Question

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 receiver finds it out since the sender forced the sum to be an even number. Find the probability that the received message has errors, but the receiver does not detect it, in terms of n and p. If for p=0.1, this probability is equal to (1+(a^n))/2−b^n, what is the value of a+b?

Answer #1

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...

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].

(1) Consider a noisy wireless channel which flips each bit ( 0
becomes 1 or 1 becomes 0 ) with probability p. To guarantee the
information is received reliably, each bit is transmitted m times
(called repetition coding). For example, if m = 3 and “0” needs to
be sent, you transmit “000” instead of “0”.
(1)
Consideranoisywirelesschannelwhichflipseachbit(0becomes1or1becomes0)withprobabilityp.
To guarantee the information is received reliably, each bit is
transmitted m times (called repetition coding). For example, if m =
3...

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...

Question 1 In communications let p denote the probability that a
bit sent by the transmitter will be received erroneously on the
other end of the channel. A telecom company has determined that for
a communication channel an error rate of p > 0.05 is
unacceptable. To perform the test, a predetermined 32 bit long
message is sent (this is a sample with n = 32) and the number of
erroneous bits are counted at the receiving end. The number...

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...

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