convolutional encoder - explanation needed

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Aya2002

Joined: 12 Dec 2006
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Location: Iraq

06 Nov 2009 22:55 convolutional encoder

hi Friends,

i have this example and i want to understand it but i cant Crying or Very sad

can some body help me please?

Example 2.1: A convolutional encoder has the following parameters:

G=[133 171]
R=1/2
K=7 (constraint length)
Determine the structure of the encoder.

solution:
the two octal number are converted to binary forms as:

133 = 001 011 011 = 1 011 011
171 = 001 111 001 = 1 111 001
g1(x) =1•(x^0)+0•(x^1)+1•(x^2)+1•(x^3)+0•(x^4)+1•(x^5)+1•(x^6)
g2(x) =1•(x^0)+1•(x^1)+1•(x^2)+1•(x^3)+0•(x^4)+0•(x^5)+1•(x^6)

denote the input as i(x), the first digit is computed from i(x)•g1(x). The second digit is computed from i(x)•g2(x).

thus for i(x)=101=1+x^2,
first digit = (1+x^2)(1+x^2+x^3+x^5+x^6)=10 01 10 00 1
second digit=(1+x^2)(1+x+x^2+x^3+x^6)= 11 00 11 10 1
the encoder sequence is 11 01 00 10 11 01 01 00 11

my questions are:

1. the input i(x), in this example it was 101 (how?)

2. how the encoder sequence was calculated?

thanks

Communications_Engineer

Joined: 10 Oct 2008
Posts: 492
Helped: 39

08 Nov 2009 19:17 convolutional encoder

my answers are:

1. you would know what the input is, you can any thing else too

2. encoder sequence tell you the taps of the shift register. check complextoreal.com for tutorial. Some time ago there was a good discussion on conv encoder here. I was too busy then to follow it but maybe you can still search for it

Aya2002

Joined: 12 Dec 2006
Posts: 1409
Helped: 254
Location: Iraq

08 Nov 2009 19:47 convolutional encoder

ok friend i will check it

thank you too much

ahmedseu

Joined: 31 Jul 2006
Posts: 251
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Location: Bahrain

10 Nov 2009 6:06 Re: convolutional encoder

Hi Muntadhar,

The complete answer to your question is in chapter 10 of Error Control Coding (attached)

If you have any problem with the convolutional encoder or Viterbi decoder, please let me know; I can send you my programmes with turbo codes if you like.

Good Luck!!!

Ahmed J. Jameel

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Aya2002

Joined: 12 Dec 2006
Posts: 1409
Helped: 254
Location: Iraq

10 Nov 2009 19:38 Re: convolutional encoder

ahmedseu wrote:

thanks friend,

but can i know which book it was?

thanks

ahmedseu

Joined: 31 Jul 2006
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Location: Bahrain

10 Nov 2009 22:10 Re: convolutional encoder - explanation needed

Error Control Coding

Aya2002

Joined: 12 Dec 2006
Posts: 1409
Helped: 254
Location: Iraq

10 Nov 2009 22:38 convolutional encoder - explanation needed

and the author?

zorro

Joined: 06 Sep 2001
Posts: 380
Helped: 47

10 Nov 2009 22:53 Re: convolutional encoder

Hi, Aya2002

Aya2002 wrote:

my questions are:

1. the input i(x), in this example it was 101 (how?)
2. how the encoder sequence was calculated?

1) i(x) is an arbitrary sequence of bits used in the example as the input to the encoder. The binary sequence 101, put in polynomial form, is 1*x^0+0*x^1+1*x^2 = 1+x^2

2)
a) the polynomial product (modulo 2) of i(x) with g1(x) gives a sequence of bits that are the even bits of the output sequence (considering that the first bit has subscript "0")
b) the polynomial product (modulo 2) of i(x) with g2(x) gives a sequence of bits that are the odd bits of the output sequence
c) interleaving the two sequencies a) and b) above, the output sequence is obtained

Please, let me know whether this is clear for you or you have more unclear points.
Regards

Z

Aya2002

Joined: 12 Dec 2006
Posts: 1409
Helped: 254
Location: Iraq

10 Nov 2009 23:03 Re: convolutional encoder

zorro wrote:

Hi, Aya2002

2)
a) the polynomial product (modulo 2) of i(x) with g1(x) gives a sequence of bits that are the even bits of the output sequence (considering that the first bit has subscript "0")
b) the polynomial product (modulo 2) of i(x) with g2(x) gives a sequence of bits that are the odd bits of the output sequence
c) interleaving the two sequencies a) and b) above, the output sequence is obtained

could you explain more please? show your answer numerically.

thanks

zorro

Joined: 06 Sep 2001
Posts: 380
Helped: 47

11 Nov 2009 0:57 convolutional encoder - explanation needed

Hi Aya,

please can you tell what is not clear to you?
Polynomial notation? Products of polynomials? Interleaving? Other?
Numerical examples are in your first post.
regards

Z

ahmedseu

Joined: 31 Jul 2006
Posts: 251
Helped: 24
Location: Bahrain

11 Nov 2009 8:30 Re: convolutional encoder - explanation needed

Hi,

ERROR CONTROL CODING - Fundamentals and Applications
By
SHU LIN, DANIEL Ja COSTELLO, JRa

Communications_Engineer

Joined: 10 Oct 2008
Posts: 492
Helped: 39

11 Nov 2009 9:13 convolutional encoder - explanation needed

The book of Sweeney is also good

Aya2002

Joined: 12 Dec 2006
Posts: 1409
Helped: 254
Location: Iraq

11 Nov 2009 14:10 Re: convolutional encoder - explanation needed

zorro wrote:

Hi Aya,

please can you tell what is not clear to you?
Polynomial notation? Products of polynomials? Interleaving? Other?
Numerical examples are in your first post.
regards

Z

Hi Friend,

could you please show me in step by step how the encoder sequence is
11 01 00 10 11 01 01 00 11

thanks

Added after 4 minutes:

ahmedseu wrote:

Hi,

ERROR CONTROL CODING - Fundamentals and Applications
By
SHU LIN, DANIEL Ja COSTELLO, JRa

do you have a link to this book because i have just the solution manual of it.

Thanks