(b) Find the transinformation of the channel below:0101P(Y)-[0.25 0.25 0.5] and01P(Y/X)=0.1.1.9001 1t190

Answered: Find the transinformation of the…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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(b) Find the transinformation of the channel below:
01
01
P(Y)-[0.25 0.25 0.5] and
01
P(Y/X)=
0.
1.
1.
900
1 1t
190

Expert Solution

Step 1

For an information channel, transinformation is the average of mutual information. It is calculated by $I (X, Y) = \sum_{i = 1}^{n} \sum_{j = 1}^{m} P (X_{i}, Y_{j}) \log_{2} [\frac{P (Y_{j} | X_{i})}{P (Y_{j})}]$ .

The transinformation can also be calculated using the entropies. The formula in terms of entropies is $I (X, Y) = H (Y) - H (Y | X)$ where $H (Y) = - \sum_{j = 1}^{m} P (Y_{j}) \log_{2} P (Y_{j})$ is the marginal entropy and $H (Y | X) = \sum_{i = 1}^{n} \sum_{j = 1}^{m} P (X_{i}, Y_{j}) \log_{2} P (Y_{j} | X_{i})$ is the conditional entropy.

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