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single, very complicated, code, would require prohibitive computational effort. It is here that turbo codes show their great advantage: it is possible to decode two constituent codes separately, and then combine the information from these two decoders. Turbo codes are decoded iteratively, employing the exchange of soft information between constituent decoders. Figure 14.18 shows a block diagram of a turbo decoder. It consists of two Soft Input Soft Output (SISO) decoders for the constituent codes, an interleaver, and a de-interleaver. The SISO decoder puts out not only the various bits, but also the con dence it has in a speci c decision. This con dence is described by the LLR which can be computed by a Viterbi-like algorithm, suggested by Bahl et al. [1974] and known as the BCJR algorithm. The LLR is (see Eq. (14.48)) log Pr(bi = +1|r) Pr(bi = 1|r)
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of taps that can be implemented in a practical Rake combiner is limited by power consumption, design complexity, and channel estimation. A Rake receiver that processes only a subset of the available Lr resolved MPCs achieves lower complexity, while still providing a performance that is better than that of a single-path receiver. The Selective Rake (SRake) receiver selects the Lb best paths (a subset of the Lr available resolved MPCs) and then combines the selected subset using maximum-ratio combining. This combining method is hybrid selection: maximum ratio combining (as discussed in 13); however, note that the average power in the different diversity branches is different. It is also noteworthy that the SRake still requires knowledge of the instantaneous values of all MPCs so that it can perform appropriate selection. Another possibility is the Partial Rake (PRake), which uses the rst Lf MPCs. Although the performance it provides is not as good, it only needs to estimate Lf MPCs. Another generally important problem for Rake receivers is interpath interference. Paths that have delay i compared with the delay the Rake nger is tuned to are suppressed by a factor ACF( i )/ACF(0), which is in nite only when the spreading sequence has ideal ACF properties. Rake receivers with nonideal spreading sequences thus suffer from interpath interference. Finally, we note that in order for the Rake receiver to be optimal there must be no ISI i.e., the maximum excess delay of the channel must be much smaller than TS , though it can be larger than TC . If there is ISI, then the receiver must have an equalizer (working on the Rake output i.e., a signal sampled at intervals TS ) in addition to the Rake receiver. An alternative to this combination of Rake receiver and symbol-spaced equalizer is the chip-based equalizer, where an equalizer works directly on the output of the despreader sampled at the chip rate. This method is optimum, but very complex. As we showed in 16, the computational effort for equalizers increases quickly as the product of sampling frequency and channel delay spread increases.
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where Phit is the probability of having the same frequency for both 802.11 and Bluetooth. The probability of collision is given by Pcollision = 1 Psurvive . For a 1000-byte 802.11 packet at 2 Mb/s, LIE = 1000(bytes) 8(bits/byte) = 4 ms 2(Mb/s)
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Let's get down to creating multithreaded applications. Threading is handled through the System.Threading namespace. The core members of the Thread class that you will use are listed in Table 15-1. Table 15-1: Common Thread Class Members Member CurrentContext Description Returns the current context the thread is executing on. Gets the CultureInfo instance that represents the culture used by the current thread. Gets the CultureInfo instance that represents the current culture used by the ResourceManager to look up culturespecific resources at run time. Gets and sets the thread's current principal (for rolebased security). Returns a reference to the currently running thread. Resets an abort request. Suspends the current thread for a specified time. Gets or sets the apartment state of the thread. Gets a value that indicates whether the thread has been started and is not dead. Gets or sets a value indicating whether the thread is a background thread.
Figure 1.1 Average profit is less than the profit associated with average demand.
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In fading channels, the received signal power (and thus the SNR) is not constant but changes as the fading of the channel changes. In many cases, we are interested in the BER in a fading channel averaged over the different fading states. For a mathematical computation of the BER in such a channel, we have to proceed in three steps: 1. Determine the BER for any arbitrary SNR. 2. Determine the probability that a certain SNR occurs in the channel in other words, determine the pdf of the power gain of the channel. 3. Average the BER over the distribution of SNRs. In an AWGN channel, the BER decreases approximately exponentially as the SNR increases: for binary modulation formats, a 10-dB SNR is suf cient to give a BER on the order of 10 4 , for 15 dB the BER is below 10 8 . In contrast, we will see below that in a fading channel the BER decreases only linearly with the (average) SNR. At rst glance, this is astonishing: sometimes fading leads to high SNRs, sometimes it leads to low SNRs, and it could be assumed that high and low values would compensate for each other. The important point here is that the relationship between (instantaneous) BER and (instantaneous) SNR is highly nonlinear, so that the cases of low SNR essentially determine the overall BER. Example 12.3 BER in a two-state fading channel. Consider the following simple example: a fading channel has an average SNR of 10 dB, where fading causes the SNR to be dB half of the time, while it is 13 dB the rest of the time. The BERs corresponding to the two channel states are 0.5 and 10 9 respectively (assuming antipodal modulation with differential detection). The mean BER is then BER = 0.5 0.5 + 0.5 10 9 = 0.25. For an AWGN channel with a 10-dB SNR, the BER is 2 10 5 . Following this intuitive explanation, we now turn to the mathematical details of the abovementioned three-step procedure. Step 1, the determination of the BER of an arbitrary given SNR, was treated in Section 12.1. Point 2 requires computation of the SNR distribution. In 5, we mostly concentrated on the distribution of amplitude r = |r(t)|. This has to be converted to distribution of (instantaneous) received power Pinst = r 2 . Such a transformation can be done by
Figure 43-2: Give the user a name in this dialog box. 4. Give the user a name- such as Jdoe. You can provide his full name and description. 5. Give the user a password and uncheck the User must change password at next logon check box. This is just a test on your partbut it's best to force the user to do this when you create a real user in the system. 6. Once you've filled in all the necessary information- click Create. Your user now appears in the list of users in the Computer Management utility.
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