0FB149A0d01 - 6.441 Transmission of Information Mar 14,...

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Mar 14, 2006 Lecture 10 Lecturer: Madhu Sudan Scribe: Srujan Linga 1 Last lecture Universal Coding Lempel-Ziv Algorithm 2 Today Channel capacity Sample channels and their capacities AEP for channels 3 Communication System Overview The block diagram in Fig.1 shows an overview of the communication system. Figure 1 : Block diagram of the communication system The transfer of information from the transmitter to the receiver is a physical process and therefore is subject to noise and imperfections of the signalling process itself. Hence it is a property of physics that there are no perfect channels. A modified block diagram with an encoder and decoder introduced into the communication system is shown in Fig.2. Source symbols S from some finite alphabet Ω S are mapped into some sequence of channel symbols X of alphabet Ω X . The output sequence Y of the channel (input to the decoder) is random but has a distribution that depends on the input sequence X . From the output sequence, we attempt to recover the transmitted message. 3.1 Basic features of the channel Considering a block of n channel symbols, let 1. p X n ( x n ) denote the probability distribution on an n -element sequence from Ω X which is under the designer’s control. 2. p Y n | X n ( y n | x n ) denote the probability that y n is received given x n was transmitted. 3. P Y n | X n ( y n | x n ) denote an | Ω X | n ×| Ω Y | n stochastic probability transmission matrix of the channel. 10-1
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0FB149A0d01 - 6.441 Transmission of Information Mar 14,...

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