Q2. Consider a transmission system that operates according to the modified stop-and-wait ARQ protocol. Assume that a frame consists of N blocks and each block has size of m bits. Each bit may experience transmission error independently with probability p while ACKs are received error free. In the first trial, the transmitter transmits all the N blocks of the frame and the receiver accepts error free blocks. The blocks in error are retransmitted in the second trial, again the receiver accepts the error free blocks. The trials continue until all the blocks of the frame are received error free. Determine,
i) Probability that a block will be received error free on a trial.
ii) Probability that a block will be received error free on the j'th trial.
iii) Probability that by the end of n'th trial, k of the N blocks will be received error free.?
Q3. Let us consider a system that operates according to Go-Back-N ARQ protocol. Assume that the transmitter has unlimited supply of frames that need to be transmitted. Probability that a frame will be received in error in any transmission is given by and ACK transmissions are error free. Determine probability that a frame will be accepted by the receiver in its first transmission ( Justify your result).
Q4. Let us consider the detection of the framing bit in the T1 carrier by the receiver. Assume that the data bits in a frame assume values of 1 and 0 with equal probabilities of 0.5 and independent of each other. The framing bit alternates between 1 and 0 values.
i) Determine probability distribution of the number of trials that it will take for the receiver to determine that tested bit is not the frame bit ( Show your work).
ii) When a tested bit fails the receiver starts testing the bit in the position next to the failed bit as in part i). Determine the probability distribution of the number of times that the test in part i) will be repeated until the framing bit is determined.