1)
a) Consider an error detection/correction code with a minimum Hamming distance dmin.
When the code is operating in the error detection mode, it can detect up to 5 bit errors.
Calculate the minimum Hamming distance of this code.
b) How many bits can be corrected by the code of part (a) when it is operating in the error
correction mode?
c) If the minimum Hamming distance of the code in part (a) is decreased by 1, will the
number of bits that the code can correct in the error correction mode become smaller than the
answer obtained in part (b)?
d) If the minimum Hamming distance of the code in part (a) is increased by 1, will the
number of bits that the code can correct in the error correction mode become larger than the
answer obtained in part (b)?
2)
a) A cyclic code uses the 5-bit CRC divisor 1 0 1 1 1. The receiver received the 10-bit
codeword 1 0 0 1 1 1 0 0 0 1. Describe the action taken by the receiver, i.e., indicate whether
the receiver accepts or rejects this codeword. Support your answer by showing the details of
your work either using polynomials or using Modulo-2 division. Also give the binary
representation of the syndrome using the correct (exact) number of bits.
b) A cyclic code uses the 4-bit CRC divisor 1 0 0 1. A codeword of length 7 bits was
transmitted and suffered two bit errors in the most significant bit and least significant bit of
the 7-bit codeword. Give the error polynomial for this type of error and indicate if the
receiver can always detect this type of error or is not guaranteed to detect this type of error.
Show the details of your work.
3)
In the checksum error detection method, the sender wants to send the four data values 31, 16,
39 and 40. Each of the four values is encoded in 6 bits (for example, 31 is encoded as
011111 and 39 is encodes as 100111). Compute the value of the checksum to be transmitted
by the sender with these four data values. Support your answer by showing the details of the
checksum computation at the sender site.
4)
Consider a Stop-and-Wait ARQ protocol that uses a retransmission time-out period of 20
milliseconds. The round trip time between the sender and receiver is 8 milliseconds. The
sender sent two frames to the receiver. The transmission time of each frame is 2
milliseconds. The length of the ACK frames and the processing delays are small and can be
ignored. Assume that the first frame was transmitted without errors in the first attempt of
transmission. The second frame suffered bit errors in the first attempt of transmission and
was transmitted without errors in the second attempt of transmission.
a) Calculate the link utilization for the transmission of the two frames.
b) Repeat part (a) for the case when the first frame was transmitted without any errors but the
second frame suffered bit errors in the first three attempts of transmission and was
transmitted without errors in the fourth attempt of transmission.
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