Video Compression

1
Video Compression

• MPEG Motion Picture Expert Group
• Lossy compression of video
• First approximation JPEG on each frame
• Added compression remove inter-frame redundancy
• Frame types
• I frames intrapicture
• P frames predicted picture
• B frames bidirectional predicted picture

2
Motion Compensation
3
Encoding
4
Luminance
5
Example

• Example sequence transmitted as I P B B I B B

6
B and P frames

• coordinate for the macroblock in the frame
• motion vector relative to previous reference
  frame
• motion vector relative to subsequent reference
  frame (B only)
• delta for each pixel in the macro block

7
Effectiveness

• typically 90-to-1
• as high as 150-to-1
• 30-to-1 for I frames
• P B frames get another 3 to 5x

8
Frame at time N
9
Frame at time N1
10
Error without motion compensation
11
Error with motion compensation
12
Coding Order
13
MPEG Stream Format
14
Example
126 71 10
250 14 29
71 30 33

• Assume a 3x3 Macroblock after the DCT
• Given the JPEG Quantization table
• The Quantized frequency coefficients
• DCT(1,0)250
• ?250/15.5? ?17.16?17
• RLE(42,5,17,2,0,0,0,0,0)1-42,1-5,1-17,1-2,5-0
• Now do Huffman encoding with symbols 1,42,5,17,2,
  0

3 15 31
15 31 59
31 59 75
42 5 0
17 0 0
2 0 0
15
Huffman Encoding

• Huffman encoding allows you to encode data with
  the minimal number of bits
• We need to encode the RLE 1-42,1-5,1-17,1-2,5-0
• There are 10 occurrences of symbols
• 1 occurs 4/1040 of the time
• 42 occurs 1/1010
• 5 occurs 2/1020
• 17 occurs 1/1010
• 2 occurs 1/1010
• 0 occurs 1/1010

Symbol Weight
1 4
5 2
42 1
17 1
2 1
0 1
16
Algorithm

• Given a alphabet A, construct a Huffman encoding
  tree T Create one node for each character of
  the alphabet A. Let each node have a field
  containing its weight which is the probability of
  that letter appearing in a message. Now
  repeatedly perform the following two steps   
  1) pick two nodes n1 and n2 that have the
  smallest weights    2) and replace them with a
  new node whose children are n1 and n2 and whose
  weight is the sum of the weights of n1 and n2.
  Each time we perform this step will replace two
  nodes in the alphabet with one, until eventually
  only one single node remains as this is the root
  of the tree T.

17
Building Huffman Tree
1-42,1-5,1-17,1-2,5-01 0010 1 01 1 0011 1 0000
01 0001 1001 0101 1001 1100 0001 00010x959c11
W4
I5
0
1
Symbol Weight
11 4
501 2
420010 1
170011 1
20000 1
00001 1
1
I4
W6
1
0
W4
5
I3
0
1
I1
I2
W2
W2
0
0
1
1
2
0
42
17
18
LZ encoding example
Encode for characters a,b,c a b b c c a b a c a b
b b a b a b a b b b b 1 2 2 3 3 4 1 8 5 2
9 13 12 2
1 a 8 ca 15 bab
2 b 9 aba 16 bbbb
3 c 10 ac 17
4 ab 11 cab 18
5 bb 12 bbb 19
6 bc 13 ba 20
7 cc 14 abab 21
19
LZ decoding

• 1 2 2 3 3 4 1 8 5 2 9 13 12 2
• a b b c c a b a c a b b b a b a b a b b b b

1 a 8 ca 15 bab
2 b 9 aba 16 bbbb
3 c 10 ac 17
4 ab 11 cab 18
5 bb 12 bbb 19
6 bc 13 ba 20
7 cc 14 abab 21
20
PNG

• The Portable Network Graphics (PNG) format was
  designed to replace the older and simpler GIF
  format and, to some extent, the much more complex
  TIFF format.
• For the Web, PNG really has three main advantages
  over GIF
• alpha channels (variable transparency),
• gamma correction (cross-platform control of image
  brightness), and
• two-dimensional interlacing (a method of
  progressive display).

