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problem is to find the best path, or shortest path, in an oriented graph To make sense the path length should be defined Each path on the trellis represents a code sequence c, that corresponds to an information sequence I by the relation c = I*G(D) Notice that this relation can be memorized implicitly in the trellis, and the encoding is not necessary in the Viterbi decoding There is a "1-to-1" correspondence between I, c, and the trellis path The received sequence r is quantized and fed into the decoder The optimum decoding is performed under the maximum likelihood criterion: To find I* such that Pr{r/I*} = Max Pr{r/I} Pr{r/I} 1 holds always Over an AWGN channel, the positive quantity log Pr{r/I} is defined as the path length.

(4.31)

k =3 3

Since the channel is memoryless, log Pr{r/I} = log Pr{rj/Ij}, the criterion has thus the following equivalent form: To find I* such that log Pr{r/I*} = Min Pr{r/I}, or To find I* such that log Pr{r/I*} = Min log Pr{rj/Ij} This is equivalent to: To find c* such that log Pr{r/c*} = Min log Pr{rj/cj} From the received sequence r and each code sequence c, a path metric can be further defined for an AWGN channel Note that log Pr{rj/cj} = log (2 ) ||rj cj||2, the path length is now ||rj cj||2, that is just the Euclidean distance between r and c This is why the maximum likelihood decoding is to find the code sequence, or the corresponding trellis path, that is the closest to the received sequence in Euclidean distance.

Rx data Rx clock (Rx TDMA clock)

The criterion is still expressed as: To find c* such that log Pr{r/c*} = Min ||rj cj||2 The Viterbi algorithm solves this problem by applying the dynamic programming principle that assures the global optimality with local optimum decisions The local decisions reduce the computation efforts on the trellis In practice, much simpler integer metrics quantized to 3-bit are used, see [Ref 3-10] and [Ref 3-17] Roughly speaking, to find the shortest path among the 2rL ones, r being the code rate, L the sequence length, 2rL path metrics are to be evaluated and compared, if a brute-force method is used In the Viterbi algorithm (VA), much less calculation effort is necessary From the first trellis section to the L-th one, the VA progresses section by section.

So which IDE is better Well, both NetBeans and Eclipse have their strengths and weaknesses. Eclipse is a solid product and works well even on slow hardware. Eclipse looks and feels like any other native application in Windows or Linux. But Eclipse is lacking a number of useful features out of the box, which must be added in by installing and configuring plug-ins. On a fast enough machine, NetBeans slower user interface is not bothersome. But the feature set built into NetBeans is clearly more complete than the default features currently offered by Eclipse. NetBeans also provides a plug-in capability allowing it to be extended like Eclipse. However, NetBeans provides tools to automate the installation of the plug-ins within the NetBeans environment, making even this process easier than Eclipse. NetBeans is clearly a more mature product than Eclipse at this time. NetBeans also supports a broader variety of hardware and operating system platforms than Eclipse does at this time. The bottom line here is that both IDEs are excellent products, so the decision depends on platform compatibility for the platform you must use and your own personal preferences.

tup=( sdsd ,23) apply(ruf,tup)

=A1*0.03937007874

At each node, it takes a local decision by eliminating one of the two paths merged to it by taking the one having the shorter path length Each time a binary comparison is made, 1/2 paths have been eliminated in the future Once the L-th section is reached, the VA decoder begins to deliver a bit decision At the L-th section, it gives the 1st bit decision Then, it progresses on the trellis by one section, making the decision of the (t L)-th bit at the instant t In the decoder path memory, only L sections are stored All the information stored for the sections preceding t L sections are discarded This is called truncated memory Viterbi decoding, that is implementable in practice..

8

3. At the prompt Enter data:, enter:

F ESA: ESC: ETSI: European Space Agency Engineering service circuits. European Telecommunications Standards Institute.

=AVERAGE(Budget.xls!MonthlySales)

APS30A: BSS(FL) Plan/R1&2&3

The following formula returns the sum of the single-cell arguments: