Question

A binary communication channel transmits a sequence of "bits" (0s and 1s). Suppose that for any particular bit transmitted, there is a 15% chance of a transmission error (a 0 becoming a 1 or a 1 becoming a 0). Assume that bit errors occur independently of one another. (Round your answers to four decimal places.)

(a)

Consider transmitting 1000 bits. What is the approximate probability that at most 165 transmission errors occur?

(b)

Suppose the same 1000-bit message is sent two different times independently of one another. What is the approximate probability that the number of errors in the first transmission is within 60 of the number of errors in the second?

Answer #1

a)

here for expected number of errors =np=1000*0.15=150

and std deviation =sqrT(np(1-p))=11.29

hence from normal approximation and continuity correction probability that at most 165 transmission errors occur

=P(X<=165)=P(Z<(165.5-150)/11.29)=P(Z<1.37)=0.9147

b)

here let number of error in first and second message are X1 and X2

hence expected difference in errors =E(X1-X2)=E(X1)-E(X2)=150-150=0

and std deviation
=SD(X1-X2)=(11.29^{2}+11.26^{2})^{1/2}
=15.969

hence P(number of errors are within 60)=P(-60<X<60)=P(-59.5/15.969<Z<59.5/15.969)

=P(-3.73<Z<3.73)=0.9999-0.0001=0.9998

In a binary communication channel, 0s and 1s are transmitted
with equal probability. The probability that a 0 is correctly
received (as a 0) is 0.99. The probability that a 1 is correctly
received (as a 1) is 0.90. Suppose we receive a 1, what is the
probability that, in fact, a 0 was sent?
How to apply bayes rule?

Consider asymmetric binary communication channels
specified by conditional probability P[1r|0s]=0.03 and
P[0r|1s]=0.02. The prior probability of transmitting binary number
1 is given by P[1s]=0.56. It now transmits 25 bits of binary
information over this channel. What is the probability of an error
below 3 bits?

Given that the probability of error in the transmission of a bit
over a communication channel is p=10e-4
a) Compute the probability of error in transmitting a block of
1024 bits
b) What is the probability of more than three errors in
transmitting a block
of 1000 bits?
c) If a message is not transmitted correctly, a retransmission
is initiated.
This procedure is repeated until a correct transmission occurs.
Such a channel is often called a feedback channel. Assuming that...

Exercise 5.6.4: Error-correcting codes and the probability of
transmitting a message without errors
(a) A communication channel flips each transmitted bit with
probability 0.02. The event that one bit is flipped is independent
of the event that any other subset of the bits is flipped.
A 100-bit message is sent across the communication channel and
an error-correcting scheme is used that can correct up to three
errors but expands the length of the message to 110 bits. What is
the...

In a digital communication channel, assume that the number of
bits received in error can be modeled by a binomial random
variable. The probability that a bit is received in error is 0.1.
A) If 50 bits are transmitted, what is the probability that 2 or
fewer errors occur? ( Round your answer to 3 decimal places) B) If
50 bits are transmitted, what is the probability that more than 8
errors occur? ( Round your answer to 5 decimal...

When transmitting bits over a wireless transmission channel, the
probability of bit error is p=1/2 (The occurrence of bit errors is
independent.)
RV X is referred to as the number of errors in bit
transmission,
S100 is the total number of error bits when sending 100
bits.
Find a probability of [40<=S100<=60].

When transmitting bits over a wireless transmission channel, the
probability of bit error is p=1/2 (The occurrence of bit errors is
independent.)
RV X is referred to as the number of errors in bit
transmission,
S10 is the total number of error bits when sending 10 bits.
Find E[X], VAR[X], E[S10], and VAR[S10].

Consider a noisy communication channel, where each bit is
flipped with probability p (the probability that a bit is sent in
error is p). Assume that n−1 bits, b1,b2,⋯,b(n−1), are going to be
sent on this channel. A parity check bit is added to these bits so
that the sum b1+b2+⋯+bn is an even number. This way, the receiver
can distinguish occurrence of odd number of errors, that is, if
one, three, or any odd number of errors occur, the...

In a communication system, information bits are transmitted from
source to destination. However, due to the ambient white Gaussian
noise in the communication channel, an information bit may be
received erroneously by the time it arrives at the destination.
Assume that the information bits are transmitted independently, and
let p denote the bit error probability with pϵ(0; 1). Suppose a
total of N bits are transmitted from the source to the destination,
and let WN denote the total number of...

A binary message m, where m is equal either to 0 or to 1, is
sent over an information channel. Assume that if m = 0, the value s
= −1.5 is sent, and if m = 1, the value s = 1.5 is sent. The value
received is X, where X = s + E, and E ∼ N(0, 0.66). If X ≤ 0.5,
then the receiver concludes that m = 0, and if X > 0.5, then the...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 13 minutes ago

asked 23 minutes ago

asked 35 minutes ago

asked 35 minutes ago

asked 47 minutes ago

asked 53 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago