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ps3_ee550_fall08

# ps3_ee550_fall08 - UNIVERSITY OF SOUTHERN CALIFORNIA FALL...

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UNIVERSITY OF SOUTHERN CALIFORNIA, FALL 2008 1 EE 550: Problem Set # 3 Due: Wednesday Sept. 24, 2008 I. B OOK P ROBLEMS Book Problem 2 . 16 , 2 . 18 , 2 . 19 , 2 . 20 , and 2 . 21 . II. P ROOFS OF C ORRECTNESS Consider a modified version of Go-Back-n, as follows: The receiver keeps RN ( t ) values as before, but in order to reduce power expenditure at the receiver, it only transmits requests when the RN requested value is a multiple of k for some integer k . (That is, it transmits requests only for RN ( t ) ∈ { 0 , k, 2 k, 3 k, 4 k, . . . } ). The sender does the same algorithm as before, but ensures that it repeatedly, and in order, transmits: { SN min ( t ) , SN min ( t ) + 1 , . . . , SN min ( t ) + n - 1 } . It then goes back and repeats the same order, and so on, until it receives an error-free RN message requesting something larger than SN min ( t ) . a) Show that SN min ( t ) RN ( t ) SN min ( t ) + n . b) Prove that the algorithm is correct if k = n . Hint: To prove liveness, suppose that RN = i at a particular time t . Show that RN increases after a finite amount of time.
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