Consider a binary symmetric communication channel, whose input source is thealphabet X = {0,1} with probabilities (0.5,0.5); whose output alphabet is Y = {0,1}:and whose channel matrix is%3D1-€1-where e is the probability of transmission error.f 1. What is the entropy of the source, H(.X)?2. What is the probability distribution of the outputs, p(Y), and the entropy of this out-put distribution, H(Y)?

(1) The entropy of the source is 1 bit.

Consider a binary symmetric communication channel, whose input source is the alphabet X = {0.1} with probabilities (0.5,0.5): whose output alphabet is Y = {0,1}: and whose channel matrix is %3D 1-€ where e is the probability of transmission error. 1. What is the entropy of the source, H(.X)? 2. What is the probability distribution of the outputs, p(Y), and the entropy of this out- put distribution, H(Y)?

Consider a binary symmetric communication channel, whose input source is the alphabet X = {0.1} with probabilities (0.5,0.5): whose output alphabet is Y = {0,1}: and whose channel matrix is %3D 1-€ where e is the probability of transmission error. 1. What is the entropy of the source, H(.X)? 2. What is the probability distribution of the outputs, p(Y), and the entropy of this out- put distribution, H(Y)?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

Consider a binary symmetric communication channel, whose input source is the
alphabet X = {0,1} with probabilities (0.5,0.5); whose output alphabet is Y = {0,1}:
and whose channel matrix is
%3D
1-€
1-
where e is the probability of transmission error.
f 1. What is the entropy of the source, H(.X)?
2. What is the probability distribution of the outputs, p(Y), and the entropy of this out-
put distribution, H(Y)?

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