NAME: MATHEW MAKAU
REG NO: 19/02580
COURSE: BSCiT
UNIT: BIT3204A DISTRIBUTED
MULTIMEDIA SYSTEMS
ASSIGNMENT ONE
SEP-DEC
Demonstrate how the following Compression Algorithms
work?
a) Arithmetic Coding.
 Arithmetic coding is a popular compression algorithm
particularly useful for a relatively small and skewed
alphabet.
 In Theory, an arithmetic coding algorithm encodes an
entire file as a sequence of symbols into a single
decimal number.
 The input symbols are processed one at each iteration.
 Arithmetic coding is used in a variety of lossless and
lossy compression applications.
 The initial interval [0,1) (or [0,1]) is successfully
divided into subintervals on each iteration according
to the probability distribution.
 The subinterval that corresponds to the input symbol is
selected for next iteration.
 The interval derived at the end of this division process
is used to decide the codeword for the entire sequence
of symbols.
 The figure below illustrates the basic arithmetic
coding process. Here, a five-symbol sequence or
message, a1,a2,a3,a4 fro, a four symbol source is
coded. At the start of the coding process, the message
is assumed to occupy the entire half-open interval
[0,1]
This interval is divided into four regions based
on the probabilities of each source symbol.
Symbol ax for example is associated with
subinterval [0,0.2) because it is the first symbol
of the message being coded, the message
interval is initially narrowed to [0,0.2]
b) JPEG.
 The JPEG compression is a block based compression.. The
data reduction is done by the subsampling of the color
information, the quantization of the DCT-coefficients and
the Huffman-coding(reorder and coding).
 The user can control the amount of image quality loss due
to the data reduction by setting (or chose presets)
 The algorithm can be separated in different steps.
 The lossy compression of 8 bit RGB data “lossy means the
compression will also reduce some of the image content.
c) MPEG.
 MPEG achieves its high compression rate by storing only
the changes from one frame to another, instead of each
entire frame.
 The video information is then encoded using a technique
called Discrete Cosine Transform (DCT) . MPEG uses a
type of lossy compression, since some data is removed.
 The MPEG video compression algorithm relies on two
basic techniques: Block based motion compensation for
the reduction of the temporal redundancy and transform
domain based compression for the reduction of spatial
redundancy.
 Motion compensation techniques are applied with both
predictive and interpolative technique.
d) Shannon-Fano Algorithm.
 Shanno –Fano algorithm is an entropy encoding technique
for lossless data compression of multimedia.
 Named after Cloude Shannon and Robert Fano. It assigns a
code to each symbol based on their probabilities of
occurrence.
 It is a variable-length encoding scheme, that is, the codes
assigned to the symbols will be of varying length.
How It Works:
i. Create a list of probabilities or frequency counts for the
given set of symbols so that the relative frequency of
occurrence of each symbol is known.
ii. Sort the list of symbols in decreasing order of probability,
the most probable ones to the left and the least probable
ones to the right.
iii. Split the list into two parts with the total probability of
both the parts being as close to each other as possible.
iv. Assign the value 0 to the left part and 1 to the right part.
v. Repeat steps 3 and 4 for each part, until all the symbols are
split into individual subgroups.
Example:
The given task is to construct Shannon codes for the given
set of symbols using the Shannon-fano lossless compression
technique:
Step:
Tree:
Solution:
1. Upon arranging the symbols in decreasing order of
probability.
P(D) + P(B) = 0.30 + 0.2 = 0.58
And,
P(A) + P(C) + P(E) = 0.22 + 0.15 + 0.05 = 0.42
And since the equally split the table, assign them the values 0
and 1 respectively:
Tree:
2. Now, in {D,B} group:
P(D) = 0.30 and P(B) = 0.28
Which means that P(D)-P(B) so divide, {D,B} into {D} and {B}
and assign 0 to D and 1 to B.
Step:
Tree:
3. In {A,C,E} group,
P(A) = 0.22 and P(C) + P(E) = 0.20
So the group is divided into:
{A} and {C, E}
And they are assigned values 0 and 1 respectively.
4. In {C, E} group:
P(C) = 0.15 and P(E) = 0.05
So divide them into{C} and {E} and assign 0 to {C} and 1 to
{E}.
Step:
Tree:
Note: The splitting is now stopped as each symbol is separated
now.
The Shannon codes for the set of symbols are: