andswr parts a-d

3. [Automatic Repeat Request (ARQ)] The GPU A in a datacenter communicates with GPU B via a link. The link transmits data at a rate of r = 200 Gbps and makes independent bit errors with probability p = 10-3. To transmit data, GPU A constructs frames of length n = 1000-bits in which k = 950-bits are payload and n - k = 50 bits are cyclic redundancy check (CRC) bits to enable GPU B to detect frame errors defined as having at least one bit error in a frame. On detecting a frame error, GPU B sends a retransmission request (NCK) to GPU A, otherwise it sends an ACK. The round-trip delay from GPU A transmitting a frame and receiving an ACK/NCK for it is N = 10 frame duration long. In the following, let X = 1 (X = 0) if a frame is received correctly (in error). Let Y be the number of transmissions per frame. The presence of CRC and retransmissions reduces the effective data rate from r to k reff = rx - n EY] Now answer the following: (a) What is the probability of correct frame transmission Part = P{X = 1}? What type of an RV is X? (b) In ARQ1 protocol, GPU A keeps transmitting frames as the ACKs are received and retransmits only the frame for which it received a NCK. Derive an expression for the average number of transmissions per frame and the effective data rate reff in terms of r, n, k and p. (c) In ARQ2 protocol, GPU A retransmits not only the frame for which it received a NCK (lets call it frame i) but also the N -1 = 9 frames that were transmitted during the time between the first transmission of frame i and the reception of NCK. Derive an expression for the average number of retransmissions per frame and the effective data rate reff in terms of r, n, k, N, and p. (d) Both ARQ1 and ARQ2 protocols need to storage buffers in GPU A and GPU B in order to ensure that GPU A retransmits frames until received correctly by GPU B and GPU B is able to release the frames in order. Which of the two protocols do you think will need fewer buffers? Provide a qualitative answer with reasons