In a Binary Symmetric (Communication) Channel (BSC) data is sent data is sent using bits 0 and 1. When the source and the destination are far apart, there are repeaters that decode the bit and transmit generate a signal. However due to noise, there decoding error, i.e., there a probability α that a bit 0 will be decoded as (and hence transmitted) as 1. Similarly, β is the probability that a bit 1 will be decoded as (and hence transmitted as) 1. Let X0 be the bit’s initial parity and and let Xn be the bits parity after the nth repeater.1. Construct the one-step transition matrix for this Markov Chain. 2. Suppose the input stream to this communication channel consists of 80% 0s and 20% 1s. Determine the proportion of 0s and 1s after the first repeater. 3. Under the same input values as in (b) determine the proportions of 0s and 1s exiting the 5th relay.

In a Binary Symmetric (Communication) Channel (BSC) data is sent data is sent using bits 0 and 1. When the source and the destination are far apart, there are repeaters that decode the bit and transmit generate a signal. However due to noise, there decoding error, i.e., there a probability α that a bit 0 will be decoded as (and hence transmitted) as 1. Similarly, β is the probability that a bit 1 will be decoded as (and hence transmitted as) 1. Let X0 be the bit’s initial parity and and let Xn be the bits parity after the nth repeater.1. Construct the one-step transition matrix for this Markov Chain. 2. Suppose the input stream to this communication channel consists of 80% 0s and 20% 1s. Determine the proportion of 0s and 1s after the first repeater. 3. Under the same input values as in (b) determine the proportions of 0s and 1s exiting the 5th relay.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.7: Introduction To Coding Theory (optional)

Problem 7E

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