Problem 14
A 12-bit Hamming code whose hexadecimal value is \(0 \mathrm{xE} 4 \mathrm{~F}\) arrives at a receiver. What was the original value in hexadecimal? Assume that not more than 1 bit is in error.
Problem 15
One way of detecting errors is to transmit data as a block of \(n\) rows of \(k\) bits per row and add parity bits to each row and each column. The bit in the lower-right corner is a parity bit that checks its row and its column. Will this scheme detect all single errors? Double errors? Triple errors? Show that this scheme cannot detect some four-bit errors.
Problem 19
Suppose that a message 1001110010100011 is transmitted using the Internet Checksum (4-bit word). What is the value of the checksum?
Problem 20
What is the remainder obtained by dividing \(x^{7}+x^{5}+1\) by the generator polynomial \(x^{3}+1 ?\)
Problem 21
A bit stream 10011101 is transmitted using the standard CRC method described in the text. The generator polynomial is \(x^{3}+1\). Show the actual bit string transmitted. Suppose that the third bit from the left is inverted during transmission. Show that this error is detected at the receiver's end. Give an example of bit errors in the bit string transmitted that will not be detected by the receiver.
Problem 22
A 1024-bit message is sent that contains 992 data bits and 32 CRC bits. CRC is computed using the IEEE 802 standardized, 32-degree CRC polynomial. For each of the following, explain whether the errors during message transmission will be detected by the receiver: (a) There was a single-bit error. (b) There were two isolated bit errors. (c) There were 18 isolated bit errors. (d) There were 47 isolated bit errors. (e) There was a 24-bit long burst error. (f) There was a 35 -bit long burst error.
Problem 23
In the discussion of ARQ protocol in Section 3.3.3, a scenario was outlined that resulted in the receiver accepting two copies of the same frame due to a loss of acknowledgement frame. Is it possible that a receiver may accept multiple copies of the same frame when none of the frames (message or acknowledgement) are lost?
Problem 24
A channel has a bit rate of \(4 \mathrm{kbps}\) and a propagation delay of \(20 \mathrm{msec}\). For what range of frame sizes does stop-and-wait give an efficiency of at least \(50 \%\) ?
Problem 27
Imagine a sliding window protocol using so many bits for sequence numbers that wraparound never occurs. What relations must hold among the four window edges and the window size, which is constant and the same for both the sender and the receiver?
Problem 29
In protocol 6 , when a data frame arrives, a check is made to see if the sequence number differs from the one expected and no_nak is true. If both conditions hold, a NAK is sent. Otherwise, the auxiliary timer is started. Suppose that the else clause were omitted. Would this change affect the protocol's correctness?
