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Hence, if R > C, the error probability is bounded away from 0. As a result of the random coding proof, we can see that good codes are actually very easy to nd. For instance, we can randomly generate the M codewords to form a random codebook. We reveal this randomly generated codebook realization to the receiver so that the receiver can employ typical sequence decoding as illustrated in the proof. The random codebook argument presented above shows that there is a high chance that this randomly generated codebook is indeed a good code (or capacity achieving code). However, in practice, the problem lies in the receiving side. If our receiver has in nite processing power enabling us to exhaustively search in the decoding process, then there is almost no need for any code design at the transmitter. Because of limited processing power at the receiver, we have to create some arti cial structures in the channel encoder to facilitate simple decoding at the receiver. For example, we have various types of codes such as block codes, trellis codes, and turbo codes in the literature. Once these arti cial structures are added, good codes that can achieve the Shannon capacity are much harder to nd. Yet, the channel coding theorem offers a tight upper bound on the maximum achievable rate so that we know how far we are from the best possible performance when we design practical codes.

stack Adaptor for the sequential containers that yields a type that lets us add and remove elements from one end only

vector Sequential container Elements in a vector are accessed by their positional index We C++ to a vector by calling push_back or insert Adding elements to a vector add elements Primer, Fourth Edition By it be B Lippman,Jos e Lajoie, might causeStanley reallocated, invalidating all iterators into the vector Adding (or removing)Barbara E Moo in the middle of a vector invalidates all iterators to elements an element after the insertion (or deletion) point

Publisher:Addison Wesley Professional Pub Date: February 14, 2005 Print ISBN: 0-201-72148-1 Pages: 912

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If you ve chosen an unusual housing, you ll probably need to create a port of some kind for your speaker to sound through. Let s look at a few possibilities. If the speaker is really small (up to 1.5 inches), you can enlarge a hole using your hand bore set. Bring the hole up to an inch or so across. Next, glue a grill cloth or fine metal screen to the speaker and trim off any excess (see Figure 11-22).

In this section, we try to illustrate the concept of channel capacity by looking at several examples in wireless channels. We shall focus on some simple channels here. More sophisticated channels (such as the nite-state channels) will be discussed in detail in 2. In general, there is no closed-form expression for channel capacity except for a few special cases. Discrete Memoryless Channels. Real-world channels are continuous-time with continuous-time input and continuous output. From Section 1.3, we established the equivalence between continuous-time and discrete-time channels. Hence, without loss of generality, we assume a discrete-time channel model with channel input X X and channel output Y Y. In general, the channel input X and the channel output Y are continuous complex numbers. However, if we consider a superchannel including a M-ary digital modulator, a memoryless physical channel, and a digital demodulator with Q quantization levels, we have a M-input, Q-output discrete memoryless channel as illustrated in Figure 1.18. The M Q discrete memoryless channel is speci ed by the channel transition matrix p(y|x):

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