WordlengthOptICASSP2004Slides

8/2/2019 WordlengthOptICASSP2004Slides

1/26

ESPL 1

Wordlength Optimization with

Complexity-and-Distortion Measure and

Its Application to Broadband Wireless

Demodulator Design

Kyungtae Han and Brian L. Evans

Embedded Signal Processing LaboratoryWireless Networking and Communications Group

The University of Texas at Austin


2/26

ESPL 2

Fixed-Point Design

Digital signal processing

algorithms

Often developed in floating point

Later mapped into fixed point fordigital hardware realization

Fixed-point digital hardware

Lower area

Lower power

Lower per unit production cost

Idea

Floating-Point Algorithm

Quantization

Fixed-Point Algorithm

Code Generation

Target System

Alg

orithmLevel

Implementation

Level

Range Estimation

Introduction


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ESPL 3

Fixed-Point Design

Float-to-fixed point conversion required to target

ASIC and fixed-point digital signal processor core

FPGA and fixed-point microprocessor core

All variables have to be annotated manually Avoid overflow

Minimize quantization effects

Find optimum wordlength

Manual process supported by simulation

Time-consuming

Error prone

Introduction


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ESPL 4

Optimum Wordlength

Longer wordlength May improve application

performance

Increases hardware cost

Shorter wordlength May increase quantization errors

and overflows Reduces hardware cost

Optimum wordlength Maximize application performanceor minimize quantization error

Minimize hardware cost

Wordlength (w)

Cost c(w)Distortion d(w)

[1/performance]

Optimum

wordlength

Background


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ESPL 5

Wordlength Optimization

Express wordlengths in digital system as vector

Wordlength range for kth wordlength

Cost function c

),,,,(222 nwwww =w

nkwww kkk ,...,2=

RI nc :

=

=n

k

kk

nwcc

2

)()(, wIw

Background


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ESPL 6

Wordlength Optimization

Application performance functionp

Wordlength optimization problem

Iterative update equation

Good choice of update direction can reduce

number of iterations to find optimum wordlength

reqPp )(w

},)(|)({min wwPpc reqIn

wwww

)()()2( hhh+=

+ww

Background


7/26ESPL7

Sequential Search [K. Han et al. 2001]

Greedy search based on sensitivity information

(gradient)

Example

Minimum wordlengths {2,2}

Direction of sequential search

Optimum wordlengths {5,5}

12 iterations

Advantage: Fewer trials

Disadvantage: Could miss global optimum point

jjj sww

+=+2

wopt

wb

w2

w2

dw2

dw2

2

2

Search Methods


8/26ESPL 8

Measures for Optimum Wordlength

Complexity measure method[W.Sung and K.Kum 1995] Minimize complexity c(w) subject to constraint on distortion

d(w)

Update direction uses complexity sensitivity information

Distortion measure[K. Hanet al. 2001] Minimize distortion d(w) subject to constraint on complexity

c(w)

Update direction uses distortion sensitivity information

?w0w1

wn

Complexity

w

wc

)(?

w0w1

wn

Distortion

w

wd

)(

Measures


9/26ESPL 9

Combine complexity measure withdistortion measure by weightingfactor (01)

Tradeoffs between measuresby changing weighting factor

Update direction uses both sourcesof sensitivity information

Complexity-and-Distortion Measure

)()2()()( www dcf +=

)]()2()([ ww dc +=

},)(,)(|)({min wwCcDdf reqIn

wwwww

Update direction

Objective function

Optimization problem

?

w0

w1

wn

Complexity

Distortion

Measures


10/26ESPL 10

Broadband Wireless Access

(IEEE 802.16a) Demodulator

w0: Input wordlength of orthogonal frequency division multiplex (OFDM)demodulator which performs a fast Fourier transform (FFT)

w1: Input wordlength of equalizer

w2: Input wordlength of channel estimator

w3: Output wordlength of channel estimator

EncoderOFDM

Modulator

Wireless

Channel

Model

OFDM

Demodulator

Channel

Estimator

Decoder

Bit error

rate

tester

Data

Source

Channel

Equalizer

w2

w2

w2w

2

Case Study


11/26ESPL 11

Simulations

Assumptions

Internal wordlengths of blocks have been

decided

Complexity increases linearly aswordlength increases

Required application performance

Bit error rate of 1.5 x 10-3 (without error

correcting codes) Simulation tool

LabVIEW 7.0

Case Study

Input Weight

FFT 1024

Equalizer

(right)

1

Estimator 128

Equalizer(upper)

2


12/26ESPL 12

Minimum Wordlengths

Change one wordlengthvariable while keepingother variables at highprecision{1,16,16,16},{2,16,16,16},...

{16,1,16,16},{16,2,16,16},...

