A reconfigurable linear feedback shift register (LFSR) for the Bluetooth system

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© CEA 2007. Tous droits réservés. Toute reproduction totale ou partielle sur quelque support que ce soit ou utilisation du contenu de ce document est interdite sans l’autorisation écrite préalable du CEAAll rights reserved. Any reproduction in whole or in part on any medium or use of the information contained herein is prohibited without the prior written consent of CEA

2007

Author: Laurent AlausCo-Author: Dr Dominique NoguetCo-Author: Pr Jacques Palicot

A Reconfigurable Linear Feedback Shift Register

for Software Defined Radio Terminal

2


2007

A Reconfigurable Linear Feedback Shift Register

for Software Defined Radio Terminal

Summary:

I. Framework: Techniques of Parameterization and Common Operators (CO)

1. Ideas of Reconfigurability

2. Techniques of Parameterization

II. The Reconfigurable Linear Feedback Shift Register

1. Design

2. Parameterization

3. Implementation

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2007

CTCModulation

BPSKIFFT64 FFT64

Demodulation

BPSKChannel

Modulation

QPSKIFFT128 FFT128

Demodulation

QPSKChannel

Turbo

Coder

Standard 1:

Emission Chain – Standard 1

Emission Chain– Standard 2

Reception Chain – Standard 1

Reception Chain– Standard 2

Standard 2:

A Reconfigurable LFSR for SDR Terminal.

1. Reconfigurablility: Velcro Method – First Steps of SDR

Principle : Coexistence of all the required standards implementations

Switch to select the one required


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CTCModulation

BPSKIFFT64 FFT64

Demodulation

BPSKChannel

Modulation

QPSKIFFT128 FFT128

Demodulation

QPSKChannel

Turbo

Coder



Standard 1:

Standard 2:




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2007

CTCModulation

BPSKIFFT64 FFT64

Demodulation

BPSK

Channel

Modulation

QPSKIFFT128 FFT128

Demodulation

QPSK

Turbo

Coder





Standard 1 and Standard 2:


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2007

CTCModulation

BPSKIFFT64 FFT64

Demodulation

BPSKChannel

Modulation

QPSKIFFT128 FFT128

Demodulation

QPSKChannel

Turbo

Coder


1. Reconfigurablility: Sharing of Functions

Standard 1:

Standard 2:

Principle : Specific Reconfigurable General Functions


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2007

Modulation

QPSKIFFT128 FFT128

Demodulation

QPSKChannel

Turbo

Coder

CTCModulation

BPSKIFFT64 FFT64

Demodulation

BPSKChannel

Modulation

QPSKIFFT128 FFT128

Demodulation

QPSKChannel

Turbo

Coder

CTCModulation

BPSKIFFT64 FFT64

Demodulation

BPSKChannel

IFFTReconfigurable

FFTReconfigurable

DemodulationReconfigurable

ChannelFEC

Reconfigurable

ModulationReconfigurable

Modulation

QPSKIFFT128 FFT128

Demodulation

QPSKChannel

Turbo

Coder


Principle : Specific Reconfigurable General Functions

Standard 1:

Standard 2:

1. Reconfigurablility: Sharing of Functions


Standard 2:

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Standard 1:

Standard 2:

IFFT:

128

FFT:

128

Demodulation

QPSKChannel

FEC:Turbo CODER

Modulation:QPSK

IFFT:Reconfigurable

FFT:Reconfigurable

DemodulationReconfigurable

ChannelFEC:

Reconfigurable

Modulation:Reconfigurable

IFFT:

64

FFT:

64

Demodulation

BPSKChannel

FEC:

CTC

Modulation:BPSK

Modulation

QPSKIFFT128 FFT128

Demodulation

QPSKChannel

Turbo

Coder

Modulation

QPSKIFFT128 FFT128

Demodulation

QPSKChannel

Turbo

Coder

CTCModulation

BPSKIFFT64 FFT64

Demodulation

BPSKChannelCTC

Modulation

BPSKIFFT64 FFT64

Demodulation

BPSKChannel


Parameters Downlaoding

1. Reconfigurablility.

2. Techniques of Parameterization : Parameterizable Functions


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2007

Standard 1:

