Networking in Software Drawer barcode code 128 in Software Networking bar code for .NET

Networking generate, create none none for none projectscreating pdf-417 Figure 8.20 Relays with dista none for none nce loss. Example 8.

13 Relays with fourth power distance loss Suppose all nodes have equal transmitted power, and all receivers experience equal noise power, but that signal power decays as the fourth power of distance. Suppose three nodes are aligned as shown in Figure 8.20.

How can this relay problem be reformulated as above, and for what distance of the relay node from the sender does C C(P/N1) Solution The capacities are functions of SNRs. Thus an attenuation proportional to d 4 has the same effect as increasing the noise by d 4. Hence, in the previous terms N1 N2 d 4N, while 4 4 N1 d1 N.

The requirement is P/N2 > P/N1, i.e., N1 > N2.

Substituting, d1 > d 4 =2, i.e., d1 > 0.

84d . That is, capacity is not limited by the first link only when the relay is very close to the receiver node. It may be observed that this is not a very realistic result, because the additive noise mechanism in the original model was conceived more to be able to solve the problem than on physical grounds.

More naturally, the noise at the receiver does not in any way depend on the noise at the relay, so that Y X X1 Z2 and Y1 X Z1. The capacity in this formulation can be overestimated by assuming the relay can produce an exact copy of the transmitted stream which it then adds coherently to the incoming waveform, so long as the overall capacity is less than C(P/N1). (If not, the relay would be generating copies at a rate higher than it could reliably receive them.

) Here it is more convenient to think of the noise as constant power and that the desired signal attenuates. Thus the signal amplitude for the second link drops by (d d1)2, while the direct path to the end-user experiences an amplitude attenuation of d2. Summing, the amplitude is then multiplied by the factor d 2 d d1 2 d 2 d d1 2 ;.

MS Excel while the amplitude of the si gnal sent to the relay is multiplied by 1=d2 . Equating the two 1 amplitudes, d1 is just a little less than half of d for the first link to limit capacity. With this geometry, almost all the signal at the receiver originated at the relay node.

Thus, an estimate of capacity as the minimum of that of the sender to relay and relay to receiver is not a bad approximation when the relay is closer to the receiver than the sender. However, if the relay moves closer to the sender, combining of signals becomes an increasingly advantageous strategy compared with conventional packet retransmission, even though the overall capacity is maximum when the relay is about half-way to the receiver..

Network lossless source codin none for none g In dense sensor networks, it is quite likely that the measurements from nearby sensors are correlated. It is thus of interest what the minimum rate to convey this information is. Suppose there are two sources X and Y with joint distribution p(x,y).

Clearly, a minimum rate of H(X,Y) is required for joint encoding. Remarkably, however, if this joint distribution is known at the receiver then by the Slepian Wolf Encoding. 8.6 Network information theory 4 6 3 5 2. Figure 8.21 Correlated source transport problem. Theorem the two sources can b none for none e encoded independently with the same aggregate rate. Thus, while independent coding would need H(X) H(Y), the actual constraints with joint decoding are R1 ! H XjY ; R2 ! H YjX ; R1 R2 ! H X; Y : The transmission scheme is to quantize X into bins at rate R1, so that typical set members are distinguishable. This requires rate H(X).

Similarly, Y is sent with bins at rate R2 so that the binned sums are jointly typical. This requires a rate of at least H(Y. X) so that the total rate is H(X,Y). The practical difficulty, of course, is that the joint distribution is usually not known, and so adaptive methods are required. Scalability of sensor networks Collectively, the five types of network information theory problems just considered illustrate that traditional approaches that separate signal processing and networking and attempt to isolate signals from the various links do not actually lead to minimum energy solutions (however much they may ease network management).

A broader set of approaches is thus suggested. However distant the solution may appear, the remarkable success of practical source and channel coding methods in approaching fundamental limits provides motivation for further research in the network domain. Each of the five classic problems arises in network communications in complicated combinations.

To illustrate, suppose two sources are attempting to send information to some end-user through a multihop network, as illustrated in Figure 8.21. A source generates signals that are measured at nodes 1 and 2.

These signals are correlated. Node 1 could directly communicate with node 6, but with a given energy budget will do better by using nodes 3 and 4 as relays. The transmission to these nodes in part takes the form of a broadcast where it is not clear that exactly the same information should be sent to each node.

Node 2 must use either node 3 or 5 as a relay. Nodes 3 and 6 potentially experience multiple access interference. Node 3 also provides the possibility of some feedback to node 2 to limit its rate to exploit source correlation with node 1.

Alternatively, the information on paths 3 to 6 and 5 to 6 could be reduced, based on the information already forwarded. Thus, there are already many. (8:10).
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