Homework Help is Here – Start Your Trial Now!
Engineering
Electrical Engineering
(a) What is the overall capacity for a cascade of 3 independent binary symmetric channels? Express your answer as a decimal with 5 digits of precision. (b) What is the overall capacity for a cascade of 4 independent binary symmetric channels? Express your answer as a decimal with 5 digits of precision.

(a) What is the overall capacity for a cascade of 3 independent binary symmetric channels? Express your answer as a decimal with 5 digits of precision. (b) What is the overall capacity for a cascade of 4 independent binary symmetric channels? Express your answer as a decimal with 5 digits of precision.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
See similar textbooks
icon
Related questions
Question

Please help with this question

The following binary symmetric channel has a capacity of C = 1 + 0.1 log₂ 0.1 + 0.9 log₂ 0.9 0.53100 bits per channel use. input bit input bit 1 1 0 0.1 0.1 1 However, if we must go through a cascade of such channels, we reduce the overall capacity to carry information. For example, if we have two such channels in series, with independent probabilities of bits flipping (or not flipping), we can view this as one overall binary symmetric channel: 0.1 0.1 0.9 0.9 0.9 two cascaded binary symmetric channels 0.9 0.9 0.1 0.1 2.0.9 0.1 0.18 2.0.9 0.1 0.18 0.9² +0.1² = 0.82 0 0.9² +0.1² 0.82 = 1 0.9 one overall binary symmetric channel 0 1 0 1 output bit output bit The overall binary symmetric channel has a capacity of only 1+0.18 log₂ 0.18+0.82 log2 0.82≈ 0.31992 bits per overall channel use. (a) What is the overall capacity for a cascade of 3 independent binary symmetric channels? Express your answer as a decimal with 5 digits of precision. (b) What is the overall capacity for a cascade of 4 independent binary symmetric channels? Express your answer as a decimal with 5 digits of precision.
Transcribed Image Text:The following binary symmetric channel has a capacity of C = 1 + 0.1 log₂ 0.1 + 0.9 log₂ 0.9 0.53100 bits per channel use. input bit input bit 1 1 0 0.1 0.1 1 However, if we must go through a cascade of such channels, we reduce the overall capacity to carry information. For example, if we have two such channels in series, with independent probabilities of bits flipping (or not flipping), we can view this as one overall binary symmetric channel: 0.1 0.1 0.9 0.9 0.9 two cascaded binary symmetric channels 0.9 0.9 0.1 0.1 2.0.9 0.1 0.18 2.0.9 0.1 0.18 0.9² +0.1² = 0.82 0 0.9² +0.1² 0.82 = 1 0.9 one overall binary symmetric channel 0 1 0 1 output bit output bit The overall binary symmetric channel has a capacity of only 1+0.18 log₂ 0.18+0.82 log2 0.82≈ 0.31992 bits per overall channel use. (a) What is the overall capacity for a cascade of 3 independent binary symmetric channels? Express your answer as a decimal with 5 digits of precision. (b) What is the overall capacity for a cascade of 4 independent binary symmetric channels? Express your answer as a decimal with 5 digits of precision.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 5 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
MOS logic circuit
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,
SEE MORE TEXTBOOKS