Standard 2:

Modulation

QPSKIFFT128 FFT128

Demodulation

QPSKChannel

Turbo

Coder

Modulation

QPSKIFFT128 FFT128

Demodulation

QPSKChannel

Turbo

Coder

CTCModulation

BPSKIFFT64 FFT64

Demodulation

BPSKChannelCTC

Modulation

BPSKIFFT64 FFT64

Demodulation

BPSKChannel




2. Techniques of Parameterization : Parameterizable Functions

Function1

ChannelFunction2

Function3

Function4

Function5


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2007

Standard 1:

CTCModulation

BPSKIFFT64 FFT64

Demodulation

BPSKChannelCTC

Modulation

BPSKIFFT64 FFT64

Demodulation

BPSKChannel




2. Techniques of Parameterization : Common Operators

Function1

ChannelFunction2

Function3

Function4

Function5

Common Operator

1

Common Operator

2

Common Operator

3


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2007

Standard 1:

CTCModulation

BPSKIFFT64 FFT64

Demodulation

BPSKChannelCTC

Modulation

BPSKIFFT64 FFT64

Demodulation

BPSKChannel






Function1

ChannelFunction2

Function3

Function4

Function5

Common Operator

1

Common Operator

2

Common Operator

3

Function1

ChannelFunction2

Function3

Function4

Function5

Common Operator

1

Common Operator

2

Common Operator

3

Common Operator

1

Common Operator

1

Common Operator

2

Common Operator

2

Common Operator

3

A common operatoris an HW parameterizable architecture.carries out severals operations of distinct functions of different standards.could be used on different time in the same chain at the same time.

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Function1’

ChannelFunction2’

Function3’

Function4’

Function5’

Common Operator

1

Common Operator

2

Common Operator

2

Common Operator

3

Common Operator

3

Standard 1:





Function1

ChannelFunction2

Function3

Function4

Function5

Function1

ChannelFunction2

Function3

Function4

Function5

Common Operator

1

Common Operator

1

Common Operator

2

Common Operator

2

Common Operator

3

Standard 2:

A common operatoris an HW parameterizable architecture.carries out severals operations of distinct functions of different standards.could be used on different time in the same chain at the same time.

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II. The Reconfigurable Linear Feedback Shift Register: Design

1. Design & Definition

• Schematic: R-LFSR General Architecture – Transpose IIR Filter


+

0a

1−z

1a 1−ra

0b 1b 1−rb rb

+ 1−z + 1−z +

ra

x

y

∑∑ −−−− −=N

knkN

N

knkNn yaxby10

..• Equation:

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• Schematic: R-LFSR General Architecture – Galois LFSR

• Equation:

+

0a

1−z

1a 1−ra

1−rb rb

+ 1−z + 1−z +

ra

x

y

∑∑ −−−− −=N

knkN

N

knkNn yaxby10

..

1b

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• Schematic: R-LFSR General Architecture – FIR Filter


• Equation: ∑∑ −−−− −=N

knkN

N

knkNn yaxby10

..

+

0a

1−z

1a 1−ra

0b 1b 1−rb rb

+ 1−z + 1−z +

ra

x

y

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1. Design & Definition.

2. Design & Fulfilled Structures:

• Pseudo Random Sequences Generator

• Scrambler

• Non Systematic Convolutional Coder

• Recursive Systematic Convolutional Coder

• Cyclic Redundancy Check Coder

• Cyclic Redundancy Check Decoder

• Error-Correcting Cyclic Coder

• Error-Correcting Cyclic Decoder

• Galois Field Generator

• Reed Solomon Coder/Decoder


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• Scrambler










Binary Architecture (GF(2) Elements)

GF(2) & GF(2m)

Elements

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• Scrambler










Binary Architecture (GF(2) Elements)

GF(2) & GF(2m)

Elements

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1. Pseudo Random Sequences Generator & Scrambler

+

1−z1a 2a

1−z 1−zra

Y

1−rS 2−rS 0S

Pseudo Random Sequences Generator = Fibonacci LFSR

Generalized Equation: Equation of R-LFSR:

Pseudo Random Sequence with R-LFSR:

Reversing coefficients : and Fitted Initial Values.

