Discrete cosine transform (DCT) is a widely used tool in image and video compression applications. Recently, the high-throughput DCT designs have been adopted to fit the requirements of real-time application. Operating the shifting and addition in parallel, an error-compensated adder-tree (ECAT) is proposed to deal with the truncation errors and to achieve low-error and high-throughput discrete cosine transform (DCT) design. Instead of the 12 bits used in previous works, 9-bit distributed arithmetic. DA-based DCT core with an error-compensated adder-tree (ECAT). The proposed ECAT operates shifting and addition in parallel by unrolling all the words required to be computed. Furthermore, the error-compensated circuit alleviates the truncation error for high accuracy design. Based on low-error ECAT, the DA-precision in this work is chosen to be 9 bits instead of the traditional 12 bits. Therefore, the hardware cost is reduced, and the speed is improved using the proposed ECAT.

1. Distributed Arithmetic
Discrete Cosine Transform
BY
B.Satish Kumar (10N71A0405)

2. Introduction To VLSI
Acronym of VLSI
Very-Large-
Scale
Integration
A VLSI contains more
than a million or so
switching devices or
logic gates
Early in the first decade
of the 21st century, the
actual number of
transistors has
exceeded 100 million
A piece of silicon (a
chip) is typically about 1
centimeter on a side

3. HDL (Hardware Descriptive Language)
HDL is a specialized computer language used to
describe the structure, design and operation
of electronic circuits, and most
commonly, digital logic circuits.
The two most widely-used and well-supported
HDL varieties used in industry are ”Verilog(verify
logic)” and ”VHDL( (Very High Speed Integrated
Circuit) Hardware Description Language)”.

4. VLSI APPLICATIONS:
 VLSI is an implementation technology for electronic circuitry -
analogue or digital.
 It is concerned with forming a pattern of interconnected
switches and gates on the surface of a crystal of
semiconductor.
 Microprocessors
personal computers
microcontrollers
 Memory - DRAM / SRAM
 Special Purpose Processors - ASICS (CD players, DSP
applications)
 Optical Switches
 Has made highly sophisticated control systems mass-
producable and therefore cheap.

5. INTRODUCTION TO XILINX ISE
The ISE® Design Suite is the Xilinx® design
environment, which allows you to take your
design from design entry to Xilinx device
programming.

6. WHY XILINX ISE?
The ISE Design Suite: Logic Edition allows you to
go from design entry, through implementation and
verification, to device programming from within
the unified environment of the ISE Project
Navigator or from the command line.

7. DESIGN MODULES IN XILINX:
VERILOG
MODULE
VHDL
MODULE

8. VERILOG MODULE:
Verilog, standardized as IEEE
1364, is a hardware description
language (HDL) used to model
electronic systems.
It is most commonly used in the
design and verification of digital
circuits at the register-transfer
level of abstraction.
It is also used in the verification
of analog circuits and mixed-
signal circuits.

9. OVERVIEW OF PROJECT
Data compression
Compression techniques
Introduction to DA-DCT
ECAT ARCHITECTURE
DA-Butterfly-Matrix

10. DATA COMPRESSION
 Despite the many advantages of digital
representation of signals compared to the analog
counterpart, they need a very large number of bits for
storage and transmission.
 For Example, a high-quality audio signal requires
approximately 1.5 megabits per second for digital
representation and storage.

11. A television-quality low-resolution color video of 30
frames per second with each frame containing 640 x
480 pixels (24 bits per color pixel) needs more than
210 megabits per second of storage.
As a result, a digitized one-hour color movie would
require approximately 95 gigabytes of storage. The
storage requirement for upcoming high-definition
Television (hdtv) of resolution 1280 x 720 at 60
frames per second is far greater.

12. CODEC
The compression and decompression systems together called a CODEC.

13. TYPES OF COMPRESSION:
LOSSLESS
COMPRESSION
LOSSY
COMPRESSION
Depending on the output requirements either of the compression
techniques are used.

14. COMPRESSION TECHNIQUES

15. INTRODUCTION TO DA-DCT
DISTRIBUTED
ARITHMATIC-
DISCRETE
COSINE
TRANSFORM

16. DCT(DISCRETE COSINE TRANSFORM):
Discrete cosine transform (DCT) is a
widely used tool in image and video
compression applications.
Recently, the high-throughput DCT
designs have been adopted to fit the
requirements of real-time application.

17. STEPS INVOLVED IN COMPRESSION OF
THE IMAGE
Dividing the image
into pixels and
level shifting
them.
DCT is performed
on the pixels
resulting in DCT
blocks.
Quantization is
done on these
blocks.
Quantized
matrices are
arranged in zigzag
order to
differentiate low
frequency
components and
high frequency
components.
The encoder block
encodes the
quantized data
Zero run and
huffman coding
techniques are
used to encode
the data in
encoder block.

18. REDUNDANCY CODING
To remove the unnecessary data while coding is
called as Redundancy Coding.
Types of Redundancies
Coding
redundancy
Inter pixel
redundancy
Psycho-visual
redundancy

19. DISCRETE COSINE TRANSFORMATION
The forward and inverse 2-D DCT can be written as:
where x(ij) is the image pixel data, and Z(u,v) is the transport data

20. COMPUTATION OF DCT

21. The 8 x 8 DCT coefficient matrix can be written as:
Even rows of C are even-symmetric and odd rows are
odd-symmetric.