{16,16,16,15},{16,16,16,16}

Minimum wordlengthvector is {5,4,4,4}

Case Study


13/26ESPL 13

Number of Trials

Start at {5,4,4,4} wordlength

Next wordlength

combination for complexity

measure ( = 1.0)

{5,4,4,4},

{5,5,4,4},

Increase wordlength one-by-one until satisfying required

application performance

Case Study


14/26ESPL 14

Complexity and Number of Iterations

Each iteration computes complexity & distortion measures

Distortion measure: high cost, low iterations

Complexity-distortion: medium cost, fewer iterations

Complexity measure: low cost, more iterations

Full search: low cost, more iterations

Method w Complexity Iterations

Distortion Only

Complexity-Distortion

Complexity Only

Full Search

0

0.5

1

n/a

{10,9,4,10}

{7,10,4,6}

{7,7,4,6}

{7,7,4,6}

10781

7702

7699

7699

16

15

69

210

Case Study


15/26ESPL 15

Conclusion

Summary

Fixed-point conversion requires wordlength optimization

Develop complexity-and-distortion measure

Complexity-and-distortion method finds optimal solution inone-third the time that full search takes for case study

Future extensions for wordlength optimization

Automate selection of wordlength range

Combine simulation-based and analytical approaches

Employ genetic algorithms


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ESPL 16

Fixed-Point Representation

Fixed point type

Wordlength

Integer wordlength

Quantization modes

Round

Truncation

Overflow modes

Saturation

Saturation to zero

Wrap-around

S X X X X X

Wordlength

Integer wordlength

SystemC format

www.systemc.org

Introduction

X X X X X

Wordlength

Integer wordlength = 2

Back


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ESPL 17

Full Search [W. Sung and K. Kum 1995]

Exhaustive search of all possiblewordlengths

Advantages

Does not miss optimum points

Simple algorithm Disadvantage

Many trials (=experiments)

Distance

Expected number of iterations

wb

wo p t

w2

w2

d w2

d w2

2 2

2 2

2 2

2 2

2

2

Direction of full search:

minimum wordlengths {2,2}

optimum wordlengths = {5,5}

d = 6

trials = 24

!

)2)(2)...(2()(

N

dddNddE

N

FS

+++=

Ndwdwdwd +++= ...22

Search Methods

Back


18/26

ESPL 18

FFT Cost

2222

222log

2

222Cost

2FFT

=

=

NTap FFT cost

256 Tap FFT cost

NN

2FFT log2

Cost =

Back


19/26

ESPL 19

Uses complexity sensitivity information as

direction to search for optimum wordlength

Advantage: minimizes complexity

Disadvantage: demands large number of iterations

Complexity Measure [W.Sung and K.Kum 1995]

)()( ww cf =

)(wc=

},)(|)({min max wwDdfnI www

w

Update direction

Objective function


Measures

Back


20/26

ESPL 20

Applies the application performance information

to search for the optimum wordlengths

Advantage: Fewer number of iterations

Disadvantage: Not guaranteed to yield optimumwordlength for complexity

Distortion Measure[K. Han et al. 2001]

)()( ww df =

)(wd=

},)(,)(|)({min maxmax wwCcDdfnI

wwwww

Update direction

Objective function


Measures

Back

C S d


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ESPL 21

Broadband Wireless Access Demodulator

Simulation

Case Study

C S d


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ESPL 22

Top-Level Simulation

Case Study

Back

I d i


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ESPL 23

Tools for Fixed-Point Simulation

gFix (Seoul National University)

Using C++, operator overloading

Simulink (Mathworks)

Fixed-point block set 4.0

SPW (Cadence)

Hardware design system

CoCentric (Synopsys)

Fixed-point designer

gFix a(12,1);

gFix b(12,1);

gFix c(13,2);

c = a + b;

float a;

float b;

float c;

c = a + b;

Introduction

Wordlengths determined manually

Wordlength optimization tool needed

B k d


24/26

ESPL 24

Wordlength Optimization Methods

Analytical approach

Quantization error model

Overestimates signal wordlength

For feedback systems, instability and limit cycles can occur Difficult to develop analytical quantization error model of

adaptive or non-linear systems

Simulation-based approach

Wordlengths chosen while observing error criteria

Repeated until wordlengths converge

Long simulation time

Background

S h M th d


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ESPL 25

Optimum Wordlength Search Methods

Full search [W. Sung and K. Kum 1995] Min + b bit search [W. Sung and K. Kum 1995] Max b bit search [M. Cantin et al. 2002]

Hybrid search [M. Cantin et al. 2002] Sequential search [K. Han et al. 2001] Preplanned search [K. Han et al. 2001] Branch and bound search [H. Choi and W.P.Burleson

1994]

Simulated annealing search [P.D. Fiore and L. Lee1999]

Search Methods

C St d


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ESPL 26

Procedure

1. Range estimation Find maximum and minimum values for each

1. Find minimum wordlengths

Defines starting wordlength values to use1. Iterative search

Increase/decrease wordlengths one-by-one until meeting

specification using one of the measures

Case Study

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