+Data Flow Output - Scrambler

X

∑=

=−−=

rm

kkjkjj YaY

0)()()(∑

=

=−=

rm

kkjkYajY

0)()(

)()( kjFibonacci

jLFSRR aa −

− =

II. The Reconfigurable Linear Feedback Shift Register: Parameterization

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2. Convolutional Coder : Non Systematic Coder (NSC)

+

1−z1'b 2'b

1−z 1−z3'b0'b

Input (X)

Output 1 (Y1)

+

2b 3b0bOutput 2 (Y2)

1b

Non Systematic Coder = FIR Filter

Equation: Equation of R-LFSR (Transpose FIR Filter):


•Reversing coefficients :

∑ −=N

knkn XbY0

.

)()( kjNSCCTC

jLFSRR bb −

−− =

∑ −−=N

knkNn XbY0

.


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2. Convolutional Coder : Rescursive Systematic Coder (RSC)

Recursive Systematic Coder = IIR Filter

Equation:

Equation of R-LFSR (Transpose IIR Filter):


•Reversing coefficients : )()()()( , kjFilterIIR

jLFSRR

kjFilterIIR

jLFSRR bbaa −

−−−

−− ==

+

1−z1a 1−Na

1−z 1−zNa

1a 1−Na Na1a+

X

Y

∑∑=

−=

− −−−=N

kkN

N

kkN knYaknXbnY

10][.][.][

∑∑==

−−−=N

kk

N

kk knYaknXbnY

10][.][.][

,


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2. Convolutional Coder : NSC & RSC

3. Cyclic Redundancy Check: R-LFSR and Coding

,

+

0a

1−z

1a 1−ra

0b 1b 1−rb rb

+ 1−z + 1−z +

ra

x

y

))(

)(()()(xg

xMxremainderxMxxCkn

kn−

− +=Equation:

Generation of the Remainder:


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3. Cyclic Redundancy Check: R-LFSR and Coding

,

+ 1−z

1g 1−−kng

+ 1−z + 1−z +

))(

)(()()(xg

xMxremainderxMxxCkn

kn−

− +=Equation:

Generation of the Remainder:

M(x)

0r 1r 1−−knr


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3. Cyclic Redundancy Check: R-LFSR and Decoding

,

+ 1−z

1g 1−−kng

+ 1−z + 1−z +

))(

)(()()(xg

xMxremainderxMxxCkn

kn−

− +=Equation:

Generation of the Syndrome:

r(x)

0s 1s 1−−kns


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1. Common Operator Approach: Proposed Method of Implementation

Shortest R-LFSR Structure (SRS)

• Definition: « This architecture is the shortest R-LFSR structure with the Minimal number of registers required to replace in turn the whole 20 structures referenced in the standards »

• Purpose: Suitable Duplication and Comparison with the Velcro Method

,

II. The Reconfigurable Linear Feedback Shift Register: Implementation

Channel

ChannelFEC CRC

Channel

3GPP LTE:

IEEE 802.11g:

IEEE 802.16e:

CRC

FEC CRCScrambler

FEC CRCScrambler

CRC

CRC

Scrambler

Scrambler

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,


Channel

ChannelFEC CRC

Channel

3GPP LTE:

IEEE 802.11g:

IEEE 802.16e:

Tri-Standard

Transceiver:

