife handles. The steel maintains a good cutting edge, but will not give the knife one particular if it has gone blunt with no a lot of perform. The Rapala Lithium Ion is also a superior cordless fillet knife and it is handy because you can just plug it into your cigarette lighter and it will get via practically anything.
Their excellent set, which includes a knife block, would place you out $335, although their price range set only charges $190. To achieve some insight into which knives the typical residence cook basically requires, I called up chef Brendan McDermott, who teaches 20 knife expertise classes a month for household cooks through the Institute of Culinary Education (ICE) in New York City. While America's Test Kitchen does not recommend getting knife sets, their editors do have opinions on what to appear for in a set.
I have noticed this set in several retail stores all over the net with a value around $130 to $180. The only point that can be enhanced is the length of the steak knives, a little bigger steak knives with a slightly longer handle and the set could be perfect. And if the set had incorporated a utility knife with a plain blade, that would have been good. Initially of all, you Consumer Reports Best Kitchen Knife Set require a fantastic set of pots and pans.
You can usually get a single kitchen knife block or holder if you want a unified appearance for them. Now that I really use a paring knife for paring, preparing meals appears a whole lot much easier. Good hub, It seriously is worth spending money and finding a very good set of knifes. I got a set of Sabatier and have under no circumstances looked back. Hi PegCole17, for me, I feel the most important tool is a sharp knife. Chefs typically speak about a "superior" sharp knife as getting critical. Obtaining a set will be more economical.