Multimedia Communications Fall 07 Midterm Exam (Close Book) 1. (20%) (a) For video compression using motion compensated predictive coding, compare the advantages and disadvantages of using a large block-size ME and a small block-size ME? (5%) (b) For DCT-based coding schemes, compare the advantages and disadvantages of using a large block-size DCT and a small block-size DCT? (5%) (c) Explain briefly the concept of KLT. In which senses KLT is considered the optimal transform, and why? Why KLT is not used in practical video codecs? (7%) (d) What is the bit-rate for a 4:2:0 video with a luminance frame resolution of 720 pixels/line and 480 lines/frame, and a frame rate of 30 frames/s? (Each luminance and chrominance sample is represented by an 8-bit number). (3%) (a) Using a large block-size for ME will have the following advantages and disadvantages: advantages: (1) less overhead cost for sending motion vectors since fewer MVs need to be sent disadvantages: (1) higher prediction error in inter-coding due to that a large block may involve more than one moving object (b) Using a large block-size for DCT will have the following advantages and disadvantages: Large block-size (1) achieves higher coding gain due to better energy compaction disadvantages: (1) consumes a larger amount of computation (c) KLT is optimal in the sense of signal decorrelation and energy compaction. It s not practical due to large computational cost. (d) 124.416 Mb/s 2. (15%) What is the problem of the video codec shown in the following figure? Correct the architecture as required. - Q VLC channel VLD IQ : redictor, Q: Quantizer, VLC: Variable-Length-Coding, VLD: Variable-Length-Decoding, IQ: Inverse Quantization
The predictor ( in the diagram) in the encoder prediction loop stores the original picture, while the predictor in the decoder prediction loop stores the reconstructed picture (after quantization and dequantization). The contents in the two predictors generally are different due to the quantization error, and this error accumulates when decoding proceeds. The correct diagram is shown below. Note in this structure the reconstructed video signal at point A and point B must keep same for the encoder/decoder to avoid drifting error. - Q IQ VLC Channel A B VLD IQ 3. (20%) Consider a random variable F with pdf p( f) ( λ /2) below: f = e λ. A three-level quantizer is defined b Q(f) -a 0 a f -b Quantizer (a) Find b for a given a such that the centroid condition is satisfied when the distortion measure is the MSE. (5%) (b) Find a for a given b such that the nearest-neighbor condition is met. (5%) (c) Find an optimal set of a, b in terms of λ such that both conditions are satisfied. Derive the final MSE. (10%)
4. (20%) Encode and decode the following sequence generated from a three-symbol source {a, b, c} using arithmetic coding, and show the bitrate of the coded sequence. Source sequence: a c b a a b a c a c b a (a) Use the occurrence frequency of each symbol in the whole sequence as the estimate of the probability of the symbol. (7%) (b) Use the adaptive arithmetic coding scheme by assuming the initial probabilities of the three symbols are all 1/3, then updating the probabilities according to the incoming symbols. (8%) (c) Compare the bitrates of the two encoding schemes with scalar Huffman coding using the distribution in (a). (5%) (a)
假設 x 是要傳輸的數字, x [l, u),l=0.4422454833984375, u= 0.442249298095703125. 只取 x 的小數點以下六位數字當作整數來傳輸,0.442245 <= x < 0.442249 因為 2^19 > 442249, 所以使用 19 bits 傳輸, 則 bit rate= 19/12 bits/symbol (b) 13 45 2 7 477 1680 2153 75 2153 75 118403 415800 118403 415800 3078458 10774573 37837800 239 840 239 840 10763 37800 10763 37800 236801 8310 3078443 3078443 x [l, u),l=0.2847562622562622, u= 0.2847568568997140, 只取 x 的小數點以下七位數字當作整數來傳輸,0. 2847562 <= x < 0. 2847568 因為 2^22 > 2847568, 所以使用 21 bits 傳輸 則 bit rate= 7/4 bits/symbol. (c) According to the probability distribution in (a), 1 bit is required to encode symbol a, and 2 bits for symbols b and c. Totally, the sequence consumes 18 bits. Its bit-rate is 1.5 bits/symbol (the same with the sequence s entropy). 5. (20%) Assume the true probabilities of a 3-symbol source {A, B, C} are: (A) = a, (B) = b, and (C) = 1 - (ab). Further, assume that the entropy coding can achieve the entropy of the estimated model. Now, assume someone estimates the probabilities incorrectly so that the model of (A) = b and (B) = a is used in the encoding process. What is the degradation in terms of average coding bits per symbol based on the incorrectly estimated model compared to the true signal entropy? (20%)
If the probability model is correctly estimated, the codeword lengths of symbols A, B, C should be log 2 a, log 2 b, and log 2 (1-(ab)) respectively, this results in an average code length as follows: lmin = alog2 a blog 2 b (1 ( a b))log 2(1 ( a b)) (1) Now the probability distribution is incorrectly modeled as (A) = b, (B) = a, and (C) = (1- (ab)), resulting an average code length of lnonmin = alog2 b blog 2 a (1 ( a b))log 2(1 ( a b)) (2) By subtracting (2) by (1), we can obtain the degradation as follows a lnonmin lmin = ( b a) log2 b ( a b) log 2 a = ( a b) log2 (3) b which is always a nonnegative number. 6. (15%) Drifting error is caused by the mismatch between the corresponding predictions used in the encoder and in the decoder. The following video transcoder can be used to reduce the bit-rate of a pre-encoded video from R 1 bits/sec to R 2 bits/sec (R 2 < R 1 ) by requantizing the DCT coefficients with a coarser quantizer or dropping some high-frequency coefficients. Is this transcoder driftfree? Justify your answers. Rate Constraint Bit allocation analysis Incoming bitstream (R 1 ) VLD High freq. cutting / Requantization VLC Outgoing bit-stream (R 2 ) Front Encoder Incoming bit-stream Trancoder Outgoing bit-stream End Decoder With the open-loop video transcoder as shown, after high-frequency cutting or requantization of DCT coefficients, the contents of reconstructed video at the end decoder and front encoder will be different. This mismatch will also result in drifting errors, leading to error propagation..