CRC

FEC CRCScrambler

FEC CRCScrambler

CRC

CRC

Scrambler

Scrambler

Channel SRS SRSSRS SRSSRS

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2007






• Constituent Elements: Subdivision

Size of the Minimal Operator : 4Size of the most Restated Operator : 8

Two Constituent Elements : R-LFSR4 and R-LFSR8

,


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,


,

+

ia

1−z

ib

+

ia

1−z

ib

+

ia

1−z

ib

+

ia

ib

X

Y

'α+

α

Register

Feedback


Shortest R-LFSR Structure (SRS): Constituent Elements - Subdivision

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2007


,


+

ia

1−z

ib

+

ia

1−z

ib

+

ia

1−z

ib

+

ia

ib

X

Y +

ia

1−z

ib

+

ia

1−z

ib

+

ia

1−z

ib

+

ia

ib

X

Yivα

'α+ ''α+

α



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2007


,


+

ia

1−z

ib

+

ia

1−z

ib

+

ia

1−z

ib

X

+

ia

1−z

ib

+

ia

1−z

ib

+

ia

1−z

ib

+

ia

ib

Y



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2007


,


+

ia

1−z

ib

+

ia

1−z

ib

+

ia

1−z

ib

+

ia

ib

X

Y +

ia

1−z

ib

+

ia

1−z

ib

+

ia

1−z

ib

+

ia

ib

X

Yivα

'α+ ''α+

α



32


2007


,


+

ia

1−z

ib

+

ia

1−z

ib

+

ia

1−z

ib

+

ia

ib

X

Y

'α+

α +

ia

1−z

ib

+

ia

1−z

ib

+

ia

1−z

ib

+

ia

ib

X

Yivα

''α+

X

+

ia

1−z

ib

+

ia

1−z

ib

+

ia

1−z

ib

+

ia

ib

Yivα

''α+



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2007


,


+

ia

1−z

ib

+

ia

1−z

ib

+

ia

1−z

ib

+

ia

ib

X

Y

X

+

ia

1−z

ib

+

ia

1−z

ib

+

ia

1−z

ib

+

ia

ib

Y



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2007


2. Common Operators Approach: Results of Implementation1. Software Defined Radio Terminal

• Tri-Standard : IEEE 802.11g,

IEEE 802.16-2005 (Wimax),

3GPP LTE

2. Structures to Replace:

• 24 different, which 20 feature different designs,

42x4 - 2x6 - 2x9 - 3x8Convolutional Coder/Turbo Coder

148 - 12 - 16 - 24 - 32CRC Coder/Decoder

67 - 11 - 15 - 22Scrambler/Descrambler

Numbers of StructuresPolynomial DegreesClass of Functions


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2. Common Operators Approach: Results of Implementation3. Results:

Tools of Implementation: ALTERA/Cyclone II with Quartus synthesis

,


Comparison:

Velcro Method and ONE SRS:

Comparison:

Velcro Method and Duplication of SRS:

14% 12%

95%83%

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2007


,

Conclusion• We propose a practical view of the Common Operators Approach.

• We design a Common Architecture to carry out :Pseudo Random Sequences GeneratorScramblerConvolutional Coder :NSC ans RSCCRC Coder/DecoderGalois Filed GeneratorReed Solomon Coder/Decoder

• Comparison with Velcro Method:

• We create scalable and « time-tested » Operators.

• The Common Operator Approach with Shortest R-LFR8 Structure as a Common Operator give a first save of space of 17%

Standard 3:

SRS

Channel F’’6F’’5F’’2F’’1 F’’3 F’’4 F’’5

SRS SRS SRS SRS

• The SRS is oversized for many operations to substitute, the implementation is not the most optimized one.

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2007


,

Conclusion

F1 ChannelF2 F3 F4 F6F5

F’1 ChannelF’2 F’3 F’6F’5

R-LFSR Operator

R-LFSR Operator

R-LFSR Operator

R-LFSR Operator

R-LFSR Operator

R-LFSR Operator

Standard 1:

Standard 2:

In futur articles, we will present:

• An Optimized R-LFSR4/8 Structure to map all the operations required by each standard

• Three others architectures and associated operators dedicated to specific functional

perimeters.• The evaluation of operator with unspecific functional perimeter.

• The comparison between Common Operator and Common Function approach.

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2007

Innovationfor industry

Thank you for your attention

A reconfigurable linear feedback shift register (LFSR) for the Bluetooth system

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