21
PNG

• For image editing, either professional or
  otherwise, PNG provides a useful format for the
  storage of intermediate stages of editing. Since
  PNG's compression is fully lossless--and since it
  supports up to 48-bit truecolor or 16-bit
  grayscale--saving, restoring and re-saving an
  image will not degrade its quality, unlike
  standard JPEG (even at its highest quality
  settings).
• Most of all, PNG is not patented

22
MP3

• MP is short for MPEG, or Motion Picture Experts
  Group, a widely accepted way to compress digital
  video and audio.
• MP3 is short for MPEG-1, audio layer 3. It is a
  subset of MPEG compression that can take a
  20-megabyte, two-minute track on a music CD
  loaded into a PC's CD-ROM drive and reduce it to
  just a tad over 1.4 megabytes, about the size of
  a single floppy disk. Layer 3 quality is better
  than layer 2, but not as good as layer 4, which
  is coming soon and will provide full CD quality.
  MP3 was invented in 1991.

23
Overview
24
Details

• The filter bank used in MPEG Layer-3 uses
  Discrete Cosine Transform
• The perceptual model gives preference to
  frequencies we are more sensitive to
•  Joint stereo coding takes advantage of the fact
  that both channels are frequently the same 
• Quantization, larger values are automatically
  coded with less accuracy
•  The quantized values are coded by Huffman
  coding.  

25
Network Security

• Chapter 8

26
Cryptography

• Cryptography functions
• Secret key (e.g., DES)
• Public key (e.g., RSA)
• Message digest (e.g., MD5)
• Security services
• Privacy preventing unauthorized release of
  information
• Authentication verifying identity of the remote
  participant
• Integrity making sure message has not been
  altered

27
Taxonomy
28
Encryption Algorithms

• Private Key (DES)
• 64-bit key (56-bits 8-bit parity)
• 16 rounds

29
L
R
i -1
i 1

• Each round
• Function F and generation of Ki for each round
  not shown
• Repeat for larger messages

K
F
i

L
R
i
i
30
Public Key (RSA)

• Generate a public and private key
• choose two large prime numbers p and q (each 256
  bits)
• multiply p and q together to get n (at most 512
  bits)
• chose the encryption key e, such that e and n are
  relatively prime e(p-1) x (q-1).
• two numbers are relatively prime if they have no
  common factor greater than one.
• compute decryption key d such that
• d e-1 mod(n)
• construct public key as lte, ngt
• construct private key as ltd, ngt
• discard (do not disclose) original primes p and q

31
Multiplicative inverse

• With n7
• 42 mod 7 1
• 4 and 2 are multiplicative inverses mod 7

32
Encryption Decryption

• c me mod n
• m cd mod n(me mod n)d mod nmedmod n
• Since e and d are multiplicitive inverses m

plaintext
plaintext
Encrypt w/
Decrypt w/
Public Key
Private Key
ciphertext
33
Breaking RSA

• 1977 challenge to break 430-bit message with
  RSA-129
• Estimated 40 Quadrillion years to factor large
  composites
• April 1994 broken with 5000 MIP-years of CPU
• On Aug. 22, 1999, a group led by H. te Riele
  completed factorization of RSA-155, 35.7 CPU
  years 8000MIP Years
• Breakage can be easier if something is known
  about the key generation (time of day)

34
Breaking DES

• 1999 56-bit DES broken in 22 hours on network of
  machines

35
Message Digest

• Cryptographic checksum
• just as a regular checksum protects the receiver
  from accidental changes to the message, a
  cryptographic checksum protects the receiver from
  malicious changes to the message.

36
One-way function

• given a cryptographic checksum for a message, it
  is virtually impossible to figure out what
  message produced that checksum it is not
  computationally feasible to find two messages
  that hash to the same cryptographic checksum.

37
Relevance

• if you are given a checksum for a message and you
  are able to compute exactly the same checksum for
  that message, then it is highly likely this
  message produced the checksum you were given.

38
Speed

• DES on 175MHz Alpha 36Mbps
• RSA 1Kbps
• MD5 80Mbps (as much as 10x DES)
• In hardware DES1Gbps, RSA64Kbps

39
Authentication Protocols

• Three-way handshake

40
Kerberos

• Trusted third party (Kerberos)

B
A
S
A, B
E((T,L,K,B),K ),
A
E((T,L,K,A),K )
B
E((A,T),K), E(T,L,K,A),K )
B
E(T1,K)
41
Public key authentication
A
B
E(x, Public )
B
x
42
Message Integrity Protocols

• Digital signature using RSA
• special case of a message integrity where the
  code can only have been generated by one
  participant
• compute signature with private key and verify
  with public key

43
Keyed MD5

• sender
• m MD5(m k) E(k, private)
• receiver
• recovers random key using the sender's public key
• applies MD5 to the concatenation of this random
  key message
• compares result with checksum sent with message