CS475 – Networks
Lecture 24
Chapter 7: End-to-End Data
Assignments
• Reading for Lecture 25: Sections 9.1-9.2
7.2 Data Compression
Data compression can allow us to send data at a faster rate than
Compression and decompression are often time consuming.
seemingly supported by the network. Compression can, for
Greater _____________________ can only be achieved if
example, allow us to send a 10 Mbps video stream over a 1 Mbs
link.
x / Bc + x / (r Bn) < x / Bn
where x represents the amount of data (uncompressed), r is the
Compression algorithms can be categorized as lossy or lossless. compression ratio, Bc is the bandwidth at which data can be run
Greater compression _______________ can be achieved with
through the compressor/decompressor and Bn is the network
lossy algoritms. The lost data may not be noticeable in images
bandwidth.
or audio or video streams.
7.2.1 Lossless Compression - Run Length Encoding (RLE)
In RLE, consecutive occurrences of a symbol are replaced with a be achieved. It is used to transmit ________________. If there
copy of the symbol and a count. The string AAABBCDDDD
is not a lot of adjacent identical data, RLE actually can increase
would be encoded as 3A2B1C4D (an 80% compression ratio).
the size of a file.
RLE works well on scanned text images where 8 to 1 rates can
7.2.1 Lossless Compression - Differential Pulse Code Modulation
In DPCM, a reference symbol is output and then the
A variation gives ________________ encoding where each
____________________ between each symbol and the reference symbol is encoded as the difference from the previous one.
is output.
AAABBCDDDD would become A001011000. Encoding the
The string AAABBCDDDD would be output as A0001123333.
difference using only one bit gives a compression ratio of 21%.
Differences between 0 and 3 can be encoded using only 2 bits so Delta encoding may be following by RLE since there may be
the compression ratio is 35%. When the difference becomes too long strings of 0s. Delta encoding works well when adjacent
large a new reference symbol is output.
pixels in an image are similar.
7.2.1 Lossless Compression - Dictionary Methods
The UNIX __________________ command uses a variation of
The Graphical Interchange Format (_____________) image uses
the Limpel-Ziv (LZ) algorithm which is a dictionary based
8-bit pixels to index into a 256 color 24-bit palette. The image is
method.
compressed using LZ with common sequences of pixels making
With this approach a group of symbols (a word) is replaced by
up the dictionary.
its index into a dictionary. LZ generates the dictionary
Patent restrictions on the LZ algorithm spurred development in
adaptively and must transmit the dictionary along with the
1995 of the Portable Network Graphics (PNG) format as a
compressed data.
replacement format for images on the web. The patent expired
in 2003.
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7.2.2 Image Compression (JPEG)
7.2.2 Image Compression (JPEG) - DCT Phase
The JPEG (Joint Photographic Expert Group) image format uses To simplify the discussion assume that we are working only with
a __________________ compression algorithm that offers better 8-bit grayscale images where 0 is white and 255 is black.
ratios than GIF or PNG. JPEG is related to MPEG which is a
In the discrete cosine transform (DCT) phase an 8 x 8 matrix of
video data format.
pixel values is converted to an 8 x 8 matrix of frequency
JPEG compression occurs in three phases. The image is fed
coefficients. Low frequency coefficients define _____________
through the phases one 8 x 8 block at a time.
image feature while high frequency coefficients correspond to
the fine details.
The DCT and its inverse are defined by
N−1 N −1
1
DCT i , j =
C i C  j ∑ ∑ pixel  x , y
 2N
x=0 x=0
2 x1 i
 2 y1 j 
cos
cos
2N
2N
[
pixel x , y=
] [
1
2N
cos
{
1
where C i=  2
1
[
The frequency coefficient at (0, 0) is the DC coefficient and is
the ___________________ of the 64 pixel values. The other
]
coefficients correspond to higher frequencies and to finer and
N −1 N −1
finer detail.
∑ ∑ C iC  j DCT i , j 
i =0
j =0
] [
2 x1i 
2 y1  j
cos
2N
2N
]
The DCT is lossless. The image can be exactly reconstructed
from the coefficients using the inverse transform. It is in the
if i =0
Quantization Phase where loss is introduced.
if i 0
7.2.2 Image Compression (JPEG) - Quantization Phase
To see how quantization works imagine truncating numbers less Instead of using the same quantum value for all 64 freq.
than 100 to multiples of 10. For example, the numbers 45, 98,
coefficients, JPEG uses quantization tables. An example table is:
[
23, 66 and 7 would become 4, 9, 2, 6 and 0. These numbers can
3
5
7
9
Quantum=
11
13
15
17
be encoded using only 4 bits instead of 7.
The truncation operation is equivalent to dividing each of the
original numbers by a ________________ (10) using integer
division.
5
7
9
11
13
15
17
19
7
9
11
13
15
17
19
21
9
11
13
15
17
19
21
23
11
13
15
17
19
21
23
25
13
15
17
19
21
23
25
27
15
17
19
21
23
25
27
29
17
19
21
23
25
27
29
31
]
The quantized frequency coefficient values are computed using:
QuantizedValue i , j =
IntegerRound DCTi , j / Quantum i , j
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7.2.2 Image Compression (JPEG) - Encoding Phase
7.2.2 Image Compression (JPEG) -Color Images
A variant of RLE is used to compress an 8 x 8 block along a
A color image can be thought of as being made up of separate
zigzag path. The individual coefficients are encoded using a
red, green and blue images. This is known as the RGB
________________ code
representation. JPEG typically uses the YUV (luminance and
(short codes are assigned
_______________________) representation.
to the most frequently
Each of the Y, U, and V images is processed as described for a
occurring coefficients).
grayscale image.
Zigzag traversal of the
JPEG is capable of compressing 24-bit images by an
quantized frequency
approximately 30-to-1 ratio.
coefficients for RLE.
7.2.3 Video Compression (MPEG)
Video can be thought of as a succession of still images or
By additionally removing the _____________________
frames. Individual frames can be compressed using a DCT-
information that is present in successive frames compression
based technique as with JPEG.
ratios on the order of 150-to-1 can be achieved.
7.2.3 Video Compression (MPEG) - Frame Types
MPEG takes a video stream and produces intrapicture (I),
components are downsampled to an 8 x 8 block.
______________________ picture (P) and bidirectional
predicted picture (B) frames.
A _______________________ in a B frame is represented with
a 4-tuple: (1) coordinates (x and y) for the macroblock, (2) a
motion vector (xp and yp) relative to the previous reference, (3) a
I frames can be considered to be JPEG compressed frames.
They are self-contained. P and B frames specify
motion vector (xf and yf) relative to the next reference, and (4) a
delta (δ) for each pixel in the macroblock. The pixel value in the
______________________ relative to an I frame.
current frame is computed using:
Fc(x, y) = (Fp(x+xp, y+yp)+Fn(x+xf, y+yf))/2 + δ(x, y)
16 x 16 blocks of pixels are used in MPEG. The U and V
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7.2.4 Transmitting MPEG over a Network
The MPEG specification specifies the format for a video stream
but does not specify how the stream is broken into network
packets.
An MPEG main profile is a nested structure. At the top level the
video stream is broken into groups of pictures (GOP) separated
by a SeqHdr. The SeqHdr contains a quantization
_____________________ for the I frame and one for the B and
P frames.
A GOP consists of pictures (I, B, and P frames) and pictures are By using UDP and breaking the stream at selected points
broken into slices (a region of the picture). A slice consists of a
(macroblock boundaries) we can limit the loss in picture quality
macroblock. A macroblock is made up of six 8 x 8 blocks (one
due to a lost network packet. This is an example of application
each for the U and V components and 4 for the Y component
level framing.
which is 16 x 16).
The video encoding method may depend on
MPEG allows the frame rate, ____________________, mix of
____________________ as well as bandwidth. For interactive
frame types, and quantization to change between GOPs,
videoconferencing (where low latency is desirable) an encoding
allowing picture quality to be traded for network bandwidth
using only I and P frames (I P P P P I) may be preferable to one
adaptively.
also using B frames (I B B B B P B B B B I).
7.2.5 Audio Compression (MP3)
CD quality sound requires sampling at 44.1 kHz using 16-bit
MPEG also defines audio compression formats, the most popular
samples. A stereo stream implies a bit rate of
is Layer III (MP3) which reduces BW requirements to 128 Kbps
2 x 44100 x 16 = 1.41 Mbps
MP3 splits audio into frequency subbands. The subbands are
_________________________ and error correction require
broken into blocks, transformed (DCT), quantized and Huffman
sending 49 bits instead of 16 resulting in
encoded (all similar to video compression).
49/16 x 1.41 Mbps = 4.32 Mbps
The audio frames are _____________________ with video
frames to form a complete MPEG stream.
In Class Exercise
To be submitted as part of Homework 8
• Problems 7.25 and 7.26
•
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Notes for these problems on the course webpage
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