22. By exploiting this symmetry in the rows of C and
separating even and odd rows we can get 1D-DCT as
follows:

23.  For 2-D DCT computation of a 8x8 2-D data, first row-
wise 8x1 1-D DCT is taken for all rows followed by column-
wise 8x1 1-D DCT to all columns. Intermediate results of 1-D
DCT are stored in transposition memory.

24. DCT IMPLEMENTATION
16 POINT DCT:

26. ECAT ARCHITECTURE
Error-Compensated Adder Tree
ECAT Architecture For Distributed Arithmetic Based DCT
• DA-based architecture and the proposed ECAT to achieve a high-speed,
small area and low-error design.
• It is proposed to compensate for the truncation error in high-speed applications.
• Reduces the shifting and addition computation time .

27. Two Types
MP
P (MSBs)
TP
T (LSBs)
• P-bit words operate the shifting and addition in parallel
• The output Y will obtain the P-bit MSBs using a rounding operation called
Post Truncation (Post-T).
• TP is usually truncated to reduce in parallel shifting and addition operations,
known as the Direct truncation (Direct-T).

28. Proposed Error-Compensated Scheme
Where is the compensated bias from the TP to the MP

29. Proposed ECAT Architecture
• Full - Adder
• Cell with three inputs (a, b, c)
• Two outputs, a sum (s) and a carry-out (co)
• Half - Adder
• Two inputs (a &b)
• Two outputs, a sum (s) and a carry-out (co)
Proposed ECAT architecture of shifting and addition operators

30. PROPOSED 8*8 1-D DCT CORE DESIGN
xm Denotes the input data.
Zn Denotes the transform output.
Above equation can be divided into even and odd parts: Ze and Zo

31. DA-based computation, the coefficient matrix Cee and Ceo

32. DA-Butterfly-Matrix
The proposed 2-D DCT is designed using two 1-D DCT cores and one transpose buffer

33. GENERAL IMPLEMENTATION FLOW

34. RTL Schematic View
Register Transfer Logic of DA-DCT

35. Simulation results of Distributed Arithmetic DCT

36. Device Utilization Summary:
Timing Summary:
Speed Grade: -4
• Minimum period: No path found
• Minimum input arrival time before clock: 23.566ns
• Maximum output required time after clock: 4.283ns
• Maximum combinational path delay: No path found

37. ADVANTAGES
The main advantage of compression is that it reduces
the data storage requirements.
It also offers an attractive approach to reduce the
communication cost in transmitting high volumes of
data
This significantly aids in reducing the cost of
communication due to the data rate reduction.
Hence the audience can experience rich-quality
signals for audio-visual data representation.

38. we can receive toll-quality audio at the other side of
the globe at a much better price compared to a
decade ago.
A single 6 MHz broadcast television channel can
carry HDTV signals.
Because of the reduced data rate offered by the
compression techniques, computer network and
Internet usage is becoming more and more image and
graphic friendly, rather than being just data- and text-
centric phenomena.

39. SECONDARY ADVANTAGES
Data compression has great implications in
database access.
Data security can also be greatly enhanced by
encrypting the decoding parameters and
transmitting them separately from the compressed
database files.
An extra level of security can be achieved by
making the compression and decompression
processes totally transparent to unauthorized users.

40. The rate of input-output operations in a computing
device can be greatly increased due to shorter
representation of data.
Data compression obviously reduces the cost of
backup and recovery of data in computer systems by
storing the backup of large database files in
compressed form.
The advantages of data compression will enable
more multimedia applications with reduced cost.

41. DISADVANTAGES
Data compression depending on the application
area and sensitivity of the data.
The extra overhead incurred by encoding and
decoding processes is one of the most serious
drawbacks of data compression, which discourages its
usage in some areas.
This extra overhead is usually required in order to
uniquely identify or interpret the compressed data.
Data compression generally reduces the reliability of
the data records.

42. Transmission of very sensitive compressed data
(e.g., medical information) through a noisy
communication channel (such as wireless media) is
risky because the burst errors introduced by the
noisy channel can destroy the transmitted data.
Disruption of data properties, since the
compressed data is different from the original data.
In many hardware and systems implementations,
the extra complexity added by data compression can
increase the system’s cost and reduce the system’s
efficiency.

43. FUTURE SCOPE
This work can be extended
in order to increase the
accuracy by increasing the
level of transformations.
This work can improve by
implementing JPEG 2000
Image compression
standard in which ordinary
DCT transformation part
can be replaced by our
Distributed Arithmetic
Discrete Cosine Transform
(DA DCT) Design.
This can be used as a part
of the block in the full
fledged application, i.e., by
using these DA DCT, the
applications can be
developed such as
compression,
watermarking, etc.
The 8-Point Distributed
Arithmetic Discrete Cosine
Transform (DA DCT) Design
can be made to 16, 32-
point Distributed
Arithmetic Discrete Cosine
Transform (DA DCT) by
making minor
modifications to the code.

44. CONCLUSION
This paper presents an efficient architecture
for computing the 2-D DCT with distributed
arithmetic. The proposed architecture requires
less hardware than conventional architectures
which use the original DCT algorithm or the
even-odd frequency decomposition method.

45.  The modules of the transpose memory and parallel
Distributed Arithmetic 2-D DCT architecture were
designed and synthesized. The paper contributed
with specific simplifications in the multiplier stage, by
using shift and add method, which lead to hardware
simplification and speed up over architecture.

47. ANY QUERIES