Radix-4 Booth Multiplier With Neighborhood Dependent Approach For

8/7/2019 Radix-4 Booth Multiplier With Neighborhood Dependent Approach For

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Radix-4 BoothMultiplier with

Neighborhood

Dependent Approach

for Video Processing

Applications


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Abstract: Neighborhood Dependent Approach (NDA)

High performance low power Radix-4 Booth Multiplierfor kernel based operation

Such as 2-D convolution in video processingapplications

This technology reduces

1. Dynamic power consumption due to reduced switching

2. Special values, such as 0, repeated values orrepeated bit combinations are detected and data pathsare disabled accordingly

3. Input pixels are halved to increase probability ofspecial value detection


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4. Reduces operation and switching activities in 2Dconvolution upto 46% of switch rate

As a result we get; Reduced significant power

Low hardware overheads

Introduction: Due to the need of time, it is necessary to

develop low power design techniques

Dedicated hardware designers can provide lowpower system by reducing dynamic power

dissipation that;1. Relies on load capacitance

2. Clock frequency of the system

3. Toggle rate of the system


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Video applications have a unique characteristic whichis the neighboring pixels in a finite block usually havethe same pixel value or just slightly different value

This character can be exploited to reduce switching activityin arithmetic and processing modules by;

Bypassing smaller pixel values

Retaining intermediate results

Disabling data paths in architecture

This paper proposes a low power design for kernel basedoperations such as 2D-convolution, used in videoprocessing applications. The proposed features are;

1. Utilization of repetition of pixels and insignificant parts;to reduce operations and switching activities

2. Exploit the presence of repeated values, zeros,insignificant bits and special bit pattern in binaryrepresentation of pixels; to reduce switching activity inradix Booth multipliers of 2D convolution unit


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3. If special condition is detected, appropriate signal is

generated to disable parts or all data paths of the

architecture

This is called

NEIGHBORHOOD DEPENDENT APPROACH

(NDA)

4. Partitioning the input pixel data into smaller parts

increases the chances of special conditions in higher

order parts of the data


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Low Power Multipliers:

Because of massive multiplication, it is desired to have low power

multipliers, some low power multiplier techniques proposed by other

researchers are;

Multiplier using Carry Save Array (CSA)

Column bypass method

Hybrid multipliers

All these methodologies are applied to radix-2 operations.

Most widely applied implementation of high performance multiplier is

Modified Booth Algorithm

It is commonly used because it reduces number of partial products .i.e.

accumulation is faster with less switching


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According to different researchers, certain amendments are

made in the Booth Multipliers

Modification to increase probability of zero in partialproducts

Arranging CSA in Most Significant Bit First to utilize

sign extension zero encoding to reduce switching

Input data manipulation Changing operands to increase probability of zero-

encoding

Partitioning input data into smaller parts to increase

chances of data interchanging


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Neighborhood Dependent Approach (NDA)

for Kernel Based Operations In computing, the kernel is thecentral component of most

computeroperating systems; it is a

bridge between applications and

the actual data processing done atthe hardware level.

Most operating systems rely on

this concept of the kernel. The

existence of a kernel is a naturalconsequence of designing a

computer system as a series of

abstraction layers


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Image and video framing pixels have high spatial

redundancy (Elements that are duplicated within a

structure) in binary representation of pixels. Difference in consecutive pixel values in same

neighborhood is usually small

Only small number of bits will be changed in consecutive

operations; this character is used to reduce switching

activity.

Architectural approach refers to overall computation

where blocks of pixels are examined for possible

redundant computation

Spatial redundancy is exploited in higher bits of operands,by dividing them into small bits and multiple smaller

multipliers are used.


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The partitioning process of the operands in the

multiplication P=XY into higher and lower halves is

described as


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This approach is useful in 2D convolution

operations where coefficients have small

magnitudes.

Partitioning the operands will increase chances

that higher order bits are zero

If condition is detected, control signal isgenerated to turn off the corresponding registers

and functional units

If YH is zero in above equation, we are only left

with single multiplication and addition


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Similarly, the pixels and coefficients values

in the kernel-based operation with a KK

mask can be partitioned into multiplehalves as


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With this partitioning method, we can evaluate the higher

bits of the pixels in the same neighborhood to determine

if they are the same.

If the higher bits IH of the pixels in neighborhood under

consideration are the same, only one multiplication with

the sum of the coefficients is needed instead of K2

multiplications. The sum of the coefficientsWs can bepre-computed and loaded at system initialization.

The same reduction applies to additions. Whenever the

higher bits of the input pixels in the same neighborhood

are the same the operation for the term ,


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and the term,

can be reduced to one multiplication

and one addition operation for each term.


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The block diagram

in Figure shows overview of the architecture with

consideration of the neighborhood dependent approach.


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Design assumes the block of pixels is

cached in the memory block before theoperations

The block diagram shows only one Boothmultiplier being used for discussion and

simulation purposes.


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Arithmetic level Approach:

To consider the special bit patterns in the inputs to the

modified Booth multiplier and to turn off functional units

and data buses appropriately to reduce switching

activity. Inputs to the multiplier are partitioned into halves and

smaller Booth encoders and adders are used to perform

the necessary operations.


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Results And Conclusions

Five different implementations are carried out in thiswork to evaluate effectiveness of the proposedtechnique, these techniques are;

1. Conventional carry-save array multiplier (CSA)2. Radix-4 Booth multiplier (mBooth or modified Booth)

3. Conventional radix-4 Booth multiplier with dynamicrange detection and operand interchange(mBoothDRD)

4. The mBoothDRD multiplier with partitioning method(mBoothPAR)

5. NDA multiplier (mBoothNDA)


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Two commonly used kernel-based operations in image

and video processing applications are performed for

the evaluation

1. 2D convolution with a Gaussian kernel (low pass filter)

2. Edge detection operation (2D convolution with a

Laplacian kernel)

Both kernels have size of 33.

Some standard images are used to evaluate these

implementations. In this simulation;

1. The Lenna image

2. Lighthouse image

3. An outdoor image with high dynamic range

Are used


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Conclusions

The hardware design utilized special characteristics in

the video stream, to achieve;

1. Less dynamic power dissipation2. Reduced Power losses

3. Reduced switching

4. Disabling of data paths in architecture for special

values5. The architecture design helps to reduce up to 46

percent in transition rate in various applications


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Future Horizon

This approach can be further improved by

considering hybrid multipliers to reduce

the sign extension portion in the Boothmultiplier

Furthermore, partitioning the data into

smaller parts is also a good research topicto be considered.

Radix-4 Booth Multiplier With Neighborhood Dependent Approach For

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