ࡱ> =?<PM bjbj== fWWKl 4 8,$4 z(~(]AD$FzHzHzHzHzHzHz$| ~tlz ^]lz  z4  ( FzFz Fs$ T z PGٱ4 `wTz,z<zbwI Iz4 4   Viterbi Demo Application  EMBED Package  Table of Contents  TOC \o "1-3" \h \z \u  HYPERLINK \l "_Toc200728148" 1 Abstract  PAGEREF _Toc200728148 \h 3  HYPERLINK \l "_Toc200728149" 2 Mobile Phones and Viterbi  PAGEREF _Toc200728149 \h 3  HYPERLINK \l "_Toc200728150" 3 Demo Application  PAGEREF _Toc200728150 \h 4  HYPERLINK \l "_Toc200728151" 4 Download And Try It  PAGEREF _Toc200728151 \h 4  HYPERLINK \l "_Toc200728152" 5 Why Did I Write It?  PAGEREF _Toc200728152 \h 4  HYPERLINK \l "_Toc200728153" 6 Links  PAGEREF _Toc200728153 \h 5  HYPERLINK \l "_Toc200728154" 7 Miscellany  PAGEREF _Toc200728154 \h 5  Abstract The Viterbi Algorithm is named after its inventor Andrew Viterbi. Its primary use is for error correction in noisy digital communication reception. This article discusses its application in mobile phones, and presents a downloadable software application that demonstrates the algorithm in action - graphically. Mobile Phones and Viterbi It is a deliberate network design decision that means the signal that arrives at a mobile phone is not the one that got sent by the transmitter - it is invariably corrupted to some degree by noise. Most mobile phones use the Viterbi algorithm to clean up the signal they get to resurrect their 'best guess' of what the signal should have been. The reason for this seemingly bizarre position is that the network operators are extremely keen to minimise the power and network bandwidth required for each transmission, and they can achieve an optimum compromise by adding extra error correction data to their signals and then using a bandwidth / power combination that they know will cause some signal degradation, but the error correction on the receiving phone can resurrect the signal just enough. The big idea is that the way the error correction codes are added at the transmission end follows a set procedure. The error correction algorithm then at the receiving end, keeps track of what might have been the correct signal as it receives the stream of probably corrupted bits. Provided there is not too much corruption it has a very good chance using the analysis of cumulative probability of what was the most likely transmitted clean signal. Demo Application  Click a button to make a new 15-bit binary signal Click a button to add error correct codes Click a button to inject random corruption into the signal Click a button to watch the Viterbi algorithm resurrect the original signal Download And Try It Save  HYPERLINK "http://www.peterhoward42.pwp.blueyonder.co.uk/ViterbiDemoInstaller.zip" this zip file anywhere you like, and double click on 'setup.exe' inside it. Nb. I should say this this is not a thoroughly tested and validated implementation. On a practical level, the demo corrupts 4 random bits in 15, and it manages to correct these about 90% of the time. Why Did I Write It? I came across the algorithm when I was working with a company called Elixent - now part of Panasonic. They were/are developing a revolutionary new kind of chip architecture for ultra low power devices that do lots of varied numerical processing - like phones and digital cameras, and Viterbi was one of the reference algorithms they used to test out the impact of new design ideas. I find algorithms as neat as this quite inspirational - in the way that some other people might be by say poetry - and I just want to have a go at playing around with it myself somehow. I had just been reading up on the C# language and .Net which were new to me, and this was the ideal toy hobby project to give myself a consolidation exercise on what I'd learned. Links  HYPERLINK "http://ieeexplore.ieee.org/search/wrapper.jsp?arnumber=1054010" Definitive reference (from Prof V himself - scary)  HYPERLINK "http://en.wikipedia.org/wiki/Viterbi_algorithm" Wikipedia reference to algorithm (still not exactly child's play)  HYPERLINK "http://home.netcom.com/%7Echip.f/viterbi/tutorial.html" The tutorial I managed to get the hang of it from.  HYPERLINK "http://www.electronicsweekly.com/Articles/2007/04/18/41191/matsushita-has-big-plans-for-uk-chip-technology.htm" Elixent / Panasonic's chip. Miscellany To lift a couple of quotes from the tutorial above ... In 2006, Viterbi was being used in around 1 Billion cell phones In 2006, Viterbi was decoding around 10 to the power 15 bits per second, every second of every day in digital TV receivers. That's a million-billion bits/second. Good job it doesn't get tired !     Viterbi Demo Application Page  PAGE 4 of  NUMPAGES 5 Peter Howard  HYPERLINK "mailto:peterhoward42@blueyonder.co.uk" peterhoward42@blueyonder.co.uk  HYPERLINK "http://peterhoward42.blogspot.com" http://peterhoward42.blogspot.com    *+-./?@ABCTUVmnop۾۪~nlel]elejU jU5CJOJQJaJmHnHsH j>*B*Uph0J j0JU0JCJj0JCJU 0J5^J0J!j0JB*CJU\aJphjK OJQJUV!j0J5B*CJUaJph0J5B*CJaJph 5CJ$\ 59CJ0\jUmHnHu$   %&'()*+,-.Un PP$xa$ $xx^xa$ $x^xa$#789:;<LMNhijklmnopհ՚jUj>*B*UphjUj>*B*Uphj U jUj>*B*Uph0J j0JU5CJOJQJaJmHnHsH ;nh = g & F(dd[$\$K   Eƀcf^ &   ^ `  <=>?@AFGHbcdefghijհ՚׉ j0JCJUaJmHnHujUjo>*B*UphjUju>*B*UphjU jU5CJOJQJaJmHnHsH 0J j0JUj{>*B*Uph3  < = \]^klz{|:;DE~uvCJaJmH sH CJaJ0Jj7FU jU CJOJPJQJ^JaJmH sH  jiU5\6]jUmHnHu mHnHu0JCJ0JCJaJmHnHu? ttz  ^ + & F ^ K   Eƀcf^ !"#01 + & F ^  !$a$    #12efgݹԩݹjeHCJUaJ mH sH 0JCJaJ mH sH jNGCJUaJ mH sH CJaJ mH sH jCJUaJ mH sH 5CJ aJ mH sH  mHnHu jUh+p,p-p.p1h/R / =!"#$%4567F'e$JFIFC    "$$"!!&+7.&(4)!!0A049:=>=%.CHCU`?V ѕ3a+ ˤV0(T+ eǠ< Vo6X`q enU|hxGBE$R.8@n?\"<Ҡ0MЈ@ @e VB1P@_"<"0 A00 A@@'BH`LR0`7+_BN4X74@H*,Z@/G<XTe)B% 0V5Q/ `i5LD<#,dR(AX*3@fACKtBI} "V+ 13V0ђR xt!FXEJDZ(gtxOQA aX A@vExeLPT̩@)XPa} h(tU U30 I ZEtvT"3t&ݐPCu%$@UE'BG?W(2XP~| ŽGr2UCt( P )@EIJVeI0#%LɀBOHteQPH ɐ7X7h3ŁeEQCǁ P%M~H 0&(P A"'H 7l(¡Q&siHPF F"L ]_HOa[7a( C(֐ v耥L -J2(x(Yg2Z(/00pf@P.I;d1(h-HTb4-, BvF@$8nX oPH *2Tt&x+*)\xeI 1t"."@@/  T(D5R+ '4 "Ȋ0E0ȕ '`(R*9戤J4,dUQI"+.ʝSP\PDhVP:}*5˸% 'lʺ5!! 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