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# convolutional encoder - explanation needed

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#### Aya2002

convolutional encoder

hi Friends,

i have this example and i want to understand it but i cant 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

convolutional encoder

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

Points: 2
convolutional encoder

ok friend i will check it

thank you too much

Re: convolutional encoder

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

### Aya2002

Points: 2
Re: convolutional encoder

ahmedseu said:

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

thanks friend,

but can i know which book it was?

thanks

Error Control Coding

and the author?

Re: convolutional encoder

Hi, Aya2002

Aya2002 said:
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

Re: convolutional encoder

zorro said:
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

thanks

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

### Aya2002

Points: 2
Hi,

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

### Aya2002

Points: 2
The book of Sweeney is also good

zorro said:
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

ahmedseu said:
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

lcaruso

Points: 2