Information Theory for Electrical Engineers by Orhan Gazi

Author:Orhan Gazi
Language: eng
Format: epub, pdf
Publisher: Springer Singapore, Singapore

Exercise

For the communication channel show in Fig. 2.23, show that it is not possible to have uniform distribution at the output of the communication channel.

Fig. 2.23Discrete communication channel for exercise

Example 2.27

Find the channel capacity of the discrete memoryless channel shown in Fig. 2.24.

Fig. 2.24Discrete communication channel for Example 2.27

Solution 2.27

Let the input distribution be given as

First, let’s calculate the mutual information

(2.95)

in terms of the variable and then try to optimize the mutual information considering the parameter. The conditional entropy in (2.95) can be calculated using

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