Question

17.2 Problem Compression - reliability tradeoff* In this question, we will examine the tradeoff between compression and error resilience through a back - of- the - envelope calculation. Suppose we have 15 frames to transmit and two possible GOP structures: (A) IPB and (B) IPBBB. Suppose an I frame costs 7 kB, a P frame costs 3 kB, and a B frame costs 1 kB If an entire GoP is not received correctly, we assume that the GoP must be sent again. As our metric of error resilience, consider the expected number of bits that must be retransmitted at least once, The probability of dropping a frame is 1% and assumed to be independent. (These assumptions are made to simplify this homework problem. In a P or B frame in a GoP is lost, the entire GoP does not need to be retransmitted. Loss is not independent and usually much less than 1%. And there should be many more frames.) (a) In case A, the video frame structure is IPB/IPB/IPB/ IPB/IPB. What is the total cost of the video in KB? What is the cost per GoP? (b] What is the probability than an entire GoP is transmitted successfully in case A? What is the expected number of GoPs that ere successful on the first transmission attempt of the entire video? What is the expected number of GoPs that must be retransmitted at least once? How much does the first

Answer 1

Given:

Type of frame	Cost (kB)
I	7
P	3
B	1

Probability of dropping a frame = 1% = 0.01

=> Probability of successfully transmitting a frame = 1 - (Probability of dropping a frame) = 1 - 0.01 = 0.99

Case A:

Video frame structure is IPB/IPB/IPB/IPB/IPB.

Number of GoPs in video = 5

(a) Total cost of video (in kB)

= Number of I-frames * I-frame cost + Number of P-frames * P-frame cost + Number of B-frames * B-frame cost

= 5 * 7 + 5 * 3 + 5 * 1

= 35 + 15 + 5

= 55 kB

Cost per GoP = Total cost of video / Number of GoPs in video = 55 / 5 = 11 kB

(b) Probability that an entire GoP (3 frames) is transmitted successfully

= 0.99 * 0.99 * 0.99

= 0.970299

= 97% (approx)

Expected number of GoPs that are successfull on the first transmission attempt of video

= Number of GoPs in video * Probability that an entire GoP is transmitted successfully

= 5 * 97%

= 4.85 GoPs

Expected number of GoPs in video that must be retransmitted at least once

= Number of GoPs - Expected number of GoPs that are successfull on the first transmission attempt of video

= 5 - 4.85

= 0.15 GoPs

First retransmission cost

= Cost per GoP * Expected number of GoPs that must be retransmitted at least once

= 11 * 0.15

= 1.65 kB

Case B:

Video frame structure is IPBBB/IPBBB/IPBBB.

Number of GoPs in video = 3

(c) Total cost of video (in kB)

= Number of I-frames * I-frame cost + Number of P-frames * P-frame cost + Number of B-frames * B-frame cost

= 3 * 7 + 3 * 3 + 9 * 1

= 21 + 9 + 9

= 39 kB

Cost per GoP = Total cost of video / Number of GoPs in video = 39 / 3 = 13 kB

(d) Probability that an entire GoP (5 frames) is transmitted successfully

= 0.99 * 0.99 * 0.99 * 0.99 * 0.99

= 0.95099005

= 95% (approx)

Expected number of GoPs that are successfull on the first transmission attempt of video

= Number of GoPs in video * Probability that an entire GoP is transmitted successfully

= 3 * 95%

= 2.85 GoPs

Expected number of GoPs in video that must be retransmitted at least once

= Number of GoPs - Expected number of GoPs that are successfull on the first transmission attempt of video

= 3 - 2.85

= 0.15 GoPs

First retransmission cost

= Cost per GoP * Expected number of GoPs that must be retransmitted at least once

= 13 * 0.15

= 1.95 kB

(e) Compressibility and cost of retransmission (based on results from (a), (b), (c), (d)) are summarized in table below for Case A and Case B. We can draw the inference based on these results that the greater the compressibility the greater is the cost of retransmission. However, overall cost (including retransmission cost) reduces with greater compressibility !

Measure	Case A	Case B	Remarks (if any)
Total Cost (without any retransmission)	55 kB	39 kB	Compressability is greater in Case B
First retransmission cost	1.65 kB	1.95 kB	Retransmission cost is greater in Case B