hw2 - EE 284 F Tobagi Autumn 2010-2011 EE284 Homework...

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EE 284 F. Tobagi Autumn 2010-2011 EE284 Homework Assignment No. 2 Topics: Error Detection Handed out: 28 September, 2010 Due: 5 October, 2010 ALL WORK MUST BE SHOWN TO RECEIVE FULL CREDIT Problem 1: Error Correction vs Error Detection (8 points) We consider a data link between two devices, A and B, connected by a channel of data rate W bits/sec, and one-way propagation delay of τ sec. Data frames are to be transmitted from device A to device B. All data frames are D bits long (data+header). We wish to compare two error recovery mechanisms at our disposal: (i) an error correction mechanism and (ii) an error detection mechanism, specified as follows: (i) In the error correction mechanism, α redundancy bits are added to each data frame, so that the receiver can reliably correct any bit error pattern that can occur on the channel. (ii) In the error detection and retransmission mechanism, a checksum of β bits is added to each frame. Sender A sends one frame at a time and waits for a response from B. If B receives the frame correctly, it transmits back an ACK control frame; otherwise, it transmits back to A a NACK control frame. If A receives an ACK, it proceeds with the transmission of the next frame. If A receives a NACK, it retransmits the same frame. The number of bits in the control frames (ACK or NACK) is c bits. We assume that the control frames (ACKs or NACKs) are always free of errors. Also, we consider that A has an infinite number of frames to be transmitted to B and we assume that the frame transmission errors are independent and let p denote the probability that a frame transmitted on the channel is in error.
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